Download Anna University (AU) MBA ( Master of Business Administration) Important Question Bank 1st Sem 1918108 Statistics for Management (Latest Important Questions Unit Wise)
1
(An
Ka ttankulathur ?
DEPARTMENT OF MATHEMATICS
QUESTION BANK
I SEMESTER
1918108 ? STATISTICS FOR MANAGEMENT
Regulation ? 2019
Academic Year 2019 - 2020
Prepared by
Ms. B. Vasuki, Assistant Professor/Mathematics
Ms.B.Elakkiavani, Assistant Professor/Mathematics
FirstRanker.com - FirstRanker's Choice
1
(An
Ka ttankulathur ?
DEPARTMENT OF MATHEMATICS
QUESTION BANK
I SEMESTER
1918108 ? STATISTICS FOR MANAGEMENT
Regulation ? 2019
Academic Year 2019 - 2020
Prepared by
Ms. B. Vasuki, Assistant Professor/Mathematics
Ms.B.Elakkiavani, Assistant Professor/Mathematics
2
(An
? .
DEPARTMENT OF MATHEMATICS
QUESTION BANK
SUBJECT : 1918108 ? STATISTICS FOR MANAGEMENT
SEM / YEAR : I Semester / I Year
UNIT I - INTRODUCTION
SYLLABUS: Basic definitions and rules for probability, conditional probability independence of events, Baye?s
theorem, and random variables, Probability distributions: Binomial, Poisson, Uniform and Normal distributions.
PART- A
S.NO QUESTIONS
BT Level
COMPETENCE
PART ? A
1. Define Statistics. BTL -6 Creating
2. What is the addition and multiplication theorem on probability. BTL -1 Remembering
3. Distinguish between a priori and posterior probability?. BTL -6 Creating
4.
The price of the selected stock over a five day period shown as 170, 110,
130, 170 and 160. Compute mean , median and mode.
BTL -6 Creating
5.
A car travels 25 miles at 25 mph, 25 miles at 50 mph and 25 miles at 75
mph. Find the harmonic of three velocities?
BTL -4 Analyse
6.
A ball is drawn at random from a box containg 6 red balls, 4 white balls
and 5 blue balls. Find the probability that the ball drawn is not red.
BTL -4 Analyse
7.
Find the median and mode for the weights (kgs) of 15 persons given as
68, 85, 70, 65, 71, 67, 65, 55, 80, 62, 65, 64, 70, 60, 56.
BTL -3 Applying
8. Name few measures of dispersion. BTL -1 Remembering
9. write the common measures of central tendency? BTL -1 Remembering
10. Define continuous and discrete variables examples. BTL -1 Remembering
11.
Let X be the lifetime in years of a mechanical part. Assume that X has
the cdf F(x) = 1- e
-x
, x ? 0. Find P[1< X ? 3].
BTL -1 Remembering
12. Define independent events. BTL -1 Remembering
13. State the theorem of total probability BTL -1 Remembering
14. What is the use of Baye?s theorem? BTL -6 Creating
15. Mention the properties of a discrete probability distribution. BTL -1 Remembering
16. Define a Poisson distribution and mention its mean and variance. BTL -1 Remembering
17. If the mean and variance of a binomial distribution are respectively 6 BTL -3 Applying
FirstRanker.com - FirstRanker's Choice
1
(An
Ka ttankulathur ?
DEPARTMENT OF MATHEMATICS
QUESTION BANK
I SEMESTER
1918108 ? STATISTICS FOR MANAGEMENT
Regulation ? 2019
Academic Year 2019 - 2020
Prepared by
Ms. B. Vasuki, Assistant Professor/Mathematics
Ms.B.Elakkiavani, Assistant Professor/Mathematics
2
(An
? .
DEPARTMENT OF MATHEMATICS
QUESTION BANK
SUBJECT : 1918108 ? STATISTICS FOR MANAGEMENT
SEM / YEAR : I Semester / I Year
UNIT I - INTRODUCTION
SYLLABUS: Basic definitions and rules for probability, conditional probability independence of events, Baye?s
theorem, and random variables, Probability distributions: Binomial, Poisson, Uniform and Normal distributions.
PART- A
S.NO QUESTIONS
BT Level
COMPETENCE
PART ? A
1. Define Statistics. BTL -6 Creating
2. What is the addition and multiplication theorem on probability. BTL -1 Remembering
3. Distinguish between a priori and posterior probability?. BTL -6 Creating
4.
The price of the selected stock over a five day period shown as 170, 110,
130, 170 and 160. Compute mean , median and mode.
BTL -6 Creating
5.
A car travels 25 miles at 25 mph, 25 miles at 50 mph and 25 miles at 75
mph. Find the harmonic of three velocities?
BTL -4 Analyse
6.
A ball is drawn at random from a box containg 6 red balls, 4 white balls
and 5 blue balls. Find the probability that the ball drawn is not red.
BTL -4 Analyse
7.
Find the median and mode for the weights (kgs) of 15 persons given as
68, 85, 70, 65, 71, 67, 65, 55, 80, 62, 65, 64, 70, 60, 56.
BTL -3 Applying
8. Name few measures of dispersion. BTL -1 Remembering
9. write the common measures of central tendency? BTL -1 Remembering
10. Define continuous and discrete variables examples. BTL -1 Remembering
11.
Let X be the lifetime in years of a mechanical part. Assume that X has
the cdf F(x) = 1- e
-x
, x ? 0. Find P[1< X ? 3].
BTL -1 Remembering
12. Define independent events. BTL -1 Remembering
13. State the theorem of total probability BTL -1 Remembering
14. What is the use of Baye?s theorem? BTL -6 Creating
15. Mention the properties of a discrete probability distribution. BTL -1 Remembering
16. Define a Poisson distribution and mention its mean and variance. BTL -1 Remembering
17. If the mean and variance of a binomial distribution are respectively 6 BTL -3 Applying
3
and 2.4, find P(x=2).
18.
If x is a Poisson distribution such that P(x=1)=4P(x=2). Find its
mean and variance.
BTL -3 Applying
19.
Suppose that X has a Poisson distribution with parameter ? = 2.
Compute P[X ? 1].
BTL -1 Remembering
20. Define mutually exclusive events. BTL -1 Remembering
PART-B
1(a).
Calculate the mean and standard deviation for the following table
giving the age distribution of 542 members.
Age
20-30 30-40 40-50 50-60 60-70 70-80 80-90
No 3 61 132 153 140 51 2
BTL-2 Understanding
1(b).
Find the geometric mean for the following data:
Group
2-4 4-6 6-8 8-10
Frequency 200 400 300 100
BTL-2
Understanding
2(a).
Find the mean, median and modal ages of married women at first
child birth
Age at the
birth of
first child
13
14
15
16
17
18
19
20
21
22
23
24
25
No of
married
women
37
162
343
390
256
433
161
355
65
85
49
46
40
BTL -6 Creating
2(b).
If A and B are independent event with P(A)=2/5, and P(B)=3/5,
find P(A ?B). Let S= {1,2,3,4,5,6} if A = {2,4,6} then find the
probability of A complement.
BTL -3 Applying
3(a).
Given: The probabilities of three events A, B and C occurring are
P(A) = 0.35, P(B) = 0.45 and P(C) = 0.2. Assuming that A, B, or
C has occurred, the probabilities of another event X occurring are
P(X/A) = 0.8, P(X/B) = 0.65 and P(X/C) = 0.3. Find P(A/X),
P(B/X) and P(C/X).
BTL -6 Creating
3(b).
4 cards are drawn from a well shuffled pack of cards. Find the
probability that
(i) All the four are queens
(ii) There is one card from each suit.
(iii) Two cards are diamonds and two are spades
All the four cards are hearts and one of them is jack
BTL -6 Creating
4(a).
Three machines all turn out non ferrous castings. Machine A
produces 1% defective and Machine B- 2% and machine C ? 5%.
Each machine produces 1/3 of the output. An inspector examines
a single casting, which he determines as non defective. Estimate
the probabilities of its having been produced by each machine.
BTL -6 Creating
4(b).
If the random variable X takes values 1, 2, 3, 4 such that
2P(X = 1) = 3P(X = 2) = P( X=3) = 5P(X = 4), find the
probability distribution and cumulative distribution of X.
BTL-2 Understanding
5(a).
Two dice are thrown together once. Find the probabilities for
BTL -3 Applying
FirstRanker.com - FirstRanker's Choice
1
(An
Ka ttankulathur ?
DEPARTMENT OF MATHEMATICS
QUESTION BANK
I SEMESTER
1918108 ? STATISTICS FOR MANAGEMENT
Regulation ? 2019
Academic Year 2019 - 2020
Prepared by
Ms. B. Vasuki, Assistant Professor/Mathematics
Ms.B.Elakkiavani, Assistant Professor/Mathematics
2
(An
? .
DEPARTMENT OF MATHEMATICS
QUESTION BANK
SUBJECT : 1918108 ? STATISTICS FOR MANAGEMENT
SEM / YEAR : I Semester / I Year
UNIT I - INTRODUCTION
SYLLABUS: Basic definitions and rules for probability, conditional probability independence of events, Baye?s
theorem, and random variables, Probability distributions: Binomial, Poisson, Uniform and Normal distributions.
PART- A
S.NO QUESTIONS
BT Level
COMPETENCE
PART ? A
1. Define Statistics. BTL -6 Creating
2. What is the addition and multiplication theorem on probability. BTL -1 Remembering
3. Distinguish between a priori and posterior probability?. BTL -6 Creating
4.
The price of the selected stock over a five day period shown as 170, 110,
130, 170 and 160. Compute mean , median and mode.
BTL -6 Creating
5.
A car travels 25 miles at 25 mph, 25 miles at 50 mph and 25 miles at 75
mph. Find the harmonic of three velocities?
BTL -4 Analyse
6.
A ball is drawn at random from a box containg 6 red balls, 4 white balls
and 5 blue balls. Find the probability that the ball drawn is not red.
BTL -4 Analyse
7.
Find the median and mode for the weights (kgs) of 15 persons given as
68, 85, 70, 65, 71, 67, 65, 55, 80, 62, 65, 64, 70, 60, 56.
BTL -3 Applying
8. Name few measures of dispersion. BTL -1 Remembering
9. write the common measures of central tendency? BTL -1 Remembering
10. Define continuous and discrete variables examples. BTL -1 Remembering
11.
Let X be the lifetime in years of a mechanical part. Assume that X has
the cdf F(x) = 1- e
-x
, x ? 0. Find P[1< X ? 3].
BTL -1 Remembering
12. Define independent events. BTL -1 Remembering
13. State the theorem of total probability BTL -1 Remembering
14. What is the use of Baye?s theorem? BTL -6 Creating
15. Mention the properties of a discrete probability distribution. BTL -1 Remembering
16. Define a Poisson distribution and mention its mean and variance. BTL -1 Remembering
17. If the mean and variance of a binomial distribution are respectively 6 BTL -3 Applying
3
and 2.4, find P(x=2).
18.
If x is a Poisson distribution such that P(x=1)=4P(x=2). Find its
mean and variance.
BTL -3 Applying
19.
Suppose that X has a Poisson distribution with parameter ? = 2.
Compute P[X ? 1].
BTL -1 Remembering
20. Define mutually exclusive events. BTL -1 Remembering
PART-B
1(a).
Calculate the mean and standard deviation for the following table
giving the age distribution of 542 members.
Age
20-30 30-40 40-50 50-60 60-70 70-80 80-90
No 3 61 132 153 140 51 2
BTL-2 Understanding
1(b).
Find the geometric mean for the following data:
Group
2-4 4-6 6-8 8-10
Frequency 200 400 300 100
BTL-2
Understanding
2(a).
Find the mean, median and modal ages of married women at first
child birth
Age at the
birth of
first child
13
14
15
16
17
18
19
20
21
22
23
24
25
No of
married
women
37
162
343
390
256
433
161
355
65
85
49
46
40
BTL -6 Creating
2(b).
If A and B are independent event with P(A)=2/5, and P(B)=3/5,
find P(A ?B). Let S= {1,2,3,4,5,6} if A = {2,4,6} then find the
probability of A complement.
BTL -3 Applying
3(a).
Given: The probabilities of three events A, B and C occurring are
P(A) = 0.35, P(B) = 0.45 and P(C) = 0.2. Assuming that A, B, or
C has occurred, the probabilities of another event X occurring are
P(X/A) = 0.8, P(X/B) = 0.65 and P(X/C) = 0.3. Find P(A/X),
P(B/X) and P(C/X).
BTL -6 Creating
3(b).
4 cards are drawn from a well shuffled pack of cards. Find the
probability that
(i) All the four are queens
(ii) There is one card from each suit.
(iii) Two cards are diamonds and two are spades
All the four cards are hearts and one of them is jack
BTL -6 Creating
4(a).
Three machines all turn out non ferrous castings. Machine A
produces 1% defective and Machine B- 2% and machine C ? 5%.
Each machine produces 1/3 of the output. An inspector examines
a single casting, which he determines as non defective. Estimate
the probabilities of its having been produced by each machine.
BTL -6 Creating
4(b).
If the random variable X takes values 1, 2, 3, 4 such that
2P(X = 1) = 3P(X = 2) = P( X=3) = 5P(X = 4), find the
probability distribution and cumulative distribution of X.
BTL-2 Understanding
5(a).
Two dice are thrown together once. Find the probabilities for
BTL -3 Applying
4
getting the sum of the two numbers (i) equal to 5, (ii) multiple of
3, (iii) divisible by 4.
5(b).
Given ? = 4.2, for a poisson distribution. Find (a) P(X ? 2) (b)
P(X ? 5) (c) P(X = 8).
BTL -6 Creating
6(a).
An urn contains 5 balls. Two balls are drawn and found to be
white. What is the probability that all the balls are white?
BTL-1 Remembering
6(b).
The contents of urns I, II, III are as follows:
1 white, 2 black and 3 red balls;
2 white, 1 black and 1 red balls;
4 white, 5 black and 3 red balls;
One urn is chosen at random and two balls drawn. They happen to
be white and red. What is the probability that they come from
urns I, II, III?
BTL -3 Applying
7(a).
In 1989, there were three candidates for the position of principal
Mr. Chatterji, Mr. Ayangar and Dr. Singh. Whose chances of
getting the appointment are in the proportion 4:2:3 respectively.
The probability that Mr. Chatterji is selected, would introduce co-
education in the is 0.3. The probabilities of Mr. Ayangar
and Dr. Singh doing the same are respectively 0.5 and .08. What
is the probability that there was co-education in the in
1990?
BTL -3
Applying
7(b).
Find the probability that atmost 5 defective bolts will be found in
a box of 200 bolts, if it is known that 2% of such bolts are
expected to be defective. (e
-4
= 0.0183)
BTL -6 Creating
8(a).
A coin is tossed 6 times what is the probability of obtaining (a) 4
heads (b) 5 heads (c) 6 heads (d) getting 4 or more heads.
BTL -3 Applying
8(b).
In a bolt factory machines A, B, C manufacture respectively 25%,
35% and 40% of the total of their output 5, 4, 2 percent are
defective bolts. If A bolt is drawn at random from the product and
is found to be defective, what are the probabilities that is was
manufactured by machines A, B and C?
BTL -6 Creating
9(a).
In a test of 2000 electric blubs it was found that the life of a
particular make was normally distributed with an average life of
2040 hours and S. D. of 60 hours. Estimate the number of blubs
likely to burn for
(1) More than 2150 hours
(2) Less than 1950 hours
(3) More than 1920 hours but less than 2160 hours.
BTL -3 Applying
9(b).
The latest nationwide political poll indicates that for Americans
who are randomly selected, the probability that they are
conservative is 0.55, the probability that they are liberal is 0.30
and the probability that they are middle of the road is 0.15.
Assuming these probabilities are accurate, answer the following
BTL -4 Analyzing
FirstRanker.com - FirstRanker's Choice
1
(An
Ka ttankulathur ?
DEPARTMENT OF MATHEMATICS
QUESTION BANK
I SEMESTER
1918108 ? STATISTICS FOR MANAGEMENT
Regulation ? 2019
Academic Year 2019 - 2020
Prepared by
Ms. B. Vasuki, Assistant Professor/Mathematics
Ms.B.Elakkiavani, Assistant Professor/Mathematics
2
(An
? .
DEPARTMENT OF MATHEMATICS
QUESTION BANK
SUBJECT : 1918108 ? STATISTICS FOR MANAGEMENT
SEM / YEAR : I Semester / I Year
UNIT I - INTRODUCTION
SYLLABUS: Basic definitions and rules for probability, conditional probability independence of events, Baye?s
theorem, and random variables, Probability distributions: Binomial, Poisson, Uniform and Normal distributions.
PART- A
S.NO QUESTIONS
BT Level
COMPETENCE
PART ? A
1. Define Statistics. BTL -6 Creating
2. What is the addition and multiplication theorem on probability. BTL -1 Remembering
3. Distinguish between a priori and posterior probability?. BTL -6 Creating
4.
The price of the selected stock over a five day period shown as 170, 110,
130, 170 and 160. Compute mean , median and mode.
BTL -6 Creating
5.
A car travels 25 miles at 25 mph, 25 miles at 50 mph and 25 miles at 75
mph. Find the harmonic of three velocities?
BTL -4 Analyse
6.
A ball is drawn at random from a box containg 6 red balls, 4 white balls
and 5 blue balls. Find the probability that the ball drawn is not red.
BTL -4 Analyse
7.
Find the median and mode for the weights (kgs) of 15 persons given as
68, 85, 70, 65, 71, 67, 65, 55, 80, 62, 65, 64, 70, 60, 56.
BTL -3 Applying
8. Name few measures of dispersion. BTL -1 Remembering
9. write the common measures of central tendency? BTL -1 Remembering
10. Define continuous and discrete variables examples. BTL -1 Remembering
11.
Let X be the lifetime in years of a mechanical part. Assume that X has
the cdf F(x) = 1- e
-x
, x ? 0. Find P[1< X ? 3].
BTL -1 Remembering
12. Define independent events. BTL -1 Remembering
13. State the theorem of total probability BTL -1 Remembering
14. What is the use of Baye?s theorem? BTL -6 Creating
15. Mention the properties of a discrete probability distribution. BTL -1 Remembering
16. Define a Poisson distribution and mention its mean and variance. BTL -1 Remembering
17. If the mean and variance of a binomial distribution are respectively 6 BTL -3 Applying
3
and 2.4, find P(x=2).
18.
If x is a Poisson distribution such that P(x=1)=4P(x=2). Find its
mean and variance.
BTL -3 Applying
19.
Suppose that X has a Poisson distribution with parameter ? = 2.
Compute P[X ? 1].
BTL -1 Remembering
20. Define mutually exclusive events. BTL -1 Remembering
PART-B
1(a).
Calculate the mean and standard deviation for the following table
giving the age distribution of 542 members.
Age
20-30 30-40 40-50 50-60 60-70 70-80 80-90
No 3 61 132 153 140 51 2
BTL-2 Understanding
1(b).
Find the geometric mean for the following data:
Group
2-4 4-6 6-8 8-10
Frequency 200 400 300 100
BTL-2
Understanding
2(a).
Find the mean, median and modal ages of married women at first
child birth
Age at the
birth of
first child
13
14
15
16
17
18
19
20
21
22
23
24
25
No of
married
women
37
162
343
390
256
433
161
355
65
85
49
46
40
BTL -6 Creating
2(b).
If A and B are independent event with P(A)=2/5, and P(B)=3/5,
find P(A ?B). Let S= {1,2,3,4,5,6} if A = {2,4,6} then find the
probability of A complement.
BTL -3 Applying
3(a).
Given: The probabilities of three events A, B and C occurring are
P(A) = 0.35, P(B) = 0.45 and P(C) = 0.2. Assuming that A, B, or
C has occurred, the probabilities of another event X occurring are
P(X/A) = 0.8, P(X/B) = 0.65 and P(X/C) = 0.3. Find P(A/X),
P(B/X) and P(C/X).
BTL -6 Creating
3(b).
4 cards are drawn from a well shuffled pack of cards. Find the
probability that
(i) All the four are queens
(ii) There is one card from each suit.
(iii) Two cards are diamonds and two are spades
All the four cards are hearts and one of them is jack
BTL -6 Creating
4(a).
Three machines all turn out non ferrous castings. Machine A
produces 1% defective and Machine B- 2% and machine C ? 5%.
Each machine produces 1/3 of the output. An inspector examines
a single casting, which he determines as non defective. Estimate
the probabilities of its having been produced by each machine.
BTL -6 Creating
4(b).
If the random variable X takes values 1, 2, 3, 4 such that
2P(X = 1) = 3P(X = 2) = P( X=3) = 5P(X = 4), find the
probability distribution and cumulative distribution of X.
BTL-2 Understanding
5(a).
Two dice are thrown together once. Find the probabilities for
BTL -3 Applying
4
getting the sum of the two numbers (i) equal to 5, (ii) multiple of
3, (iii) divisible by 4.
5(b).
Given ? = 4.2, for a poisson distribution. Find (a) P(X ? 2) (b)
P(X ? 5) (c) P(X = 8).
BTL -6 Creating
6(a).
An urn contains 5 balls. Two balls are drawn and found to be
white. What is the probability that all the balls are white?
BTL-1 Remembering
6(b).
The contents of urns I, II, III are as follows:
1 white, 2 black and 3 red balls;
2 white, 1 black and 1 red balls;
4 white, 5 black and 3 red balls;
One urn is chosen at random and two balls drawn. They happen to
be white and red. What is the probability that they come from
urns I, II, III?
BTL -3 Applying
7(a).
In 1989, there were three candidates for the position of principal
Mr. Chatterji, Mr. Ayangar and Dr. Singh. Whose chances of
getting the appointment are in the proportion 4:2:3 respectively.
The probability that Mr. Chatterji is selected, would introduce co-
education in the is 0.3. The probabilities of Mr. Ayangar
and Dr. Singh doing the same are respectively 0.5 and .08. What
is the probability that there was co-education in the in
1990?
BTL -3
Applying
7(b).
Find the probability that atmost 5 defective bolts will be found in
a box of 200 bolts, if it is known that 2% of such bolts are
expected to be defective. (e
-4
= 0.0183)
BTL -6 Creating
8(a).
A coin is tossed 6 times what is the probability of obtaining (a) 4
heads (b) 5 heads (c) 6 heads (d) getting 4 or more heads.
BTL -3 Applying
8(b).
In a bolt factory machines A, B, C manufacture respectively 25%,
35% and 40% of the total of their output 5, 4, 2 percent are
defective bolts. If A bolt is drawn at random from the product and
is found to be defective, what are the probabilities that is was
manufactured by machines A, B and C?
BTL -6 Creating
9(a).
In a test of 2000 electric blubs it was found that the life of a
particular make was normally distributed with an average life of
2040 hours and S. D. of 60 hours. Estimate the number of blubs
likely to burn for
(1) More than 2150 hours
(2) Less than 1950 hours
(3) More than 1920 hours but less than 2160 hours.
BTL -3 Applying
9(b).
The latest nationwide political poll indicates that for Americans
who are randomly selected, the probability that they are
conservative is 0.55, the probability that they are liberal is 0.30
and the probability that they are middle of the road is 0.15.
Assuming these probabilities are accurate, answer the following
BTL -4 Analyzing
5
questions from a randomly chosen group of 10 Americans
(a) What the probability that 4 are liberal?
(b) What the probability that none are conservative
(c) What the probability that two are middle of the road
(d) What the probability that a least 8 are liberal
10.
If X follows a normal distribution with mean 12 and variance 16
cm, find the probabilities for (i) X ? 20 (ii) X ? 20, and (iii) 0 ? X
? 12.
BTL -3 Applying
11.
A discerete random variable X has the probability function given
below:
Value of X=x: 0 1 2 3 4 5 6 7
P(X=x) : 0 k 2k 2k 3k k
2
2k
2
7k
2
+k
Find (1) The value of k
(2) P(1.5 < X < 4.5 / X > 2)
(3) P(X < 6), P(X ? 5), P( 0 < X < 4)
(4) The distribution of X.
BTL -3 Applying
12.
X is a normal variable with mean 30 and standard deviation of 5.
Find (i) P[26 ? X ? 40] (ii) P [X?45] (iii) P [ ?X - 30 ?> 5] use
normal distribution tables
BTL -4 Analyzing
13.
In an intelligence test administered on 1000 students, the average
was 42 and standard deviation 24, find (i) the number of students
exceeding a score 50. (ii) the number of students lying between
30 and 54(iii) the value of score exceeded by top 100 students.
BTL -4 Analyzing
14(a).
The probability that an entering student will graduate is 0.4
Determine the probability that out of 5 students atleast one will
graduate.
BTL-5
Evaluating
14(b).
Fit a Poisson Distribution to the following data which gives the
number of doddens in a sample of clover seeds
No 0 1 2 3 4 5 6 7 8
f 56 156 132 92 37 22 4 0 1
.
BTL -4 Analyzing
PART-C
1(a).
A disciplinary committee is formed from the staff of XYZ
Company which has three departments Marketing, Finance and
Production of the 10,5,20 members respectively. All departments
have two female staff each. A department is selected at random
and from which two matters are selected for the committee,
What is the probability that both the team members are female?
BTL-6 Creating
FirstRanker.com - FirstRanker's Choice
1
(An
Ka ttankulathur ?
DEPARTMENT OF MATHEMATICS
QUESTION BANK
I SEMESTER
1918108 ? STATISTICS FOR MANAGEMENT
Regulation ? 2019
Academic Year 2019 - 2020
Prepared by
Ms. B. Vasuki, Assistant Professor/Mathematics
Ms.B.Elakkiavani, Assistant Professor/Mathematics
2
(An
? .
DEPARTMENT OF MATHEMATICS
QUESTION BANK
SUBJECT : 1918108 ? STATISTICS FOR MANAGEMENT
SEM / YEAR : I Semester / I Year
UNIT I - INTRODUCTION
SYLLABUS: Basic definitions and rules for probability, conditional probability independence of events, Baye?s
theorem, and random variables, Probability distributions: Binomial, Poisson, Uniform and Normal distributions.
PART- A
S.NO QUESTIONS
BT Level
COMPETENCE
PART ? A
1. Define Statistics. BTL -6 Creating
2. What is the addition and multiplication theorem on probability. BTL -1 Remembering
3. Distinguish between a priori and posterior probability?. BTL -6 Creating
4.
The price of the selected stock over a five day period shown as 170, 110,
130, 170 and 160. Compute mean , median and mode.
BTL -6 Creating
5.
A car travels 25 miles at 25 mph, 25 miles at 50 mph and 25 miles at 75
mph. Find the harmonic of three velocities?
BTL -4 Analyse
6.
A ball is drawn at random from a box containg 6 red balls, 4 white balls
and 5 blue balls. Find the probability that the ball drawn is not red.
BTL -4 Analyse
7.
Find the median and mode for the weights (kgs) of 15 persons given as
68, 85, 70, 65, 71, 67, 65, 55, 80, 62, 65, 64, 70, 60, 56.
BTL -3 Applying
8. Name few measures of dispersion. BTL -1 Remembering
9. write the common measures of central tendency? BTL -1 Remembering
10. Define continuous and discrete variables examples. BTL -1 Remembering
11.
Let X be the lifetime in years of a mechanical part. Assume that X has
the cdf F(x) = 1- e
-x
, x ? 0. Find P[1< X ? 3].
BTL -1 Remembering
12. Define independent events. BTL -1 Remembering
13. State the theorem of total probability BTL -1 Remembering
14. What is the use of Baye?s theorem? BTL -6 Creating
15. Mention the properties of a discrete probability distribution. BTL -1 Remembering
16. Define a Poisson distribution and mention its mean and variance. BTL -1 Remembering
17. If the mean and variance of a binomial distribution are respectively 6 BTL -3 Applying
3
and 2.4, find P(x=2).
18.
If x is a Poisson distribution such that P(x=1)=4P(x=2). Find its
mean and variance.
BTL -3 Applying
19.
Suppose that X has a Poisson distribution with parameter ? = 2.
Compute P[X ? 1].
BTL -1 Remembering
20. Define mutually exclusive events. BTL -1 Remembering
PART-B
1(a).
Calculate the mean and standard deviation for the following table
giving the age distribution of 542 members.
Age
20-30 30-40 40-50 50-60 60-70 70-80 80-90
No 3 61 132 153 140 51 2
BTL-2 Understanding
1(b).
Find the geometric mean for the following data:
Group
2-4 4-6 6-8 8-10
Frequency 200 400 300 100
BTL-2
Understanding
2(a).
Find the mean, median and modal ages of married women at first
child birth
Age at the
birth of
first child
13
14
15
16
17
18
19
20
21
22
23
24
25
No of
married
women
37
162
343
390
256
433
161
355
65
85
49
46
40
BTL -6 Creating
2(b).
If A and B are independent event with P(A)=2/5, and P(B)=3/5,
find P(A ?B). Let S= {1,2,3,4,5,6} if A = {2,4,6} then find the
probability of A complement.
BTL -3 Applying
3(a).
Given: The probabilities of three events A, B and C occurring are
P(A) = 0.35, P(B) = 0.45 and P(C) = 0.2. Assuming that A, B, or
C has occurred, the probabilities of another event X occurring are
P(X/A) = 0.8, P(X/B) = 0.65 and P(X/C) = 0.3. Find P(A/X),
P(B/X) and P(C/X).
BTL -6 Creating
3(b).
4 cards are drawn from a well shuffled pack of cards. Find the
probability that
(i) All the four are queens
(ii) There is one card from each suit.
(iii) Two cards are diamonds and two are spades
All the four cards are hearts and one of them is jack
BTL -6 Creating
4(a).
Three machines all turn out non ferrous castings. Machine A
produces 1% defective and Machine B- 2% and machine C ? 5%.
Each machine produces 1/3 of the output. An inspector examines
a single casting, which he determines as non defective. Estimate
the probabilities of its having been produced by each machine.
BTL -6 Creating
4(b).
If the random variable X takes values 1, 2, 3, 4 such that
2P(X = 1) = 3P(X = 2) = P( X=3) = 5P(X = 4), find the
probability distribution and cumulative distribution of X.
BTL-2 Understanding
5(a).
Two dice are thrown together once. Find the probabilities for
BTL -3 Applying
4
getting the sum of the two numbers (i) equal to 5, (ii) multiple of
3, (iii) divisible by 4.
5(b).
Given ? = 4.2, for a poisson distribution. Find (a) P(X ? 2) (b)
P(X ? 5) (c) P(X = 8).
BTL -6 Creating
6(a).
An urn contains 5 balls. Two balls are drawn and found to be
white. What is the probability that all the balls are white?
BTL-1 Remembering
6(b).
The contents of urns I, II, III are as follows:
1 white, 2 black and 3 red balls;
2 white, 1 black and 1 red balls;
4 white, 5 black and 3 red balls;
One urn is chosen at random and two balls drawn. They happen to
be white and red. What is the probability that they come from
urns I, II, III?
BTL -3 Applying
7(a).
In 1989, there were three candidates for the position of principal
Mr. Chatterji, Mr. Ayangar and Dr. Singh. Whose chances of
getting the appointment are in the proportion 4:2:3 respectively.
The probability that Mr. Chatterji is selected, would introduce co-
education in the is 0.3. The probabilities of Mr. Ayangar
and Dr. Singh doing the same are respectively 0.5 and .08. What
is the probability that there was co-education in the in
1990?
BTL -3
Applying
7(b).
Find the probability that atmost 5 defective bolts will be found in
a box of 200 bolts, if it is known that 2% of such bolts are
expected to be defective. (e
-4
= 0.0183)
BTL -6 Creating
8(a).
A coin is tossed 6 times what is the probability of obtaining (a) 4
heads (b) 5 heads (c) 6 heads (d) getting 4 or more heads.
BTL -3 Applying
8(b).
In a bolt factory machines A, B, C manufacture respectively 25%,
35% and 40% of the total of their output 5, 4, 2 percent are
defective bolts. If A bolt is drawn at random from the product and
is found to be defective, what are the probabilities that is was
manufactured by machines A, B and C?
BTL -6 Creating
9(a).
In a test of 2000 electric blubs it was found that the life of a
particular make was normally distributed with an average life of
2040 hours and S. D. of 60 hours. Estimate the number of blubs
likely to burn for
(1) More than 2150 hours
(2) Less than 1950 hours
(3) More than 1920 hours but less than 2160 hours.
BTL -3 Applying
9(b).
The latest nationwide political poll indicates that for Americans
who are randomly selected, the probability that they are
conservative is 0.55, the probability that they are liberal is 0.30
and the probability that they are middle of the road is 0.15.
Assuming these probabilities are accurate, answer the following
BTL -4 Analyzing
5
questions from a randomly chosen group of 10 Americans
(a) What the probability that 4 are liberal?
(b) What the probability that none are conservative
(c) What the probability that two are middle of the road
(d) What the probability that a least 8 are liberal
10.
If X follows a normal distribution with mean 12 and variance 16
cm, find the probabilities for (i) X ? 20 (ii) X ? 20, and (iii) 0 ? X
? 12.
BTL -3 Applying
11.
A discerete random variable X has the probability function given
below:
Value of X=x: 0 1 2 3 4 5 6 7
P(X=x) : 0 k 2k 2k 3k k
2
2k
2
7k
2
+k
Find (1) The value of k
(2) P(1.5 < X < 4.5 / X > 2)
(3) P(X < 6), P(X ? 5), P( 0 < X < 4)
(4) The distribution of X.
BTL -3 Applying
12.
X is a normal variable with mean 30 and standard deviation of 5.
Find (i) P[26 ? X ? 40] (ii) P [X?45] (iii) P [ ?X - 30 ?> 5] use
normal distribution tables
BTL -4 Analyzing
13.
In an intelligence test administered on 1000 students, the average
was 42 and standard deviation 24, find (i) the number of students
exceeding a score 50. (ii) the number of students lying between
30 and 54(iii) the value of score exceeded by top 100 students.
BTL -4 Analyzing
14(a).
The probability that an entering student will graduate is 0.4
Determine the probability that out of 5 students atleast one will
graduate.
BTL-5
Evaluating
14(b).
Fit a Poisson Distribution to the following data which gives the
number of doddens in a sample of clover seeds
No 0 1 2 3 4 5 6 7 8
f 56 156 132 92 37 22 4 0 1
.
BTL -4 Analyzing
PART-C
1(a).
A disciplinary committee is formed from the staff of XYZ
Company which has three departments Marketing, Finance and
Production of the 10,5,20 members respectively. All departments
have two female staff each. A department is selected at random
and from which two matters are selected for the committee,
What is the probability that both the team members are female?
BTL-6 Creating
6
1(b).
In a bolt factory machines A, B, C manufacture respectively 25,
35 and 40 percent of the total. Of their output 5, 4 and 2 percent
are defective bolts respectively. A bolt is drawn at random from
the product and is found o be defective. What are the probabilities
that it was manufactured by machines A, B or C?
BTL-2
Understanding
2(a). State Bayes theorem and brief about its applications. BTL-2 Understanding
2(b).
Out of 800 families with 4 children each, how many families
would be expected to have (i) 2 boys and 2 girls (ii) at least 1 boy
(iii) at most 2 girls (iv) children of both sexes? Assume equal
probabilities for boys and girls.
BTL-1 Remembering
3. Describe the classifications of probability ? BTL-1 Remembering
4. What are the applications of Normal distribution in statistics? BTL-6 Creating
UNIT ?II- SAMPLING DISTRIBUTION & ESTIMATION.
SYLLABUS: Introduction to sampling distributions, sampling distribution of mean and proportion, application of central
limit theorem, sampling techniques. Estimation: Point and Interval estimates for population parameters of large sample and
small samples, determining the sample size.
PART - A
S.N
O
QUESTIONS
BT Level
COMPETENCE
1. Define Sampling distribution of proportion. BTL -1 Remembering
2. Define Probable standard error. BTL -1 Remembering
3. Define standard error and mention its importance BTL -1 Remembering
4. Define central limit theorem BTL -1 Remembering
5.
What is the role of central limit theorem in estimation and testing
problems
BTL -6 Creating
6. Define stratified sampling technique BTL -1 Remembering
7. Briefly describe the significance level. BTL -1 Remembering
8. Distinguish between parameter and statistic. BTL -2 Understanding
9. Define estimator, estimate and estimation. BTL -1 Remembering
10. Distinguish between point estimation and interval estimation BTL -2 Understanding
11. Mention the properties of a good estimator. BTL -1 Remembering
12. Define confidence coefficient. BTL -1 Remembering
13. What is the level of significance in testing of hypothesis BTL -6 Creating
14. Define confidence limits for a parameter BTL -1 Remembering
15.
State the conditions under which a binomial distribution becomes a
normal distribution
BTL -4 Analyzing
16.
If the random sample comes from a normal population, what can
be said about the sampling distribution of the mean.
BTL -5 Evaluating
17.
An automobile repair shop has taken a random sample of 40
services that the average service time on an automobile is 130
minutes with a standard deviation of 26 minutes. Compute the
standard error of the mean.
BTL -6 Creating
FirstRanker.com - FirstRanker's Choice
1
(An
Ka ttankulathur ?
DEPARTMENT OF MATHEMATICS
QUESTION BANK
I SEMESTER
1918108 ? STATISTICS FOR MANAGEMENT
Regulation ? 2019
Academic Year 2019 - 2020
Prepared by
Ms. B. Vasuki, Assistant Professor/Mathematics
Ms.B.Elakkiavani, Assistant Professor/Mathematics
2
(An
? .
DEPARTMENT OF MATHEMATICS
QUESTION BANK
SUBJECT : 1918108 ? STATISTICS FOR MANAGEMENT
SEM / YEAR : I Semester / I Year
UNIT I - INTRODUCTION
SYLLABUS: Basic definitions and rules for probability, conditional probability independence of events, Baye?s
theorem, and random variables, Probability distributions: Binomial, Poisson, Uniform and Normal distributions.
PART- A
S.NO QUESTIONS
BT Level
COMPETENCE
PART ? A
1. Define Statistics. BTL -6 Creating
2. What is the addition and multiplication theorem on probability. BTL -1 Remembering
3. Distinguish between a priori and posterior probability?. BTL -6 Creating
4.
The price of the selected stock over a five day period shown as 170, 110,
130, 170 and 160. Compute mean , median and mode.
BTL -6 Creating
5.
A car travels 25 miles at 25 mph, 25 miles at 50 mph and 25 miles at 75
mph. Find the harmonic of three velocities?
BTL -4 Analyse
6.
A ball is drawn at random from a box containg 6 red balls, 4 white balls
and 5 blue balls. Find the probability that the ball drawn is not red.
BTL -4 Analyse
7.
Find the median and mode for the weights (kgs) of 15 persons given as
68, 85, 70, 65, 71, 67, 65, 55, 80, 62, 65, 64, 70, 60, 56.
BTL -3 Applying
8. Name few measures of dispersion. BTL -1 Remembering
9. write the common measures of central tendency? BTL -1 Remembering
10. Define continuous and discrete variables examples. BTL -1 Remembering
11.
Let X be the lifetime in years of a mechanical part. Assume that X has
the cdf F(x) = 1- e
-x
, x ? 0. Find P[1< X ? 3].
BTL -1 Remembering
12. Define independent events. BTL -1 Remembering
13. State the theorem of total probability BTL -1 Remembering
14. What is the use of Baye?s theorem? BTL -6 Creating
15. Mention the properties of a discrete probability distribution. BTL -1 Remembering
16. Define a Poisson distribution and mention its mean and variance. BTL -1 Remembering
17. If the mean and variance of a binomial distribution are respectively 6 BTL -3 Applying
3
and 2.4, find P(x=2).
18.
If x is a Poisson distribution such that P(x=1)=4P(x=2). Find its
mean and variance.
BTL -3 Applying
19.
Suppose that X has a Poisson distribution with parameter ? = 2.
Compute P[X ? 1].
BTL -1 Remembering
20. Define mutually exclusive events. BTL -1 Remembering
PART-B
1(a).
Calculate the mean and standard deviation for the following table
giving the age distribution of 542 members.
Age
20-30 30-40 40-50 50-60 60-70 70-80 80-90
No 3 61 132 153 140 51 2
BTL-2 Understanding
1(b).
Find the geometric mean for the following data:
Group
2-4 4-6 6-8 8-10
Frequency 200 400 300 100
BTL-2
Understanding
2(a).
Find the mean, median and modal ages of married women at first
child birth
Age at the
birth of
first child
13
14
15
16
17
18
19
20
21
22
23
24
25
No of
married
women
37
162
343
390
256
433
161
355
65
85
49
46
40
BTL -6 Creating
2(b).
If A and B are independent event with P(A)=2/5, and P(B)=3/5,
find P(A ?B). Let S= {1,2,3,4,5,6} if A = {2,4,6} then find the
probability of A complement.
BTL -3 Applying
3(a).
Given: The probabilities of three events A, B and C occurring are
P(A) = 0.35, P(B) = 0.45 and P(C) = 0.2. Assuming that A, B, or
C has occurred, the probabilities of another event X occurring are
P(X/A) = 0.8, P(X/B) = 0.65 and P(X/C) = 0.3. Find P(A/X),
P(B/X) and P(C/X).
BTL -6 Creating
3(b).
4 cards are drawn from a well shuffled pack of cards. Find the
probability that
(i) All the four are queens
(ii) There is one card from each suit.
(iii) Two cards are diamonds and two are spades
All the four cards are hearts and one of them is jack
BTL -6 Creating
4(a).
Three machines all turn out non ferrous castings. Machine A
produces 1% defective and Machine B- 2% and machine C ? 5%.
Each machine produces 1/3 of the output. An inspector examines
a single casting, which he determines as non defective. Estimate
the probabilities of its having been produced by each machine.
BTL -6 Creating
4(b).
If the random variable X takes values 1, 2, 3, 4 such that
2P(X = 1) = 3P(X = 2) = P( X=3) = 5P(X = 4), find the
probability distribution and cumulative distribution of X.
BTL-2 Understanding
5(a).
Two dice are thrown together once. Find the probabilities for
BTL -3 Applying
4
getting the sum of the two numbers (i) equal to 5, (ii) multiple of
3, (iii) divisible by 4.
5(b).
Given ? = 4.2, for a poisson distribution. Find (a) P(X ? 2) (b)
P(X ? 5) (c) P(X = 8).
BTL -6 Creating
6(a).
An urn contains 5 balls. Two balls are drawn and found to be
white. What is the probability that all the balls are white?
BTL-1 Remembering
6(b).
The contents of urns I, II, III are as follows:
1 white, 2 black and 3 red balls;
2 white, 1 black and 1 red balls;
4 white, 5 black and 3 red balls;
One urn is chosen at random and two balls drawn. They happen to
be white and red. What is the probability that they come from
urns I, II, III?
BTL -3 Applying
7(a).
In 1989, there were three candidates for the position of principal
Mr. Chatterji, Mr. Ayangar and Dr. Singh. Whose chances of
getting the appointment are in the proportion 4:2:3 respectively.
The probability that Mr. Chatterji is selected, would introduce co-
education in the is 0.3. The probabilities of Mr. Ayangar
and Dr. Singh doing the same are respectively 0.5 and .08. What
is the probability that there was co-education in the in
1990?
BTL -3
Applying
7(b).
Find the probability that atmost 5 defective bolts will be found in
a box of 200 bolts, if it is known that 2% of such bolts are
expected to be defective. (e
-4
= 0.0183)
BTL -6 Creating
8(a).
A coin is tossed 6 times what is the probability of obtaining (a) 4
heads (b) 5 heads (c) 6 heads (d) getting 4 or more heads.
BTL -3 Applying
8(b).
In a bolt factory machines A, B, C manufacture respectively 25%,
35% and 40% of the total of their output 5, 4, 2 percent are
defective bolts. If A bolt is drawn at random from the product and
is found to be defective, what are the probabilities that is was
manufactured by machines A, B and C?
BTL -6 Creating
9(a).
In a test of 2000 electric blubs it was found that the life of a
particular make was normally distributed with an average life of
2040 hours and S. D. of 60 hours. Estimate the number of blubs
likely to burn for
(1) More than 2150 hours
(2) Less than 1950 hours
(3) More than 1920 hours but less than 2160 hours.
BTL -3 Applying
9(b).
The latest nationwide political poll indicates that for Americans
who are randomly selected, the probability that they are
conservative is 0.55, the probability that they are liberal is 0.30
and the probability that they are middle of the road is 0.15.
Assuming these probabilities are accurate, answer the following
BTL -4 Analyzing
5
questions from a randomly chosen group of 10 Americans
(a) What the probability that 4 are liberal?
(b) What the probability that none are conservative
(c) What the probability that two are middle of the road
(d) What the probability that a least 8 are liberal
10.
If X follows a normal distribution with mean 12 and variance 16
cm, find the probabilities for (i) X ? 20 (ii) X ? 20, and (iii) 0 ? X
? 12.
BTL -3 Applying
11.
A discerete random variable X has the probability function given
below:
Value of X=x: 0 1 2 3 4 5 6 7
P(X=x) : 0 k 2k 2k 3k k
2
2k
2
7k
2
+k
Find (1) The value of k
(2) P(1.5 < X < 4.5 / X > 2)
(3) P(X < 6), P(X ? 5), P( 0 < X < 4)
(4) The distribution of X.
BTL -3 Applying
12.
X is a normal variable with mean 30 and standard deviation of 5.
Find (i) P[26 ? X ? 40] (ii) P [X?45] (iii) P [ ?X - 30 ?> 5] use
normal distribution tables
BTL -4 Analyzing
13.
In an intelligence test administered on 1000 students, the average
was 42 and standard deviation 24, find (i) the number of students
exceeding a score 50. (ii) the number of students lying between
30 and 54(iii) the value of score exceeded by top 100 students.
BTL -4 Analyzing
14(a).
The probability that an entering student will graduate is 0.4
Determine the probability that out of 5 students atleast one will
graduate.
BTL-5
Evaluating
14(b).
Fit a Poisson Distribution to the following data which gives the
number of doddens in a sample of clover seeds
No 0 1 2 3 4 5 6 7 8
f 56 156 132 92 37 22 4 0 1
.
BTL -4 Analyzing
PART-C
1(a).
A disciplinary committee is formed from the staff of XYZ
Company which has three departments Marketing, Finance and
Production of the 10,5,20 members respectively. All departments
have two female staff each. A department is selected at random
and from which two matters are selected for the committee,
What is the probability that both the team members are female?
BTL-6 Creating
6
1(b).
In a bolt factory machines A, B, C manufacture respectively 25,
35 and 40 percent of the total. Of their output 5, 4 and 2 percent
are defective bolts respectively. A bolt is drawn at random from
the product and is found o be defective. What are the probabilities
that it was manufactured by machines A, B or C?
BTL-2
Understanding
2(a). State Bayes theorem and brief about its applications. BTL-2 Understanding
2(b).
Out of 800 families with 4 children each, how many families
would be expected to have (i) 2 boys and 2 girls (ii) at least 1 boy
(iii) at most 2 girls (iv) children of both sexes? Assume equal
probabilities for boys and girls.
BTL-1 Remembering
3. Describe the classifications of probability ? BTL-1 Remembering
4. What are the applications of Normal distribution in statistics? BTL-6 Creating
UNIT ?II- SAMPLING DISTRIBUTION & ESTIMATION.
SYLLABUS: Introduction to sampling distributions, sampling distribution of mean and proportion, application of central
limit theorem, sampling techniques. Estimation: Point and Interval estimates for population parameters of large sample and
small samples, determining the sample size.
PART - A
S.N
O
QUESTIONS
BT Level
COMPETENCE
1. Define Sampling distribution of proportion. BTL -1 Remembering
2. Define Probable standard error. BTL -1 Remembering
3. Define standard error and mention its importance BTL -1 Remembering
4. Define central limit theorem BTL -1 Remembering
5.
What is the role of central limit theorem in estimation and testing
problems
BTL -6 Creating
6. Define stratified sampling technique BTL -1 Remembering
7. Briefly describe the significance level. BTL -1 Remembering
8. Distinguish between parameter and statistic. BTL -2 Understanding
9. Define estimator, estimate and estimation. BTL -1 Remembering
10. Distinguish between point estimation and interval estimation BTL -2 Understanding
11. Mention the properties of a good estimator. BTL -1 Remembering
12. Define confidence coefficient. BTL -1 Remembering
13. What is the level of significance in testing of hypothesis BTL -6 Creating
14. Define confidence limits for a parameter BTL -1 Remembering
15.
State the conditions under which a binomial distribution becomes a
normal distribution
BTL -4 Analyzing
16.
If the random sample comes from a normal population, what can
be said about the sampling distribution of the mean.
BTL -5 Evaluating
17.
An automobile repair shop has taken a random sample of 40
services that the average service time on an automobile is 130
minutes with a standard deviation of 26 minutes. Compute the
standard error of the mean.
BTL -6 Creating
7
18. What is a random number? How it is useful in sampling? BTL -6 Creating
19.
A population has the numbers: 12, 8, 10, 30, 12, 16, 40, 5, 16, 24,
22, 31, 30, 16, 15. Draw a systematic sample of size 5. Find out its
mean.
BTL -3 Applying
20. How large sample is useful in estimation and testing BTL -4 Analyzing
PART -B
1(a).
A random sample of 700 units from a large consignment showed
that 200 were damaged. Find (i) 95% (ii) 99% confidence limits
for the proportion of damaged units in the consignment.
BTL -3 Applying
1(b).
A random sample of size 9 is obtained from a Normal population
with mean 25 and if the variance 100 find the probability that the
sample mean exceeds 31.2.
BTL -4 Analyzing
2(a).
In a normally distributed population, average income per
household is Rs.20,000 with a standard deviation of Rs. 1,600.
Find the probability that the sample mean will be between
Rs.19,600 and Rs.20,200 in a survey of a random sample of 100
households.
BTL -6 Creating
2(b).
A university wants to determine the percentage of students who
would accept proposed fees hike for improving facilities. The
university wants to be 90% confident that the percentage is
within2% of the true value. Find the sample size to achieve the
accuracy regardless of the true percentage assuming the percentage
of students accepting the increase in tuition fees to be 0.5.
BTL -6 Creating
3(a).
A bank has kept records of the checking balances of its customers
and determined that the average daily balances of its customers is
Rs.300 with a standard deviation of Rs. 48. A random sample of
144 checking accounts is selected.
(i) What is the probability that the sample mean will be more
than Rs. 306.60?
(ii) What is the probability that the sample mean will be less
than Rs. 308?
BTL -6 Creating
3(b).
From the question 3(a)
(i) What is probability that the sample mean will between Rs.
302 and Rs. 308?
(ii) What is probability that the sample mean will be atleast
Rs. 296?
BTL -6 Creating
4(a).
Explain Stratified sampling technique and discuss how it is better
than simple random sampling in a particular situation.
BTL -4
Analyzing
4(b). Discuss the standard error of proportion BTL-2 Understanding
5.
Explain the methods of drawing simple random sample from a
finite population.
BTL -4 Analyzing
FirstRanker.com - FirstRanker's Choice
1
(An
Ka ttankulathur ?
DEPARTMENT OF MATHEMATICS
QUESTION BANK
I SEMESTER
1918108 ? STATISTICS FOR MANAGEMENT
Regulation ? 2019
Academic Year 2019 - 2020
Prepared by
Ms. B. Vasuki, Assistant Professor/Mathematics
Ms.B.Elakkiavani, Assistant Professor/Mathematics
2
(An
? .
DEPARTMENT OF MATHEMATICS
QUESTION BANK
SUBJECT : 1918108 ? STATISTICS FOR MANAGEMENT
SEM / YEAR : I Semester / I Year
UNIT I - INTRODUCTION
SYLLABUS: Basic definitions and rules for probability, conditional probability independence of events, Baye?s
theorem, and random variables, Probability distributions: Binomial, Poisson, Uniform and Normal distributions.
PART- A
S.NO QUESTIONS
BT Level
COMPETENCE
PART ? A
1. Define Statistics. BTL -6 Creating
2. What is the addition and multiplication theorem on probability. BTL -1 Remembering
3. Distinguish between a priori and posterior probability?. BTL -6 Creating
4.
The price of the selected stock over a five day period shown as 170, 110,
130, 170 and 160. Compute mean , median and mode.
BTL -6 Creating
5.
A car travels 25 miles at 25 mph, 25 miles at 50 mph and 25 miles at 75
mph. Find the harmonic of three velocities?
BTL -4 Analyse
6.
A ball is drawn at random from a box containg 6 red balls, 4 white balls
and 5 blue balls. Find the probability that the ball drawn is not red.
BTL -4 Analyse
7.
Find the median and mode for the weights (kgs) of 15 persons given as
68, 85, 70, 65, 71, 67, 65, 55, 80, 62, 65, 64, 70, 60, 56.
BTL -3 Applying
8. Name few measures of dispersion. BTL -1 Remembering
9. write the common measures of central tendency? BTL -1 Remembering
10. Define continuous and discrete variables examples. BTL -1 Remembering
11.
Let X be the lifetime in years of a mechanical part. Assume that X has
the cdf F(x) = 1- e
-x
, x ? 0. Find P[1< X ? 3].
BTL -1 Remembering
12. Define independent events. BTL -1 Remembering
13. State the theorem of total probability BTL -1 Remembering
14. What is the use of Baye?s theorem? BTL -6 Creating
15. Mention the properties of a discrete probability distribution. BTL -1 Remembering
16. Define a Poisson distribution and mention its mean and variance. BTL -1 Remembering
17. If the mean and variance of a binomial distribution are respectively 6 BTL -3 Applying
3
and 2.4, find P(x=2).
18.
If x is a Poisson distribution such that P(x=1)=4P(x=2). Find its
mean and variance.
BTL -3 Applying
19.
Suppose that X has a Poisson distribution with parameter ? = 2.
Compute P[X ? 1].
BTL -1 Remembering
20. Define mutually exclusive events. BTL -1 Remembering
PART-B
1(a).
Calculate the mean and standard deviation for the following table
giving the age distribution of 542 members.
Age
20-30 30-40 40-50 50-60 60-70 70-80 80-90
No 3 61 132 153 140 51 2
BTL-2 Understanding
1(b).
Find the geometric mean for the following data:
Group
2-4 4-6 6-8 8-10
Frequency 200 400 300 100
BTL-2
Understanding
2(a).
Find the mean, median and modal ages of married women at first
child birth
Age at the
birth of
first child
13
14
15
16
17
18
19
20
21
22
23
24
25
No of
married
women
37
162
343
390
256
433
161
355
65
85
49
46
40
BTL -6 Creating
2(b).
If A and B are independent event with P(A)=2/5, and P(B)=3/5,
find P(A ?B). Let S= {1,2,3,4,5,6} if A = {2,4,6} then find the
probability of A complement.
BTL -3 Applying
3(a).
Given: The probabilities of three events A, B and C occurring are
P(A) = 0.35, P(B) = 0.45 and P(C) = 0.2. Assuming that A, B, or
C has occurred, the probabilities of another event X occurring are
P(X/A) = 0.8, P(X/B) = 0.65 and P(X/C) = 0.3. Find P(A/X),
P(B/X) and P(C/X).
BTL -6 Creating
3(b).
4 cards are drawn from a well shuffled pack of cards. Find the
probability that
(i) All the four are queens
(ii) There is one card from each suit.
(iii) Two cards are diamonds and two are spades
All the four cards are hearts and one of them is jack
BTL -6 Creating
4(a).
Three machines all turn out non ferrous castings. Machine A
produces 1% defective and Machine B- 2% and machine C ? 5%.
Each machine produces 1/3 of the output. An inspector examines
a single casting, which he determines as non defective. Estimate
the probabilities of its having been produced by each machine.
BTL -6 Creating
4(b).
If the random variable X takes values 1, 2, 3, 4 such that
2P(X = 1) = 3P(X = 2) = P( X=3) = 5P(X = 4), find the
probability distribution and cumulative distribution of X.
BTL-2 Understanding
5(a).
Two dice are thrown together once. Find the probabilities for
BTL -3 Applying
4
getting the sum of the two numbers (i) equal to 5, (ii) multiple of
3, (iii) divisible by 4.
5(b).
Given ? = 4.2, for a poisson distribution. Find (a) P(X ? 2) (b)
P(X ? 5) (c) P(X = 8).
BTL -6 Creating
6(a).
An urn contains 5 balls. Two balls are drawn and found to be
white. What is the probability that all the balls are white?
BTL-1 Remembering
6(b).
The contents of urns I, II, III are as follows:
1 white, 2 black and 3 red balls;
2 white, 1 black and 1 red balls;
4 white, 5 black and 3 red balls;
One urn is chosen at random and two balls drawn. They happen to
be white and red. What is the probability that they come from
urns I, II, III?
BTL -3 Applying
7(a).
In 1989, there were three candidates for the position of principal
Mr. Chatterji, Mr. Ayangar and Dr. Singh. Whose chances of
getting the appointment are in the proportion 4:2:3 respectively.
The probability that Mr. Chatterji is selected, would introduce co-
education in the is 0.3. The probabilities of Mr. Ayangar
and Dr. Singh doing the same are respectively 0.5 and .08. What
is the probability that there was co-education in the in
1990?
BTL -3
Applying
7(b).
Find the probability that atmost 5 defective bolts will be found in
a box of 200 bolts, if it is known that 2% of such bolts are
expected to be defective. (e
-4
= 0.0183)
BTL -6 Creating
8(a).
A coin is tossed 6 times what is the probability of obtaining (a) 4
heads (b) 5 heads (c) 6 heads (d) getting 4 or more heads.
BTL -3 Applying
8(b).
In a bolt factory machines A, B, C manufacture respectively 25%,
35% and 40% of the total of their output 5, 4, 2 percent are
defective bolts. If A bolt is drawn at random from the product and
is found to be defective, what are the probabilities that is was
manufactured by machines A, B and C?
BTL -6 Creating
9(a).
In a test of 2000 electric blubs it was found that the life of a
particular make was normally distributed with an average life of
2040 hours and S. D. of 60 hours. Estimate the number of blubs
likely to burn for
(1) More than 2150 hours
(2) Less than 1950 hours
(3) More than 1920 hours but less than 2160 hours.
BTL -3 Applying
9(b).
The latest nationwide political poll indicates that for Americans
who are randomly selected, the probability that they are
conservative is 0.55, the probability that they are liberal is 0.30
and the probability that they are middle of the road is 0.15.
Assuming these probabilities are accurate, answer the following
BTL -4 Analyzing
5
questions from a randomly chosen group of 10 Americans
(a) What the probability that 4 are liberal?
(b) What the probability that none are conservative
(c) What the probability that two are middle of the road
(d) What the probability that a least 8 are liberal
10.
If X follows a normal distribution with mean 12 and variance 16
cm, find the probabilities for (i) X ? 20 (ii) X ? 20, and (iii) 0 ? X
? 12.
BTL -3 Applying
11.
A discerete random variable X has the probability function given
below:
Value of X=x: 0 1 2 3 4 5 6 7
P(X=x) : 0 k 2k 2k 3k k
2
2k
2
7k
2
+k
Find (1) The value of k
(2) P(1.5 < X < 4.5 / X > 2)
(3) P(X < 6), P(X ? 5), P( 0 < X < 4)
(4) The distribution of X.
BTL -3 Applying
12.
X is a normal variable with mean 30 and standard deviation of 5.
Find (i) P[26 ? X ? 40] (ii) P [X?45] (iii) P [ ?X - 30 ?> 5] use
normal distribution tables
BTL -4 Analyzing
13.
In an intelligence test administered on 1000 students, the average
was 42 and standard deviation 24, find (i) the number of students
exceeding a score 50. (ii) the number of students lying between
30 and 54(iii) the value of score exceeded by top 100 students.
BTL -4 Analyzing
14(a).
The probability that an entering student will graduate is 0.4
Determine the probability that out of 5 students atleast one will
graduate.
BTL-5
Evaluating
14(b).
Fit a Poisson Distribution to the following data which gives the
number of doddens in a sample of clover seeds
No 0 1 2 3 4 5 6 7 8
f 56 156 132 92 37 22 4 0 1
.
BTL -4 Analyzing
PART-C
1(a).
A disciplinary committee is formed from the staff of XYZ
Company which has three departments Marketing, Finance and
Production of the 10,5,20 members respectively. All departments
have two female staff each. A department is selected at random
and from which two matters are selected for the committee,
What is the probability that both the team members are female?
BTL-6 Creating
6
1(b).
In a bolt factory machines A, B, C manufacture respectively 25,
35 and 40 percent of the total. Of their output 5, 4 and 2 percent
are defective bolts respectively. A bolt is drawn at random from
the product and is found o be defective. What are the probabilities
that it was manufactured by machines A, B or C?
BTL-2
Understanding
2(a). State Bayes theorem and brief about its applications. BTL-2 Understanding
2(b).
Out of 800 families with 4 children each, how many families
would be expected to have (i) 2 boys and 2 girls (ii) at least 1 boy
(iii) at most 2 girls (iv) children of both sexes? Assume equal
probabilities for boys and girls.
BTL-1 Remembering
3. Describe the classifications of probability ? BTL-1 Remembering
4. What are the applications of Normal distribution in statistics? BTL-6 Creating
UNIT ?II- SAMPLING DISTRIBUTION & ESTIMATION.
SYLLABUS: Introduction to sampling distributions, sampling distribution of mean and proportion, application of central
limit theorem, sampling techniques. Estimation: Point and Interval estimates for population parameters of large sample and
small samples, determining the sample size.
PART - A
S.N
O
QUESTIONS
BT Level
COMPETENCE
1. Define Sampling distribution of proportion. BTL -1 Remembering
2. Define Probable standard error. BTL -1 Remembering
3. Define standard error and mention its importance BTL -1 Remembering
4. Define central limit theorem BTL -1 Remembering
5.
What is the role of central limit theorem in estimation and testing
problems
BTL -6 Creating
6. Define stratified sampling technique BTL -1 Remembering
7. Briefly describe the significance level. BTL -1 Remembering
8. Distinguish between parameter and statistic. BTL -2 Understanding
9. Define estimator, estimate and estimation. BTL -1 Remembering
10. Distinguish between point estimation and interval estimation BTL -2 Understanding
11. Mention the properties of a good estimator. BTL -1 Remembering
12. Define confidence coefficient. BTL -1 Remembering
13. What is the level of significance in testing of hypothesis BTL -6 Creating
14. Define confidence limits for a parameter BTL -1 Remembering
15.
State the conditions under which a binomial distribution becomes a
normal distribution
BTL -4 Analyzing
16.
If the random sample comes from a normal population, what can
be said about the sampling distribution of the mean.
BTL -5 Evaluating
17.
An automobile repair shop has taken a random sample of 40
services that the average service time on an automobile is 130
minutes with a standard deviation of 26 minutes. Compute the
standard error of the mean.
BTL -6 Creating
7
18. What is a random number? How it is useful in sampling? BTL -6 Creating
19.
A population has the numbers: 12, 8, 10, 30, 12, 16, 40, 5, 16, 24,
22, 31, 30, 16, 15. Draw a systematic sample of size 5. Find out its
mean.
BTL -3 Applying
20. How large sample is useful in estimation and testing BTL -4 Analyzing
PART -B
1(a).
A random sample of 700 units from a large consignment showed
that 200 were damaged. Find (i) 95% (ii) 99% confidence limits
for the proportion of damaged units in the consignment.
BTL -3 Applying
1(b).
A random sample of size 9 is obtained from a Normal population
with mean 25 and if the variance 100 find the probability that the
sample mean exceeds 31.2.
BTL -4 Analyzing
2(a).
In a normally distributed population, average income per
household is Rs.20,000 with a standard deviation of Rs. 1,600.
Find the probability that the sample mean will be between
Rs.19,600 and Rs.20,200 in a survey of a random sample of 100
households.
BTL -6 Creating
2(b).
A university wants to determine the percentage of students who
would accept proposed fees hike for improving facilities. The
university wants to be 90% confident that the percentage is
within2% of the true value. Find the sample size to achieve the
accuracy regardless of the true percentage assuming the percentage
of students accepting the increase in tuition fees to be 0.5.
BTL -6 Creating
3(a).
A bank has kept records of the checking balances of its customers
and determined that the average daily balances of its customers is
Rs.300 with a standard deviation of Rs. 48. A random sample of
144 checking accounts is selected.
(i) What is the probability that the sample mean will be more
than Rs. 306.60?
(ii) What is the probability that the sample mean will be less
than Rs. 308?
BTL -6 Creating
3(b).
From the question 3(a)
(i) What is probability that the sample mean will between Rs.
302 and Rs. 308?
(ii) What is probability that the sample mean will be atleast
Rs. 296?
BTL -6 Creating
4(a).
Explain Stratified sampling technique and discuss how it is better
than simple random sampling in a particular situation.
BTL -4
Analyzing
4(b). Discuss the standard error of proportion BTL-2 Understanding
5.
Explain the methods of drawing simple random sample from a
finite population.
BTL -4 Analyzing
8
6(a).
In a sample of 1000 citizens of India, 540 are wheat eaters and the
rest are rice eaters. Can we assume that both rice and wheat
equally popular in India at 1 % level of significance?
BTL-5
Evaluating
6(b).
A simple random sample of 144 items resulted in a sample mean
of 1257.85 and standard deviation of 480. Develop a 95%
confidence interval for the population mean
BTL -6
Creating
7(a).
A car dealer wants to estimate the proportion of customers who
still own the cars they purchased 5 years earlier. A random sample
of 500 customers selected from the dealer?s records indicate that
315 customers still own cars that they were purchased 5 years
earlier. Set up 95% confidence interval estimation of the
population proportion of all the customers who still own the cars 5
years after they were purchased.
BTL-2
Understanding
7(b).
A movie maker sampled 55 fans who viewed his master piece
movie and asked them whether they had planned to see it again.
Only 10 of them believed that the movie was worthy of a second
look. Find the standard error of the population of fans who will
view the film a second time. Construct a 90% confidence interval
for this population.
BTL -5 Evaluating
8(a).
From a population of size 600, a sample of 60 individuals revealed
mean and standard deviation as 6.2 and 1.45 respectively. (i) Find
the estimated standard error (ii) Construct 96% confidence
interval for the mean.
BTL -3 Applying
8(b).
The age of employees in a company follows normal distribution
with its mean and variance as 40 years and 121 years respectively.
If a random sample of 36 employees is taken from a finite normal
population of size 1000, what is the probability that the sample
mean is
(i) less than 45
(ii) greater than 42 and
(iii) between 40 and 42?
BTL -6
Creating
9(a).
A firm wishes to estimate with an error of not more than 0.03 and
a level of confidence of 98%, the proportion of consumers that
prefer its brand of household detergent. Sales report indicate the
about 0.20 of all consumers prefer the firm?s brand. What is the
requisite sample size?
BTL -5 Evaluating
9(b).
A random sample of 700 units from a large consignment should
that 200 were damaged.
Find (i) 95%
(ii) 99% confidence limits for the proportion of damaged
units in the consignment
BTL -3 Applying
10(a).
From a population of 500 items with a mean of 100 gms and
standard deviation of 12.5 gms, 65 items were chosen. (i) What is
the standard error? (ii) Find P(99.5 < X < 101.5).
BTL -6 Creating
10(b).
A non-normal distribution representing the number of trips
BTL -6 Creating
FirstRanker.com - FirstRanker's Choice
1
(An
Ka ttankulathur ?
DEPARTMENT OF MATHEMATICS
QUESTION BANK
I SEMESTER
1918108 ? STATISTICS FOR MANAGEMENT
Regulation ? 2019
Academic Year 2019 - 2020
Prepared by
Ms. B. Vasuki, Assistant Professor/Mathematics
Ms.B.Elakkiavani, Assistant Professor/Mathematics
2
(An
? .
DEPARTMENT OF MATHEMATICS
QUESTION BANK
SUBJECT : 1918108 ? STATISTICS FOR MANAGEMENT
SEM / YEAR : I Semester / I Year
UNIT I - INTRODUCTION
SYLLABUS: Basic definitions and rules for probability, conditional probability independence of events, Baye?s
theorem, and random variables, Probability distributions: Binomial, Poisson, Uniform and Normal distributions.
PART- A
S.NO QUESTIONS
BT Level
COMPETENCE
PART ? A
1. Define Statistics. BTL -6 Creating
2. What is the addition and multiplication theorem on probability. BTL -1 Remembering
3. Distinguish between a priori and posterior probability?. BTL -6 Creating
4.
The price of the selected stock over a five day period shown as 170, 110,
130, 170 and 160. Compute mean , median and mode.
BTL -6 Creating
5.
A car travels 25 miles at 25 mph, 25 miles at 50 mph and 25 miles at 75
mph. Find the harmonic of three velocities?
BTL -4 Analyse
6.
A ball is drawn at random from a box containg 6 red balls, 4 white balls
and 5 blue balls. Find the probability that the ball drawn is not red.
BTL -4 Analyse
7.
Find the median and mode for the weights (kgs) of 15 persons given as
68, 85, 70, 65, 71, 67, 65, 55, 80, 62, 65, 64, 70, 60, 56.
BTL -3 Applying
8. Name few measures of dispersion. BTL -1 Remembering
9. write the common measures of central tendency? BTL -1 Remembering
10. Define continuous and discrete variables examples. BTL -1 Remembering
11.
Let X be the lifetime in years of a mechanical part. Assume that X has
the cdf F(x) = 1- e
-x
, x ? 0. Find P[1< X ? 3].
BTL -1 Remembering
12. Define independent events. BTL -1 Remembering
13. State the theorem of total probability BTL -1 Remembering
14. What is the use of Baye?s theorem? BTL -6 Creating
15. Mention the properties of a discrete probability distribution. BTL -1 Remembering
16. Define a Poisson distribution and mention its mean and variance. BTL -1 Remembering
17. If the mean and variance of a binomial distribution are respectively 6 BTL -3 Applying
3
and 2.4, find P(x=2).
18.
If x is a Poisson distribution such that P(x=1)=4P(x=2). Find its
mean and variance.
BTL -3 Applying
19.
Suppose that X has a Poisson distribution with parameter ? = 2.
Compute P[X ? 1].
BTL -1 Remembering
20. Define mutually exclusive events. BTL -1 Remembering
PART-B
1(a).
Calculate the mean and standard deviation for the following table
giving the age distribution of 542 members.
Age
20-30 30-40 40-50 50-60 60-70 70-80 80-90
No 3 61 132 153 140 51 2
BTL-2 Understanding
1(b).
Find the geometric mean for the following data:
Group
2-4 4-6 6-8 8-10
Frequency 200 400 300 100
BTL-2
Understanding
2(a).
Find the mean, median and modal ages of married women at first
child birth
Age at the
birth of
first child
13
14
15
16
17
18
19
20
21
22
23
24
25
No of
married
women
37
162
343
390
256
433
161
355
65
85
49
46
40
BTL -6 Creating
2(b).
If A and B are independent event with P(A)=2/5, and P(B)=3/5,
find P(A ?B). Let S= {1,2,3,4,5,6} if A = {2,4,6} then find the
probability of A complement.
BTL -3 Applying
3(a).
Given: The probabilities of three events A, B and C occurring are
P(A) = 0.35, P(B) = 0.45 and P(C) = 0.2. Assuming that A, B, or
C has occurred, the probabilities of another event X occurring are
P(X/A) = 0.8, P(X/B) = 0.65 and P(X/C) = 0.3. Find P(A/X),
P(B/X) and P(C/X).
BTL -6 Creating
3(b).
4 cards are drawn from a well shuffled pack of cards. Find the
probability that
(i) All the four are queens
(ii) There is one card from each suit.
(iii) Two cards are diamonds and two are spades
All the four cards are hearts and one of them is jack
BTL -6 Creating
4(a).
Three machines all turn out non ferrous castings. Machine A
produces 1% defective and Machine B- 2% and machine C ? 5%.
Each machine produces 1/3 of the output. An inspector examines
a single casting, which he determines as non defective. Estimate
the probabilities of its having been produced by each machine.
BTL -6 Creating
4(b).
If the random variable X takes values 1, 2, 3, 4 such that
2P(X = 1) = 3P(X = 2) = P( X=3) = 5P(X = 4), find the
probability distribution and cumulative distribution of X.
BTL-2 Understanding
5(a).
Two dice are thrown together once. Find the probabilities for
BTL -3 Applying
4
getting the sum of the two numbers (i) equal to 5, (ii) multiple of
3, (iii) divisible by 4.
5(b).
Given ? = 4.2, for a poisson distribution. Find (a) P(X ? 2) (b)
P(X ? 5) (c) P(X = 8).
BTL -6 Creating
6(a).
An urn contains 5 balls. Two balls are drawn and found to be
white. What is the probability that all the balls are white?
BTL-1 Remembering
6(b).
The contents of urns I, II, III are as follows:
1 white, 2 black and 3 red balls;
2 white, 1 black and 1 red balls;
4 white, 5 black and 3 red balls;
One urn is chosen at random and two balls drawn. They happen to
be white and red. What is the probability that they come from
urns I, II, III?
BTL -3 Applying
7(a).
In 1989, there were three candidates for the position of principal
Mr. Chatterji, Mr. Ayangar and Dr. Singh. Whose chances of
getting the appointment are in the proportion 4:2:3 respectively.
The probability that Mr. Chatterji is selected, would introduce co-
education in the is 0.3. The probabilities of Mr. Ayangar
and Dr. Singh doing the same are respectively 0.5 and .08. What
is the probability that there was co-education in the in
1990?
BTL -3
Applying
7(b).
Find the probability that atmost 5 defective bolts will be found in
a box of 200 bolts, if it is known that 2% of such bolts are
expected to be defective. (e
-4
= 0.0183)
BTL -6 Creating
8(a).
A coin is tossed 6 times what is the probability of obtaining (a) 4
heads (b) 5 heads (c) 6 heads (d) getting 4 or more heads.
BTL -3 Applying
8(b).
In a bolt factory machines A, B, C manufacture respectively 25%,
35% and 40% of the total of their output 5, 4, 2 percent are
defective bolts. If A bolt is drawn at random from the product and
is found to be defective, what are the probabilities that is was
manufactured by machines A, B and C?
BTL -6 Creating
9(a).
In a test of 2000 electric blubs it was found that the life of a
particular make was normally distributed with an average life of
2040 hours and S. D. of 60 hours. Estimate the number of blubs
likely to burn for
(1) More than 2150 hours
(2) Less than 1950 hours
(3) More than 1920 hours but less than 2160 hours.
BTL -3 Applying
9(b).
The latest nationwide political poll indicates that for Americans
who are randomly selected, the probability that they are
conservative is 0.55, the probability that they are liberal is 0.30
and the probability that they are middle of the road is 0.15.
Assuming these probabilities are accurate, answer the following
BTL -4 Analyzing
5
questions from a randomly chosen group of 10 Americans
(a) What the probability that 4 are liberal?
(b) What the probability that none are conservative
(c) What the probability that two are middle of the road
(d) What the probability that a least 8 are liberal
10.
If X follows a normal distribution with mean 12 and variance 16
cm, find the probabilities for (i) X ? 20 (ii) X ? 20, and (iii) 0 ? X
? 12.
BTL -3 Applying
11.
A discerete random variable X has the probability function given
below:
Value of X=x: 0 1 2 3 4 5 6 7
P(X=x) : 0 k 2k 2k 3k k
2
2k
2
7k
2
+k
Find (1) The value of k
(2) P(1.5 < X < 4.5 / X > 2)
(3) P(X < 6), P(X ? 5), P( 0 < X < 4)
(4) The distribution of X.
BTL -3 Applying
12.
X is a normal variable with mean 30 and standard deviation of 5.
Find (i) P[26 ? X ? 40] (ii) P [X?45] (iii) P [ ?X - 30 ?> 5] use
normal distribution tables
BTL -4 Analyzing
13.
In an intelligence test administered on 1000 students, the average
was 42 and standard deviation 24, find (i) the number of students
exceeding a score 50. (ii) the number of students lying between
30 and 54(iii) the value of score exceeded by top 100 students.
BTL -4 Analyzing
14(a).
The probability that an entering student will graduate is 0.4
Determine the probability that out of 5 students atleast one will
graduate.
BTL-5
Evaluating
14(b).
Fit a Poisson Distribution to the following data which gives the
number of doddens in a sample of clover seeds
No 0 1 2 3 4 5 6 7 8
f 56 156 132 92 37 22 4 0 1
.
BTL -4 Analyzing
PART-C
1(a).
A disciplinary committee is formed from the staff of XYZ
Company which has three departments Marketing, Finance and
Production of the 10,5,20 members respectively. All departments
have two female staff each. A department is selected at random
and from which two matters are selected for the committee,
What is the probability that both the team members are female?
BTL-6 Creating
6
1(b).
In a bolt factory machines A, B, C manufacture respectively 25,
35 and 40 percent of the total. Of their output 5, 4 and 2 percent
are defective bolts respectively. A bolt is drawn at random from
the product and is found o be defective. What are the probabilities
that it was manufactured by machines A, B or C?
BTL-2
Understanding
2(a). State Bayes theorem and brief about its applications. BTL-2 Understanding
2(b).
Out of 800 families with 4 children each, how many families
would be expected to have (i) 2 boys and 2 girls (ii) at least 1 boy
(iii) at most 2 girls (iv) children of both sexes? Assume equal
probabilities for boys and girls.
BTL-1 Remembering
3. Describe the classifications of probability ? BTL-1 Remembering
4. What are the applications of Normal distribution in statistics? BTL-6 Creating
UNIT ?II- SAMPLING DISTRIBUTION & ESTIMATION.
SYLLABUS: Introduction to sampling distributions, sampling distribution of mean and proportion, application of central
limit theorem, sampling techniques. Estimation: Point and Interval estimates for population parameters of large sample and
small samples, determining the sample size.
PART - A
S.N
O
QUESTIONS
BT Level
COMPETENCE
1. Define Sampling distribution of proportion. BTL -1 Remembering
2. Define Probable standard error. BTL -1 Remembering
3. Define standard error and mention its importance BTL -1 Remembering
4. Define central limit theorem BTL -1 Remembering
5.
What is the role of central limit theorem in estimation and testing
problems
BTL -6 Creating
6. Define stratified sampling technique BTL -1 Remembering
7. Briefly describe the significance level. BTL -1 Remembering
8. Distinguish between parameter and statistic. BTL -2 Understanding
9. Define estimator, estimate and estimation. BTL -1 Remembering
10. Distinguish between point estimation and interval estimation BTL -2 Understanding
11. Mention the properties of a good estimator. BTL -1 Remembering
12. Define confidence coefficient. BTL -1 Remembering
13. What is the level of significance in testing of hypothesis BTL -6 Creating
14. Define confidence limits for a parameter BTL -1 Remembering
15.
State the conditions under which a binomial distribution becomes a
normal distribution
BTL -4 Analyzing
16.
If the random sample comes from a normal population, what can
be said about the sampling distribution of the mean.
BTL -5 Evaluating
17.
An automobile repair shop has taken a random sample of 40
services that the average service time on an automobile is 130
minutes with a standard deviation of 26 minutes. Compute the
standard error of the mean.
BTL -6 Creating
7
18. What is a random number? How it is useful in sampling? BTL -6 Creating
19.
A population has the numbers: 12, 8, 10, 30, 12, 16, 40, 5, 16, 24,
22, 31, 30, 16, 15. Draw a systematic sample of size 5. Find out its
mean.
BTL -3 Applying
20. How large sample is useful in estimation and testing BTL -4 Analyzing
PART -B
1(a).
A random sample of 700 units from a large consignment showed
that 200 were damaged. Find (i) 95% (ii) 99% confidence limits
for the proportion of damaged units in the consignment.
BTL -3 Applying
1(b).
A random sample of size 9 is obtained from a Normal population
with mean 25 and if the variance 100 find the probability that the
sample mean exceeds 31.2.
BTL -4 Analyzing
2(a).
In a normally distributed population, average income per
household is Rs.20,000 with a standard deviation of Rs. 1,600.
Find the probability that the sample mean will be between
Rs.19,600 and Rs.20,200 in a survey of a random sample of 100
households.
BTL -6 Creating
2(b).
A university wants to determine the percentage of students who
would accept proposed fees hike for improving facilities. The
university wants to be 90% confident that the percentage is
within2% of the true value. Find the sample size to achieve the
accuracy regardless of the true percentage assuming the percentage
of students accepting the increase in tuition fees to be 0.5.
BTL -6 Creating
3(a).
A bank has kept records of the checking balances of its customers
and determined that the average daily balances of its customers is
Rs.300 with a standard deviation of Rs. 48. A random sample of
144 checking accounts is selected.
(i) What is the probability that the sample mean will be more
than Rs. 306.60?
(ii) What is the probability that the sample mean will be less
than Rs. 308?
BTL -6 Creating
3(b).
From the question 3(a)
(i) What is probability that the sample mean will between Rs.
302 and Rs. 308?
(ii) What is probability that the sample mean will be atleast
Rs. 296?
BTL -6 Creating
4(a).
Explain Stratified sampling technique and discuss how it is better
than simple random sampling in a particular situation.
BTL -4
Analyzing
4(b). Discuss the standard error of proportion BTL-2 Understanding
5.
Explain the methods of drawing simple random sample from a
finite population.
BTL -4 Analyzing
8
6(a).
In a sample of 1000 citizens of India, 540 are wheat eaters and the
rest are rice eaters. Can we assume that both rice and wheat
equally popular in India at 1 % level of significance?
BTL-5
Evaluating
6(b).
A simple random sample of 144 items resulted in a sample mean
of 1257.85 and standard deviation of 480. Develop a 95%
confidence interval for the population mean
BTL -6
Creating
7(a).
A car dealer wants to estimate the proportion of customers who
still own the cars they purchased 5 years earlier. A random sample
of 500 customers selected from the dealer?s records indicate that
315 customers still own cars that they were purchased 5 years
earlier. Set up 95% confidence interval estimation of the
population proportion of all the customers who still own the cars 5
years after they were purchased.
BTL-2
Understanding
7(b).
A movie maker sampled 55 fans who viewed his master piece
movie and asked them whether they had planned to see it again.
Only 10 of them believed that the movie was worthy of a second
look. Find the standard error of the population of fans who will
view the film a second time. Construct a 90% confidence interval
for this population.
BTL -5 Evaluating
8(a).
From a population of size 600, a sample of 60 individuals revealed
mean and standard deviation as 6.2 and 1.45 respectively. (i) Find
the estimated standard error (ii) Construct 96% confidence
interval for the mean.
BTL -3 Applying
8(b).
The age of employees in a company follows normal distribution
with its mean and variance as 40 years and 121 years respectively.
If a random sample of 36 employees is taken from a finite normal
population of size 1000, what is the probability that the sample
mean is
(i) less than 45
(ii) greater than 42 and
(iii) between 40 and 42?
BTL -6
Creating
9(a).
A firm wishes to estimate with an error of not more than 0.03 and
a level of confidence of 98%, the proportion of consumers that
prefer its brand of household detergent. Sales report indicate the
about 0.20 of all consumers prefer the firm?s brand. What is the
requisite sample size?
BTL -5 Evaluating
9(b).
A random sample of 700 units from a large consignment should
that 200 were damaged.
Find (i) 95%
(ii) 99% confidence limits for the proportion of damaged
units in the consignment
BTL -3 Applying
10(a).
From a population of 500 items with a mean of 100 gms and
standard deviation of 12.5 gms, 65 items were chosen. (i) What is
the standard error? (ii) Find P(99.5 < X < 101.5).
BTL -6 Creating
10(b).
A non-normal distribution representing the number of trips
BTL -6 Creating
9
performed by lorries per week in a coal field has a mean of 100
trips and variance of 121 trips. A random sample of 36 lorries is
taken from the non-normal population. What is the probability that
the sample mean is
(i) greater than 105
(ii) less than 102
(iii) between 101 and 103 trips?
11.
Test the significance of the difference between the means of the
sample from the following data
Size of sample Mean SD
Sample A 100 61 4
Sample B 200 63 6
BTL -4 Analyzing
12(a).
A cigarete manufacturing firm claims that its brand. A outsells
brand B by 8%. If it is found that 42 out of a sample of 200
smokers prefer brand a and 18 out of another sample of 100
smokers prefer brand B, test whether the 8% difference is a valid
claim(use 5% level of significance).
BTL -4
Analyzing
12(b).
In an automotive safety test conducted by the North Carolina
Highway Safety Research center, the average tyre pressure in a
sample of 62 tyres was found to be 24 pounds per square inch, and
the standard deviation was 2.1 pounds per square inch.
(i) What is the estimated population standard deviation for this
population
(ii) Calculate the estimated standard error of the mean
(iii) Construct a 95% confidence interval for the population mean.
BTL -3 Applying
13(a).
The manager of a shop selling beverages wants to estimate the
actual amount of beverages in one litre bottles from a nationally
known manufacturer. As per manufacturer?s specifications, the
standard deviation of the volume of the beverage is 0.02 litre. The
average amount of beverage per 1 litre bottle is found to be 0.995
litre on checking 50 bottles. Setup 99% confidence interval
estimate of the true population average amount of beverage in a 1
liter bottle. Check whether the manufacturer is genuine in filling
the beverage.
BTL -6
Creating
13(b).
In a batch chemical process used for etching printed circuit boards,
two different catalysts are being compared to determine whether
they require different emersion times for removal of identical
quantities of photo resist material. Twelve batch were run with
catalyst 1, resulting in a sample mean emersion time of 24.6
minutes and sample standard deviation of 0.85 minutes. Fifteen
batches were run with catalyst 2, resulting in a mean emersion time
of 22.1 minutes and a standard deviation of 0.98 minutes. Find a
95% confidence interval on the difference in means, assuming that
2
2
2
1
? ? ? .
BTL -3 Applying
FirstRanker.com - FirstRanker's Choice
1
(An
Ka ttankulathur ?
DEPARTMENT OF MATHEMATICS
QUESTION BANK
I SEMESTER
1918108 ? STATISTICS FOR MANAGEMENT
Regulation ? 2019
Academic Year 2019 - 2020
Prepared by
Ms. B. Vasuki, Assistant Professor/Mathematics
Ms.B.Elakkiavani, Assistant Professor/Mathematics
2
(An
? .
DEPARTMENT OF MATHEMATICS
QUESTION BANK
SUBJECT : 1918108 ? STATISTICS FOR MANAGEMENT
SEM / YEAR : I Semester / I Year
UNIT I - INTRODUCTION
SYLLABUS: Basic definitions and rules for probability, conditional probability independence of events, Baye?s
theorem, and random variables, Probability distributions: Binomial, Poisson, Uniform and Normal distributions.
PART- A
S.NO QUESTIONS
BT Level
COMPETENCE
PART ? A
1. Define Statistics. BTL -6 Creating
2. What is the addition and multiplication theorem on probability. BTL -1 Remembering
3. Distinguish between a priori and posterior probability?. BTL -6 Creating
4.
The price of the selected stock over a five day period shown as 170, 110,
130, 170 and 160. Compute mean , median and mode.
BTL -6 Creating
5.
A car travels 25 miles at 25 mph, 25 miles at 50 mph and 25 miles at 75
mph. Find the harmonic of three velocities?
BTL -4 Analyse
6.
A ball is drawn at random from a box containg 6 red balls, 4 white balls
and 5 blue balls. Find the probability that the ball drawn is not red.
BTL -4 Analyse
7.
Find the median and mode for the weights (kgs) of 15 persons given as
68, 85, 70, 65, 71, 67, 65, 55, 80, 62, 65, 64, 70, 60, 56.
BTL -3 Applying
8. Name few measures of dispersion. BTL -1 Remembering
9. write the common measures of central tendency? BTL -1 Remembering
10. Define continuous and discrete variables examples. BTL -1 Remembering
11.
Let X be the lifetime in years of a mechanical part. Assume that X has
the cdf F(x) = 1- e
-x
, x ? 0. Find P[1< X ? 3].
BTL -1 Remembering
12. Define independent events. BTL -1 Remembering
13. State the theorem of total probability BTL -1 Remembering
14. What is the use of Baye?s theorem? BTL -6 Creating
15. Mention the properties of a discrete probability distribution. BTL -1 Remembering
16. Define a Poisson distribution and mention its mean and variance. BTL -1 Remembering
17. If the mean and variance of a binomial distribution are respectively 6 BTL -3 Applying
3
and 2.4, find P(x=2).
18.
If x is a Poisson distribution such that P(x=1)=4P(x=2). Find its
mean and variance.
BTL -3 Applying
19.
Suppose that X has a Poisson distribution with parameter ? = 2.
Compute P[X ? 1].
BTL -1 Remembering
20. Define mutually exclusive events. BTL -1 Remembering
PART-B
1(a).
Calculate the mean and standard deviation for the following table
giving the age distribution of 542 members.
Age
20-30 30-40 40-50 50-60 60-70 70-80 80-90
No 3 61 132 153 140 51 2
BTL-2 Understanding
1(b).
Find the geometric mean for the following data:
Group
2-4 4-6 6-8 8-10
Frequency 200 400 300 100
BTL-2
Understanding
2(a).
Find the mean, median and modal ages of married women at first
child birth
Age at the
birth of
first child
13
14
15
16
17
18
19
20
21
22
23
24
25
No of
married
women
37
162
343
390
256
433
161
355
65
85
49
46
40
BTL -6 Creating
2(b).
If A and B are independent event with P(A)=2/5, and P(B)=3/5,
find P(A ?B). Let S= {1,2,3,4,5,6} if A = {2,4,6} then find the
probability of A complement.
BTL -3 Applying
3(a).
Given: The probabilities of three events A, B and C occurring are
P(A) = 0.35, P(B) = 0.45 and P(C) = 0.2. Assuming that A, B, or
C has occurred, the probabilities of another event X occurring are
P(X/A) = 0.8, P(X/B) = 0.65 and P(X/C) = 0.3. Find P(A/X),
P(B/X) and P(C/X).
BTL -6 Creating
3(b).
4 cards are drawn from a well shuffled pack of cards. Find the
probability that
(i) All the four are queens
(ii) There is one card from each suit.
(iii) Two cards are diamonds and two are spades
All the four cards are hearts and one of them is jack
BTL -6 Creating
4(a).
Three machines all turn out non ferrous castings. Machine A
produces 1% defective and Machine B- 2% and machine C ? 5%.
Each machine produces 1/3 of the output. An inspector examines
a single casting, which he determines as non defective. Estimate
the probabilities of its having been produced by each machine.
BTL -6 Creating
4(b).
If the random variable X takes values 1, 2, 3, 4 such that
2P(X = 1) = 3P(X = 2) = P( X=3) = 5P(X = 4), find the
probability distribution and cumulative distribution of X.
BTL-2 Understanding
5(a).
Two dice are thrown together once. Find the probabilities for
BTL -3 Applying
4
getting the sum of the two numbers (i) equal to 5, (ii) multiple of
3, (iii) divisible by 4.
5(b).
Given ? = 4.2, for a poisson distribution. Find (a) P(X ? 2) (b)
P(X ? 5) (c) P(X = 8).
BTL -6 Creating
6(a).
An urn contains 5 balls. Two balls are drawn and found to be
white. What is the probability that all the balls are white?
BTL-1 Remembering
6(b).
The contents of urns I, II, III are as follows:
1 white, 2 black and 3 red balls;
2 white, 1 black and 1 red balls;
4 white, 5 black and 3 red balls;
One urn is chosen at random and two balls drawn. They happen to
be white and red. What is the probability that they come from
urns I, II, III?
BTL -3 Applying
7(a).
In 1989, there were three candidates for the position of principal
Mr. Chatterji, Mr. Ayangar and Dr. Singh. Whose chances of
getting the appointment are in the proportion 4:2:3 respectively.
The probability that Mr. Chatterji is selected, would introduce co-
education in the is 0.3. The probabilities of Mr. Ayangar
and Dr. Singh doing the same are respectively 0.5 and .08. What
is the probability that there was co-education in the in
1990?
BTL -3
Applying
7(b).
Find the probability that atmost 5 defective bolts will be found in
a box of 200 bolts, if it is known that 2% of such bolts are
expected to be defective. (e
-4
= 0.0183)
BTL -6 Creating
8(a).
A coin is tossed 6 times what is the probability of obtaining (a) 4
heads (b) 5 heads (c) 6 heads (d) getting 4 or more heads.
BTL -3 Applying
8(b).
In a bolt factory machines A, B, C manufacture respectively 25%,
35% and 40% of the total of their output 5, 4, 2 percent are
defective bolts. If A bolt is drawn at random from the product and
is found to be defective, what are the probabilities that is was
manufactured by machines A, B and C?
BTL -6 Creating
9(a).
In a test of 2000 electric blubs it was found that the life of a
particular make was normally distributed with an average life of
2040 hours and S. D. of 60 hours. Estimate the number of blubs
likely to burn for
(1) More than 2150 hours
(2) Less than 1950 hours
(3) More than 1920 hours but less than 2160 hours.
BTL -3 Applying
9(b).
The latest nationwide political poll indicates that for Americans
who are randomly selected, the probability that they are
conservative is 0.55, the probability that they are liberal is 0.30
and the probability that they are middle of the road is 0.15.
Assuming these probabilities are accurate, answer the following
BTL -4 Analyzing
5
questions from a randomly chosen group of 10 Americans
(a) What the probability that 4 are liberal?
(b) What the probability that none are conservative
(c) What the probability that two are middle of the road
(d) What the probability that a least 8 are liberal
10.
If X follows a normal distribution with mean 12 and variance 16
cm, find the probabilities for (i) X ? 20 (ii) X ? 20, and (iii) 0 ? X
? 12.
BTL -3 Applying
11.
A discerete random variable X has the probability function given
below:
Value of X=x: 0 1 2 3 4 5 6 7
P(X=x) : 0 k 2k 2k 3k k
2
2k
2
7k
2
+k
Find (1) The value of k
(2) P(1.5 < X < 4.5 / X > 2)
(3) P(X < 6), P(X ? 5), P( 0 < X < 4)
(4) The distribution of X.
BTL -3 Applying
12.
X is a normal variable with mean 30 and standard deviation of 5.
Find (i) P[26 ? X ? 40] (ii) P [X?45] (iii) P [ ?X - 30 ?> 5] use
normal distribution tables
BTL -4 Analyzing
13.
In an intelligence test administered on 1000 students, the average
was 42 and standard deviation 24, find (i) the number of students
exceeding a score 50. (ii) the number of students lying between
30 and 54(iii) the value of score exceeded by top 100 students.
BTL -4 Analyzing
14(a).
The probability that an entering student will graduate is 0.4
Determine the probability that out of 5 students atleast one will
graduate.
BTL-5
Evaluating
14(b).
Fit a Poisson Distribution to the following data which gives the
number of doddens in a sample of clover seeds
No 0 1 2 3 4 5 6 7 8
f 56 156 132 92 37 22 4 0 1
.
BTL -4 Analyzing
PART-C
1(a).
A disciplinary committee is formed from the staff of XYZ
Company which has three departments Marketing, Finance and
Production of the 10,5,20 members respectively. All departments
have two female staff each. A department is selected at random
and from which two matters are selected for the committee,
What is the probability that both the team members are female?
BTL-6 Creating
6
1(b).
In a bolt factory machines A, B, C manufacture respectively 25,
35 and 40 percent of the total. Of their output 5, 4 and 2 percent
are defective bolts respectively. A bolt is drawn at random from
the product and is found o be defective. What are the probabilities
that it was manufactured by machines A, B or C?
BTL-2
Understanding
2(a). State Bayes theorem and brief about its applications. BTL-2 Understanding
2(b).
Out of 800 families with 4 children each, how many families
would be expected to have (i) 2 boys and 2 girls (ii) at least 1 boy
(iii) at most 2 girls (iv) children of both sexes? Assume equal
probabilities for boys and girls.
BTL-1 Remembering
3. Describe the classifications of probability ? BTL-1 Remembering
4. What are the applications of Normal distribution in statistics? BTL-6 Creating
UNIT ?II- SAMPLING DISTRIBUTION & ESTIMATION.
SYLLABUS: Introduction to sampling distributions, sampling distribution of mean and proportion, application of central
limit theorem, sampling techniques. Estimation: Point and Interval estimates for population parameters of large sample and
small samples, determining the sample size.
PART - A
S.N
O
QUESTIONS
BT Level
COMPETENCE
1. Define Sampling distribution of proportion. BTL -1 Remembering
2. Define Probable standard error. BTL -1 Remembering
3. Define standard error and mention its importance BTL -1 Remembering
4. Define central limit theorem BTL -1 Remembering
5.
What is the role of central limit theorem in estimation and testing
problems
BTL -6 Creating
6. Define stratified sampling technique BTL -1 Remembering
7. Briefly describe the significance level. BTL -1 Remembering
8. Distinguish between parameter and statistic. BTL -2 Understanding
9. Define estimator, estimate and estimation. BTL -1 Remembering
10. Distinguish between point estimation and interval estimation BTL -2 Understanding
11. Mention the properties of a good estimator. BTL -1 Remembering
12. Define confidence coefficient. BTL -1 Remembering
13. What is the level of significance in testing of hypothesis BTL -6 Creating
14. Define confidence limits for a parameter BTL -1 Remembering
15.
State the conditions under which a binomial distribution becomes a
normal distribution
BTL -4 Analyzing
16.
If the random sample comes from a normal population, what can
be said about the sampling distribution of the mean.
BTL -5 Evaluating
17.
An automobile repair shop has taken a random sample of 40
services that the average service time on an automobile is 130
minutes with a standard deviation of 26 minutes. Compute the
standard error of the mean.
BTL -6 Creating
7
18. What is a random number? How it is useful in sampling? BTL -6 Creating
19.
A population has the numbers: 12, 8, 10, 30, 12, 16, 40, 5, 16, 24,
22, 31, 30, 16, 15. Draw a systematic sample of size 5. Find out its
mean.
BTL -3 Applying
20. How large sample is useful in estimation and testing BTL -4 Analyzing
PART -B
1(a).
A random sample of 700 units from a large consignment showed
that 200 were damaged. Find (i) 95% (ii) 99% confidence limits
for the proportion of damaged units in the consignment.
BTL -3 Applying
1(b).
A random sample of size 9 is obtained from a Normal population
with mean 25 and if the variance 100 find the probability that the
sample mean exceeds 31.2.
BTL -4 Analyzing
2(a).
In a normally distributed population, average income per
household is Rs.20,000 with a standard deviation of Rs. 1,600.
Find the probability that the sample mean will be between
Rs.19,600 and Rs.20,200 in a survey of a random sample of 100
households.
BTL -6 Creating
2(b).
A university wants to determine the percentage of students who
would accept proposed fees hike for improving facilities. The
university wants to be 90% confident that the percentage is
within2% of the true value. Find the sample size to achieve the
accuracy regardless of the true percentage assuming the percentage
of students accepting the increase in tuition fees to be 0.5.
BTL -6 Creating
3(a).
A bank has kept records of the checking balances of its customers
and determined that the average daily balances of its customers is
Rs.300 with a standard deviation of Rs. 48. A random sample of
144 checking accounts is selected.
(i) What is the probability that the sample mean will be more
than Rs. 306.60?
(ii) What is the probability that the sample mean will be less
than Rs. 308?
BTL -6 Creating
3(b).
From the question 3(a)
(i) What is probability that the sample mean will between Rs.
302 and Rs. 308?
(ii) What is probability that the sample mean will be atleast
Rs. 296?
BTL -6 Creating
4(a).
Explain Stratified sampling technique and discuss how it is better
than simple random sampling in a particular situation.
BTL -4
Analyzing
4(b). Discuss the standard error of proportion BTL-2 Understanding
5.
Explain the methods of drawing simple random sample from a
finite population.
BTL -4 Analyzing
8
6(a).
In a sample of 1000 citizens of India, 540 are wheat eaters and the
rest are rice eaters. Can we assume that both rice and wheat
equally popular in India at 1 % level of significance?
BTL-5
Evaluating
6(b).
A simple random sample of 144 items resulted in a sample mean
of 1257.85 and standard deviation of 480. Develop a 95%
confidence interval for the population mean
BTL -6
Creating
7(a).
A car dealer wants to estimate the proportion of customers who
still own the cars they purchased 5 years earlier. A random sample
of 500 customers selected from the dealer?s records indicate that
315 customers still own cars that they were purchased 5 years
earlier. Set up 95% confidence interval estimation of the
population proportion of all the customers who still own the cars 5
years after they were purchased.
BTL-2
Understanding
7(b).
A movie maker sampled 55 fans who viewed his master piece
movie and asked them whether they had planned to see it again.
Only 10 of them believed that the movie was worthy of a second
look. Find the standard error of the population of fans who will
view the film a second time. Construct a 90% confidence interval
for this population.
BTL -5 Evaluating
8(a).
From a population of size 600, a sample of 60 individuals revealed
mean and standard deviation as 6.2 and 1.45 respectively. (i) Find
the estimated standard error (ii) Construct 96% confidence
interval for the mean.
BTL -3 Applying
8(b).
The age of employees in a company follows normal distribution
with its mean and variance as 40 years and 121 years respectively.
If a random sample of 36 employees is taken from a finite normal
population of size 1000, what is the probability that the sample
mean is
(i) less than 45
(ii) greater than 42 and
(iii) between 40 and 42?
BTL -6
Creating
9(a).
A firm wishes to estimate with an error of not more than 0.03 and
a level of confidence of 98%, the proportion of consumers that
prefer its brand of household detergent. Sales report indicate the
about 0.20 of all consumers prefer the firm?s brand. What is the
requisite sample size?
BTL -5 Evaluating
9(b).
A random sample of 700 units from a large consignment should
that 200 were damaged.
Find (i) 95%
(ii) 99% confidence limits for the proportion of damaged
units in the consignment
BTL -3 Applying
10(a).
From a population of 500 items with a mean of 100 gms and
standard deviation of 12.5 gms, 65 items were chosen. (i) What is
the standard error? (ii) Find P(99.5 < X < 101.5).
BTL -6 Creating
10(b).
A non-normal distribution representing the number of trips
BTL -6 Creating
9
performed by lorries per week in a coal field has a mean of 100
trips and variance of 121 trips. A random sample of 36 lorries is
taken from the non-normal population. What is the probability that
the sample mean is
(i) greater than 105
(ii) less than 102
(iii) between 101 and 103 trips?
11.
Test the significance of the difference between the means of the
sample from the following data
Size of sample Mean SD
Sample A 100 61 4
Sample B 200 63 6
BTL -4 Analyzing
12(a).
A cigarete manufacturing firm claims that its brand. A outsells
brand B by 8%. If it is found that 42 out of a sample of 200
smokers prefer brand a and 18 out of another sample of 100
smokers prefer brand B, test whether the 8% difference is a valid
claim(use 5% level of significance).
BTL -4
Analyzing
12(b).
In an automotive safety test conducted by the North Carolina
Highway Safety Research center, the average tyre pressure in a
sample of 62 tyres was found to be 24 pounds per square inch, and
the standard deviation was 2.1 pounds per square inch.
(i) What is the estimated population standard deviation for this
population
(ii) Calculate the estimated standard error of the mean
(iii) Construct a 95% confidence interval for the population mean.
BTL -3 Applying
13(a).
The manager of a shop selling beverages wants to estimate the
actual amount of beverages in one litre bottles from a nationally
known manufacturer. As per manufacturer?s specifications, the
standard deviation of the volume of the beverage is 0.02 litre. The
average amount of beverage per 1 litre bottle is found to be 0.995
litre on checking 50 bottles. Setup 99% confidence interval
estimate of the true population average amount of beverage in a 1
liter bottle. Check whether the manufacturer is genuine in filling
the beverage.
BTL -6
Creating
13(b).
In a batch chemical process used for etching printed circuit boards,
two different catalysts are being compared to determine whether
they require different emersion times for removal of identical
quantities of photo resist material. Twelve batch were run with
catalyst 1, resulting in a sample mean emersion time of 24.6
minutes and sample standard deviation of 0.85 minutes. Fifteen
batches were run with catalyst 2, resulting in a mean emersion time
of 22.1 minutes and a standard deviation of 0.98 minutes. Find a
95% confidence interval on the difference in means, assuming that
2
2
2
1
? ? ? .
BTL -3 Applying
10
14.
In a random sample of 75 axle shafts. 12 have a surface finish that
is rougher than the specifications will allow. Suppose that a
modification is made in the surface finishing process and
subsequently a second random sample of 85 axle shafts is
obtained. The number of defective shafts in this second sample is
10. Obtain an approximate 95% confidence interval on the
difference in the proportions of defectives produced under the two
processes
BTL -5 Evaluating
PART-C
1.
In a sample of 25 observations from a Normal distribution with
mean 98.6 and standard deviation 17.2.
(i)What is P(92<102)
(ii)Find the corresponding probability given a sample of 36.
BTL -6 Creating
2.
Mary, an auditor for a large credit card company, knows that, on
average, the monthly balance of any customer is Rs.112, and the
standard deviation is Rs.56. If Mary audits 50 randomly selected
accounts, What is the probability that the sample average balance
is
(i) Below Rs. 100
(ii)Between Rs.100 and Rs.130
BTL -6 Creating
3(a).
Write the type of sampling methods and the uses of standard error?
BTL -1 Remembering
3(b).
From a population of 540, a sample of 60 individual is taken. From
this sample, the mean is found to 6.2 and the standard deviation
1.368
(i) Find the estimated standard error of the mean.
(ii) Construct a 96 % confidence interval for the mean.
BTL-2 Understanding
4(a).
Explain the properties of good point estimator.
BTL -4 Analyzing
4(b).
What do you mean by interval estimation? Give examples
BTL-6 Creating
UNIT III - TESTS OF HYPOTHESIS- PARAMETRIC TESTS
SYLLABUS: Hypothesis testing: one sample and two sample tests for means and proportions of large samples (z-test),
one sample and two sample tests for means of small samples (t-test), F-test for two sample standard deviations. ANOVA
one and two way.
PART-A
Q.
No.
Question
Bloom?s
Taxonomy
Level
Domain
1. Define Test of Significance. BTL-1 Remembering
2. What are the Type I and Type II errors? BTL-6 Creating
3. What do you mean by one tail test? BTL-6 Creating
4. State the applications of Z-test and t-test. BTL-4 Analyzing
5. Define critical region BTL-1 Remembering
6. Distinguish between one tail and two tail tests BTL-2 Understanding
7. What is the aim of design of experiments? BTL-6 Creating
8. Distinguish between one-way and two-way analysis of variance. BTL-2 Understanding
9. When does the Z-test apply? BTL-1 Remembering
10. Explain SSB , SSW and SSY
and relationship in ANOVA. BTL-4 Analyzing
FirstRanker.com - FirstRanker's Choice
1
(An
Ka ttankulathur ?
DEPARTMENT OF MATHEMATICS
QUESTION BANK
I SEMESTER
1918108 ? STATISTICS FOR MANAGEMENT
Regulation ? 2019
Academic Year 2019 - 2020
Prepared by
Ms. B. Vasuki, Assistant Professor/Mathematics
Ms.B.Elakkiavani, Assistant Professor/Mathematics
2
(An
? .
DEPARTMENT OF MATHEMATICS
QUESTION BANK
SUBJECT : 1918108 ? STATISTICS FOR MANAGEMENT
SEM / YEAR : I Semester / I Year
UNIT I - INTRODUCTION
SYLLABUS: Basic definitions and rules for probability, conditional probability independence of events, Baye?s
theorem, and random variables, Probability distributions: Binomial, Poisson, Uniform and Normal distributions.
PART- A
S.NO QUESTIONS
BT Level
COMPETENCE
PART ? A
1. Define Statistics. BTL -6 Creating
2. What is the addition and multiplication theorem on probability. BTL -1 Remembering
3. Distinguish between a priori and posterior probability?. BTL -6 Creating
4.
The price of the selected stock over a five day period shown as 170, 110,
130, 170 and 160. Compute mean , median and mode.
BTL -6 Creating
5.
A car travels 25 miles at 25 mph, 25 miles at 50 mph and 25 miles at 75
mph. Find the harmonic of three velocities?
BTL -4 Analyse
6.
A ball is drawn at random from a box containg 6 red balls, 4 white balls
and 5 blue balls. Find the probability that the ball drawn is not red.
BTL -4 Analyse
7.
Find the median and mode for the weights (kgs) of 15 persons given as
68, 85, 70, 65, 71, 67, 65, 55, 80, 62, 65, 64, 70, 60, 56.
BTL -3 Applying
8. Name few measures of dispersion. BTL -1 Remembering
9. write the common measures of central tendency? BTL -1 Remembering
10. Define continuous and discrete variables examples. BTL -1 Remembering
11.
Let X be the lifetime in years of a mechanical part. Assume that X has
the cdf F(x) = 1- e
-x
, x ? 0. Find P[1< X ? 3].
BTL -1 Remembering
12. Define independent events. BTL -1 Remembering
13. State the theorem of total probability BTL -1 Remembering
14. What is the use of Baye?s theorem? BTL -6 Creating
15. Mention the properties of a discrete probability distribution. BTL -1 Remembering
16. Define a Poisson distribution and mention its mean and variance. BTL -1 Remembering
17. If the mean and variance of a binomial distribution are respectively 6 BTL -3 Applying
3
and 2.4, find P(x=2).
18.
If x is a Poisson distribution such that P(x=1)=4P(x=2). Find its
mean and variance.
BTL -3 Applying
19.
Suppose that X has a Poisson distribution with parameter ? = 2.
Compute P[X ? 1].
BTL -1 Remembering
20. Define mutually exclusive events. BTL -1 Remembering
PART-B
1(a).
Calculate the mean and standard deviation for the following table
giving the age distribution of 542 members.
Age
20-30 30-40 40-50 50-60 60-70 70-80 80-90
No 3 61 132 153 140 51 2
BTL-2 Understanding
1(b).
Find the geometric mean for the following data:
Group
2-4 4-6 6-8 8-10
Frequency 200 400 300 100
BTL-2
Understanding
2(a).
Find the mean, median and modal ages of married women at first
child birth
Age at the
birth of
first child
13
14
15
16
17
18
19
20
21
22
23
24
25
No of
married
women
37
162
343
390
256
433
161
355
65
85
49
46
40
BTL -6 Creating
2(b).
If A and B are independent event with P(A)=2/5, and P(B)=3/5,
find P(A ?B). Let S= {1,2,3,4,5,6} if A = {2,4,6} then find the
probability of A complement.
BTL -3 Applying
3(a).
Given: The probabilities of three events A, B and C occurring are
P(A) = 0.35, P(B) = 0.45 and P(C) = 0.2. Assuming that A, B, or
C has occurred, the probabilities of another event X occurring are
P(X/A) = 0.8, P(X/B) = 0.65 and P(X/C) = 0.3. Find P(A/X),
P(B/X) and P(C/X).
BTL -6 Creating
3(b).
4 cards are drawn from a well shuffled pack of cards. Find the
probability that
(i) All the four are queens
(ii) There is one card from each suit.
(iii) Two cards are diamonds and two are spades
All the four cards are hearts and one of them is jack
BTL -6 Creating
4(a).
Three machines all turn out non ferrous castings. Machine A
produces 1% defective and Machine B- 2% and machine C ? 5%.
Each machine produces 1/3 of the output. An inspector examines
a single casting, which he determines as non defective. Estimate
the probabilities of its having been produced by each machine.
BTL -6 Creating
4(b).
If the random variable X takes values 1, 2, 3, 4 such that
2P(X = 1) = 3P(X = 2) = P( X=3) = 5P(X = 4), find the
probability distribution and cumulative distribution of X.
BTL-2 Understanding
5(a).
Two dice are thrown together once. Find the probabilities for
BTL -3 Applying
4
getting the sum of the two numbers (i) equal to 5, (ii) multiple of
3, (iii) divisible by 4.
5(b).
Given ? = 4.2, for a poisson distribution. Find (a) P(X ? 2) (b)
P(X ? 5) (c) P(X = 8).
BTL -6 Creating
6(a).
An urn contains 5 balls. Two balls are drawn and found to be
white. What is the probability that all the balls are white?
BTL-1 Remembering
6(b).
The contents of urns I, II, III are as follows:
1 white, 2 black and 3 red balls;
2 white, 1 black and 1 red balls;
4 white, 5 black and 3 red balls;
One urn is chosen at random and two balls drawn. They happen to
be white and red. What is the probability that they come from
urns I, II, III?
BTL -3 Applying
7(a).
In 1989, there were three candidates for the position of principal
Mr. Chatterji, Mr. Ayangar and Dr. Singh. Whose chances of
getting the appointment are in the proportion 4:2:3 respectively.
The probability that Mr. Chatterji is selected, would introduce co-
education in the is 0.3. The probabilities of Mr. Ayangar
and Dr. Singh doing the same are respectively 0.5 and .08. What
is the probability that there was co-education in the in
1990?
BTL -3
Applying
7(b).
Find the probability that atmost 5 defective bolts will be found in
a box of 200 bolts, if it is known that 2% of such bolts are
expected to be defective. (e
-4
= 0.0183)
BTL -6 Creating
8(a).
A coin is tossed 6 times what is the probability of obtaining (a) 4
heads (b) 5 heads (c) 6 heads (d) getting 4 or more heads.
BTL -3 Applying
8(b).
In a bolt factory machines A, B, C manufacture respectively 25%,
35% and 40% of the total of their output 5, 4, 2 percent are
defective bolts. If A bolt is drawn at random from the product and
is found to be defective, what are the probabilities that is was
manufactured by machines A, B and C?
BTL -6 Creating
9(a).
In a test of 2000 electric blubs it was found that the life of a
particular make was normally distributed with an average life of
2040 hours and S. D. of 60 hours. Estimate the number of blubs
likely to burn for
(1) More than 2150 hours
(2) Less than 1950 hours
(3) More than 1920 hours but less than 2160 hours.
BTL -3 Applying
9(b).
The latest nationwide political poll indicates that for Americans
who are randomly selected, the probability that they are
conservative is 0.55, the probability that they are liberal is 0.30
and the probability that they are middle of the road is 0.15.
Assuming these probabilities are accurate, answer the following
BTL -4 Analyzing
5
questions from a randomly chosen group of 10 Americans
(a) What the probability that 4 are liberal?
(b) What the probability that none are conservative
(c) What the probability that two are middle of the road
(d) What the probability that a least 8 are liberal
10.
If X follows a normal distribution with mean 12 and variance 16
cm, find the probabilities for (i) X ? 20 (ii) X ? 20, and (iii) 0 ? X
? 12.
BTL -3 Applying
11.
A discerete random variable X has the probability function given
below:
Value of X=x: 0 1 2 3 4 5 6 7
P(X=x) : 0 k 2k 2k 3k k
2
2k
2
7k
2
+k
Find (1) The value of k
(2) P(1.5 < X < 4.5 / X > 2)
(3) P(X < 6), P(X ? 5), P( 0 < X < 4)
(4) The distribution of X.
BTL -3 Applying
12.
X is a normal variable with mean 30 and standard deviation of 5.
Find (i) P[26 ? X ? 40] (ii) P [X?45] (iii) P [ ?X - 30 ?> 5] use
normal distribution tables
BTL -4 Analyzing
13.
In an intelligence test administered on 1000 students, the average
was 42 and standard deviation 24, find (i) the number of students
exceeding a score 50. (ii) the number of students lying between
30 and 54(iii) the value of score exceeded by top 100 students.
BTL -4 Analyzing
14(a).
The probability that an entering student will graduate is 0.4
Determine the probability that out of 5 students atleast one will
graduate.
BTL-5
Evaluating
14(b).
Fit a Poisson Distribution to the following data which gives the
number of doddens in a sample of clover seeds
No 0 1 2 3 4 5 6 7 8
f 56 156 132 92 37 22 4 0 1
.
BTL -4 Analyzing
PART-C
1(a).
A disciplinary committee is formed from the staff of XYZ
Company which has three departments Marketing, Finance and
Production of the 10,5,20 members respectively. All departments
have two female staff each. A department is selected at random
and from which two matters are selected for the committee,
What is the probability that both the team members are female?
BTL-6 Creating
6
1(b).
In a bolt factory machines A, B, C manufacture respectively 25,
35 and 40 percent of the total. Of their output 5, 4 and 2 percent
are defective bolts respectively. A bolt is drawn at random from
the product and is found o be defective. What are the probabilities
that it was manufactured by machines A, B or C?
BTL-2
Understanding
2(a). State Bayes theorem and brief about its applications. BTL-2 Understanding
2(b).
Out of 800 families with 4 children each, how many families
would be expected to have (i) 2 boys and 2 girls (ii) at least 1 boy
(iii) at most 2 girls (iv) children of both sexes? Assume equal
probabilities for boys and girls.
BTL-1 Remembering
3. Describe the classifications of probability ? BTL-1 Remembering
4. What are the applications of Normal distribution in statistics? BTL-6 Creating
UNIT ?II- SAMPLING DISTRIBUTION & ESTIMATION.
SYLLABUS: Introduction to sampling distributions, sampling distribution of mean and proportion, application of central
limit theorem, sampling techniques. Estimation: Point and Interval estimates for population parameters of large sample and
small samples, determining the sample size.
PART - A
S.N
O
QUESTIONS
BT Level
COMPETENCE
1. Define Sampling distribution of proportion. BTL -1 Remembering
2. Define Probable standard error. BTL -1 Remembering
3. Define standard error and mention its importance BTL -1 Remembering
4. Define central limit theorem BTL -1 Remembering
5.
What is the role of central limit theorem in estimation and testing
problems
BTL -6 Creating
6. Define stratified sampling technique BTL -1 Remembering
7. Briefly describe the significance level. BTL -1 Remembering
8. Distinguish between parameter and statistic. BTL -2 Understanding
9. Define estimator, estimate and estimation. BTL -1 Remembering
10. Distinguish between point estimation and interval estimation BTL -2 Understanding
11. Mention the properties of a good estimator. BTL -1 Remembering
12. Define confidence coefficient. BTL -1 Remembering
13. What is the level of significance in testing of hypothesis BTL -6 Creating
14. Define confidence limits for a parameter BTL -1 Remembering
15.
State the conditions under which a binomial distribution becomes a
normal distribution
BTL -4 Analyzing
16.
If the random sample comes from a normal population, what can
be said about the sampling distribution of the mean.
BTL -5 Evaluating
17.
An automobile repair shop has taken a random sample of 40
services that the average service time on an automobile is 130
minutes with a standard deviation of 26 minutes. Compute the
standard error of the mean.
BTL -6 Creating
7
18. What is a random number? How it is useful in sampling? BTL -6 Creating
19.
A population has the numbers: 12, 8, 10, 30, 12, 16, 40, 5, 16, 24,
22, 31, 30, 16, 15. Draw a systematic sample of size 5. Find out its
mean.
BTL -3 Applying
20. How large sample is useful in estimation and testing BTL -4 Analyzing
PART -B
1(a).
A random sample of 700 units from a large consignment showed
that 200 were damaged. Find (i) 95% (ii) 99% confidence limits
for the proportion of damaged units in the consignment.
BTL -3 Applying
1(b).
A random sample of size 9 is obtained from a Normal population
with mean 25 and if the variance 100 find the probability that the
sample mean exceeds 31.2.
BTL -4 Analyzing
2(a).
In a normally distributed population, average income per
household is Rs.20,000 with a standard deviation of Rs. 1,600.
Find the probability that the sample mean will be between
Rs.19,600 and Rs.20,200 in a survey of a random sample of 100
households.
BTL -6 Creating
2(b).
A university wants to determine the percentage of students who
would accept proposed fees hike for improving facilities. The
university wants to be 90% confident that the percentage is
within2% of the true value. Find the sample size to achieve the
accuracy regardless of the true percentage assuming the percentage
of students accepting the increase in tuition fees to be 0.5.
BTL -6 Creating
3(a).
A bank has kept records of the checking balances of its customers
and determined that the average daily balances of its customers is
Rs.300 with a standard deviation of Rs. 48. A random sample of
144 checking accounts is selected.
(i) What is the probability that the sample mean will be more
than Rs. 306.60?
(ii) What is the probability that the sample mean will be less
than Rs. 308?
BTL -6 Creating
3(b).
From the question 3(a)
(i) What is probability that the sample mean will between Rs.
302 and Rs. 308?
(ii) What is probability that the sample mean will be atleast
Rs. 296?
BTL -6 Creating
4(a).
Explain Stratified sampling technique and discuss how it is better
than simple random sampling in a particular situation.
BTL -4
Analyzing
4(b). Discuss the standard error of proportion BTL-2 Understanding
5.
Explain the methods of drawing simple random sample from a
finite population.
BTL -4 Analyzing
8
6(a).
In a sample of 1000 citizens of India, 540 are wheat eaters and the
rest are rice eaters. Can we assume that both rice and wheat
equally popular in India at 1 % level of significance?
BTL-5
Evaluating
6(b).
A simple random sample of 144 items resulted in a sample mean
of 1257.85 and standard deviation of 480. Develop a 95%
confidence interval for the population mean
BTL -6
Creating
7(a).
A car dealer wants to estimate the proportion of customers who
still own the cars they purchased 5 years earlier. A random sample
of 500 customers selected from the dealer?s records indicate that
315 customers still own cars that they were purchased 5 years
earlier. Set up 95% confidence interval estimation of the
population proportion of all the customers who still own the cars 5
years after they were purchased.
BTL-2
Understanding
7(b).
A movie maker sampled 55 fans who viewed his master piece
movie and asked them whether they had planned to see it again.
Only 10 of them believed that the movie was worthy of a second
look. Find the standard error of the population of fans who will
view the film a second time. Construct a 90% confidence interval
for this population.
BTL -5 Evaluating
8(a).
From a population of size 600, a sample of 60 individuals revealed
mean and standard deviation as 6.2 and 1.45 respectively. (i) Find
the estimated standard error (ii) Construct 96% confidence
interval for the mean.
BTL -3 Applying
8(b).
The age of employees in a company follows normal distribution
with its mean and variance as 40 years and 121 years respectively.
If a random sample of 36 employees is taken from a finite normal
population of size 1000, what is the probability that the sample
mean is
(i) less than 45
(ii) greater than 42 and
(iii) between 40 and 42?
BTL -6
Creating
9(a).
A firm wishes to estimate with an error of not more than 0.03 and
a level of confidence of 98%, the proportion of consumers that
prefer its brand of household detergent. Sales report indicate the
about 0.20 of all consumers prefer the firm?s brand. What is the
requisite sample size?
BTL -5 Evaluating
9(b).
A random sample of 700 units from a large consignment should
that 200 were damaged.
Find (i) 95%
(ii) 99% confidence limits for the proportion of damaged
units in the consignment
BTL -3 Applying
10(a).
From a population of 500 items with a mean of 100 gms and
standard deviation of 12.5 gms, 65 items were chosen. (i) What is
the standard error? (ii) Find P(99.5 < X < 101.5).
BTL -6 Creating
10(b).
A non-normal distribution representing the number of trips
BTL -6 Creating
9
performed by lorries per week in a coal field has a mean of 100
trips and variance of 121 trips. A random sample of 36 lorries is
taken from the non-normal population. What is the probability that
the sample mean is
(i) greater than 105
(ii) less than 102
(iii) between 101 and 103 trips?
11.
Test the significance of the difference between the means of the
sample from the following data
Size of sample Mean SD
Sample A 100 61 4
Sample B 200 63 6
BTL -4 Analyzing
12(a).
A cigarete manufacturing firm claims that its brand. A outsells
brand B by 8%. If it is found that 42 out of a sample of 200
smokers prefer brand a and 18 out of another sample of 100
smokers prefer brand B, test whether the 8% difference is a valid
claim(use 5% level of significance).
BTL -4
Analyzing
12(b).
In an automotive safety test conducted by the North Carolina
Highway Safety Research center, the average tyre pressure in a
sample of 62 tyres was found to be 24 pounds per square inch, and
the standard deviation was 2.1 pounds per square inch.
(i) What is the estimated population standard deviation for this
population
(ii) Calculate the estimated standard error of the mean
(iii) Construct a 95% confidence interval for the population mean.
BTL -3 Applying
13(a).
The manager of a shop selling beverages wants to estimate the
actual amount of beverages in one litre bottles from a nationally
known manufacturer. As per manufacturer?s specifications, the
standard deviation of the volume of the beverage is 0.02 litre. The
average amount of beverage per 1 litre bottle is found to be 0.995
litre on checking 50 bottles. Setup 99% confidence interval
estimate of the true population average amount of beverage in a 1
liter bottle. Check whether the manufacturer is genuine in filling
the beverage.
BTL -6
Creating
13(b).
In a batch chemical process used for etching printed circuit boards,
two different catalysts are being compared to determine whether
they require different emersion times for removal of identical
quantities of photo resist material. Twelve batch were run with
catalyst 1, resulting in a sample mean emersion time of 24.6
minutes and sample standard deviation of 0.85 minutes. Fifteen
batches were run with catalyst 2, resulting in a mean emersion time
of 22.1 minutes and a standard deviation of 0.98 minutes. Find a
95% confidence interval on the difference in means, assuming that
2
2
2
1
? ? ? .
BTL -3 Applying
10
14.
In a random sample of 75 axle shafts. 12 have a surface finish that
is rougher than the specifications will allow. Suppose that a
modification is made in the surface finishing process and
subsequently a second random sample of 85 axle shafts is
obtained. The number of defective shafts in this second sample is
10. Obtain an approximate 95% confidence interval on the
difference in the proportions of defectives produced under the two
processes
BTL -5 Evaluating
PART-C
1.
In a sample of 25 observations from a Normal distribution with
mean 98.6 and standard deviation 17.2.
(i)What is P(92<102)
(ii)Find the corresponding probability given a sample of 36.
BTL -6 Creating
2.
Mary, an auditor for a large credit card company, knows that, on
average, the monthly balance of any customer is Rs.112, and the
standard deviation is Rs.56. If Mary audits 50 randomly selected
accounts, What is the probability that the sample average balance
is
(i) Below Rs. 100
(ii)Between Rs.100 and Rs.130
BTL -6 Creating
3(a).
Write the type of sampling methods and the uses of standard error?
BTL -1 Remembering
3(b).
From a population of 540, a sample of 60 individual is taken. From
this sample, the mean is found to 6.2 and the standard deviation
1.368
(i) Find the estimated standard error of the mean.
(ii) Construct a 96 % confidence interval for the mean.
BTL-2 Understanding
4(a).
Explain the properties of good point estimator.
BTL -4 Analyzing
4(b).
What do you mean by interval estimation? Give examples
BTL-6 Creating
UNIT III - TESTS OF HYPOTHESIS- PARAMETRIC TESTS
SYLLABUS: Hypothesis testing: one sample and two sample tests for means and proportions of large samples (z-test),
one sample and two sample tests for means of small samples (t-test), F-test for two sample standard deviations. ANOVA
one and two way.
PART-A
Q.
No.
Question
Bloom?s
Taxonomy
Level
Domain
1. Define Test of Significance. BTL-1 Remembering
2. What are the Type I and Type II errors? BTL-6 Creating
3. What do you mean by one tail test? BTL-6 Creating
4. State the applications of Z-test and t-test. BTL-4 Analyzing
5. Define critical region BTL-1 Remembering
6. Distinguish between one tail and two tail tests BTL-2 Understanding
7. What is the aim of design of experiments? BTL-6 Creating
8. Distinguish between one-way and two-way analysis of variance. BTL-2 Understanding
9. When does the Z-test apply? BTL-1 Remembering
10. Explain SSB , SSW and SSY
and relationship in ANOVA. BTL-4 Analyzing
11
11. Describe any two applications of t-distribution BTL-1 Remembering
12. Write the uses of F-test? BTL-6 Creating
13. Define the level of significance. BTL-1 Remembering
14. Write the properties of t-distribution? BTL-6 Creating
15. What is the role of standard error? BTL-6 Creating
16. Mention any four applications of t-distribution in tests of hypothesis. BTL-1 Remembering
17. Mention any four uses of Chi-square distribution in test of hypothesis. BTL-1 Remembering
18. Define null hypothesis ? Explain. BTL-6 Creating
19.
Estimate the standard error of difference between two proportion if
p
1
=0.10,p
2=
0.133 and n
1
=50,n
2
=75.
BTL-6 Creating
20.
Mention any two assumptions made in analysis of variance
techniques.
BTL-1 Remembering
PART-B
1(a).
A study compares the effect of four 1-month point-of-purchase
promotions on sales. The unit sales for five stores using all four
promotions in different months follow.
Free Sample
78 87 81 89 58
One-pack gift
94 91 87 90 88
Cents off
73 73 78 69 83
76Refund by mail
79 83 78 69 81
(i)Compute the mean unit sales for each promotion and then
determine the grand mean.
(ii)Estimate the population variance using the between column
variance.
BTL-5 Evaluating
1(b).
From the question 1(a)
(i)Estimate the population variance using the within-column variance
computed from the variance within the samples.
(ii)Calculate the F ratio. At the 0.01 level of significance, do the
promotions produce different effects on sales.
BTL-2 Understanding
2(a).
In a low cost Toy production system, the molding machine has been
set with standard of 1% defective. The 80 sample units produced from
this machine shows defective of one unit. Is it necessary to stop the
product for corrective mechanism? Test at 5% level of significance
BTL-5 Evaluating
2(b).
Block Enterprises, a manufacturer of chips for computers. Is in the
process of deciding whether to replace its current semi automated
assembly line with a fully automated assembly line. Block has
gathered some preliminary test data about hourly chip production,
which is summarized in the following table, and it would like to know
whether it should upgrade its assembly line. State (and test at a =0.02)
appropriate hypothesis to help Block decide.
BTL-5 Evaluating
3(a).
Three samples below have been obtained from normal population
with equal variance. Test the hypothesis that the means are equal.
Sample I : 10 12 18 15 16
Sample II : 7 15 10 12 8
Sample III : 12 8 15 16 15
BTL-5 Evaluating
3(b). The I.Q.s of 16 students from one class of an showed a BTL-2 Understanding
FirstRanker.com - FirstRanker's Choice
1
(An
Ka ttankulathur ?
DEPARTMENT OF MATHEMATICS
QUESTION BANK
I SEMESTER
1918108 ? STATISTICS FOR MANAGEMENT
Regulation ? 2019
Academic Year 2019 - 2020
Prepared by
Ms. B. Vasuki, Assistant Professor/Mathematics
Ms.B.Elakkiavani, Assistant Professor/Mathematics
2
(An
? .
DEPARTMENT OF MATHEMATICS
QUESTION BANK
SUBJECT : 1918108 ? STATISTICS FOR MANAGEMENT
SEM / YEAR : I Semester / I Year
UNIT I - INTRODUCTION
SYLLABUS: Basic definitions and rules for probability, conditional probability independence of events, Baye?s
theorem, and random variables, Probability distributions: Binomial, Poisson, Uniform and Normal distributions.
PART- A
S.NO QUESTIONS
BT Level
COMPETENCE
PART ? A
1. Define Statistics. BTL -6 Creating
2. What is the addition and multiplication theorem on probability. BTL -1 Remembering
3. Distinguish between a priori and posterior probability?. BTL -6 Creating
4.
The price of the selected stock over a five day period shown as 170, 110,
130, 170 and 160. Compute mean , median and mode.
BTL -6 Creating
5.
A car travels 25 miles at 25 mph, 25 miles at 50 mph and 25 miles at 75
mph. Find the harmonic of three velocities?
BTL -4 Analyse
6.
A ball is drawn at random from a box containg 6 red balls, 4 white balls
and 5 blue balls. Find the probability that the ball drawn is not red.
BTL -4 Analyse
7.
Find the median and mode for the weights (kgs) of 15 persons given as
68, 85, 70, 65, 71, 67, 65, 55, 80, 62, 65, 64, 70, 60, 56.
BTL -3 Applying
8. Name few measures of dispersion. BTL -1 Remembering
9. write the common measures of central tendency? BTL -1 Remembering
10. Define continuous and discrete variables examples. BTL -1 Remembering
11.
Let X be the lifetime in years of a mechanical part. Assume that X has
the cdf F(x) = 1- e
-x
, x ? 0. Find P[1< X ? 3].
BTL -1 Remembering
12. Define independent events. BTL -1 Remembering
13. State the theorem of total probability BTL -1 Remembering
14. What is the use of Baye?s theorem? BTL -6 Creating
15. Mention the properties of a discrete probability distribution. BTL -1 Remembering
16. Define a Poisson distribution and mention its mean and variance. BTL -1 Remembering
17. If the mean and variance of a binomial distribution are respectively 6 BTL -3 Applying
3
and 2.4, find P(x=2).
18.
If x is a Poisson distribution such that P(x=1)=4P(x=2). Find its
mean and variance.
BTL -3 Applying
19.
Suppose that X has a Poisson distribution with parameter ? = 2.
Compute P[X ? 1].
BTL -1 Remembering
20. Define mutually exclusive events. BTL -1 Remembering
PART-B
1(a).
Calculate the mean and standard deviation for the following table
giving the age distribution of 542 members.
Age
20-30 30-40 40-50 50-60 60-70 70-80 80-90
No 3 61 132 153 140 51 2
BTL-2 Understanding
1(b).
Find the geometric mean for the following data:
Group
2-4 4-6 6-8 8-10
Frequency 200 400 300 100
BTL-2
Understanding
2(a).
Find the mean, median and modal ages of married women at first
child birth
Age at the
birth of
first child
13
14
15
16
17
18
19
20
21
22
23
24
25
No of
married
women
37
162
343
390
256
433
161
355
65
85
49
46
40
BTL -6 Creating
2(b).
If A and B are independent event with P(A)=2/5, and P(B)=3/5,
find P(A ?B). Let S= {1,2,3,4,5,6} if A = {2,4,6} then find the
probability of A complement.
BTL -3 Applying
3(a).
Given: The probabilities of three events A, B and C occurring are
P(A) = 0.35, P(B) = 0.45 and P(C) = 0.2. Assuming that A, B, or
C has occurred, the probabilities of another event X occurring are
P(X/A) = 0.8, P(X/B) = 0.65 and P(X/C) = 0.3. Find P(A/X),
P(B/X) and P(C/X).
BTL -6 Creating
3(b).
4 cards are drawn from a well shuffled pack of cards. Find the
probability that
(i) All the four are queens
(ii) There is one card from each suit.
(iii) Two cards are diamonds and two are spades
All the four cards are hearts and one of them is jack
BTL -6 Creating
4(a).
Three machines all turn out non ferrous castings. Machine A
produces 1% defective and Machine B- 2% and machine C ? 5%.
Each machine produces 1/3 of the output. An inspector examines
a single casting, which he determines as non defective. Estimate
the probabilities of its having been produced by each machine.
BTL -6 Creating
4(b).
If the random variable X takes values 1, 2, 3, 4 such that
2P(X = 1) = 3P(X = 2) = P( X=3) = 5P(X = 4), find the
probability distribution and cumulative distribution of X.
BTL-2 Understanding
5(a).
Two dice are thrown together once. Find the probabilities for
BTL -3 Applying
4
getting the sum of the two numbers (i) equal to 5, (ii) multiple of
3, (iii) divisible by 4.
5(b).
Given ? = 4.2, for a poisson distribution. Find (a) P(X ? 2) (b)
P(X ? 5) (c) P(X = 8).
BTL -6 Creating
6(a).
An urn contains 5 balls. Two balls are drawn and found to be
white. What is the probability that all the balls are white?
BTL-1 Remembering
6(b).
The contents of urns I, II, III are as follows:
1 white, 2 black and 3 red balls;
2 white, 1 black and 1 red balls;
4 white, 5 black and 3 red balls;
One urn is chosen at random and two balls drawn. They happen to
be white and red. What is the probability that they come from
urns I, II, III?
BTL -3 Applying
7(a).
In 1989, there were three candidates for the position of principal
Mr. Chatterji, Mr. Ayangar and Dr. Singh. Whose chances of
getting the appointment are in the proportion 4:2:3 respectively.
The probability that Mr. Chatterji is selected, would introduce co-
education in the is 0.3. The probabilities of Mr. Ayangar
and Dr. Singh doing the same are respectively 0.5 and .08. What
is the probability that there was co-education in the in
1990?
BTL -3
Applying
7(b).
Find the probability that atmost 5 defective bolts will be found in
a box of 200 bolts, if it is known that 2% of such bolts are
expected to be defective. (e
-4
= 0.0183)
BTL -6 Creating
8(a).
A coin is tossed 6 times what is the probability of obtaining (a) 4
heads (b) 5 heads (c) 6 heads (d) getting 4 or more heads.
BTL -3 Applying
8(b).
In a bolt factory machines A, B, C manufacture respectively 25%,
35% and 40% of the total of their output 5, 4, 2 percent are
defective bolts. If A bolt is drawn at random from the product and
is found to be defective, what are the probabilities that is was
manufactured by machines A, B and C?
BTL -6 Creating
9(a).
In a test of 2000 electric blubs it was found that the life of a
particular make was normally distributed with an average life of
2040 hours and S. D. of 60 hours. Estimate the number of blubs
likely to burn for
(1) More than 2150 hours
(2) Less than 1950 hours
(3) More than 1920 hours but less than 2160 hours.
BTL -3 Applying
9(b).
The latest nationwide political poll indicates that for Americans
who are randomly selected, the probability that they are
conservative is 0.55, the probability that they are liberal is 0.30
and the probability that they are middle of the road is 0.15.
Assuming these probabilities are accurate, answer the following
BTL -4 Analyzing
5
questions from a randomly chosen group of 10 Americans
(a) What the probability that 4 are liberal?
(b) What the probability that none are conservative
(c) What the probability that two are middle of the road
(d) What the probability that a least 8 are liberal
10.
If X follows a normal distribution with mean 12 and variance 16
cm, find the probabilities for (i) X ? 20 (ii) X ? 20, and (iii) 0 ? X
? 12.
BTL -3 Applying
11.
A discerete random variable X has the probability function given
below:
Value of X=x: 0 1 2 3 4 5 6 7
P(X=x) : 0 k 2k 2k 3k k
2
2k
2
7k
2
+k
Find (1) The value of k
(2) P(1.5 < X < 4.5 / X > 2)
(3) P(X < 6), P(X ? 5), P( 0 < X < 4)
(4) The distribution of X.
BTL -3 Applying
12.
X is a normal variable with mean 30 and standard deviation of 5.
Find (i) P[26 ? X ? 40] (ii) P [X?45] (iii) P [ ?X - 30 ?> 5] use
normal distribution tables
BTL -4 Analyzing
13.
In an intelligence test administered on 1000 students, the average
was 42 and standard deviation 24, find (i) the number of students
exceeding a score 50. (ii) the number of students lying between
30 and 54(iii) the value of score exceeded by top 100 students.
BTL -4 Analyzing
14(a).
The probability that an entering student will graduate is 0.4
Determine the probability that out of 5 students atleast one will
graduate.
BTL-5
Evaluating
14(b).
Fit a Poisson Distribution to the following data which gives the
number of doddens in a sample of clover seeds
No 0 1 2 3 4 5 6 7 8
f 56 156 132 92 37 22 4 0 1
.
BTL -4 Analyzing
PART-C
1(a).
A disciplinary committee is formed from the staff of XYZ
Company which has three departments Marketing, Finance and
Production of the 10,5,20 members respectively. All departments
have two female staff each. A department is selected at random
and from which two matters are selected for the committee,
What is the probability that both the team members are female?
BTL-6 Creating
6
1(b).
In a bolt factory machines A, B, C manufacture respectively 25,
35 and 40 percent of the total. Of their output 5, 4 and 2 percent
are defective bolts respectively. A bolt is drawn at random from
the product and is found o be defective. What are the probabilities
that it was manufactured by machines A, B or C?
BTL-2
Understanding
2(a). State Bayes theorem and brief about its applications. BTL-2 Understanding
2(b).
Out of 800 families with 4 children each, how many families
would be expected to have (i) 2 boys and 2 girls (ii) at least 1 boy
(iii) at most 2 girls (iv) children of both sexes? Assume equal
probabilities for boys and girls.
BTL-1 Remembering
3. Describe the classifications of probability ? BTL-1 Remembering
4. What are the applications of Normal distribution in statistics? BTL-6 Creating
UNIT ?II- SAMPLING DISTRIBUTION & ESTIMATION.
SYLLABUS: Introduction to sampling distributions, sampling distribution of mean and proportion, application of central
limit theorem, sampling techniques. Estimation: Point and Interval estimates for population parameters of large sample and
small samples, determining the sample size.
PART - A
S.N
O
QUESTIONS
BT Level
COMPETENCE
1. Define Sampling distribution of proportion. BTL -1 Remembering
2. Define Probable standard error. BTL -1 Remembering
3. Define standard error and mention its importance BTL -1 Remembering
4. Define central limit theorem BTL -1 Remembering
5.
What is the role of central limit theorem in estimation and testing
problems
BTL -6 Creating
6. Define stratified sampling technique BTL -1 Remembering
7. Briefly describe the significance level. BTL -1 Remembering
8. Distinguish between parameter and statistic. BTL -2 Understanding
9. Define estimator, estimate and estimation. BTL -1 Remembering
10. Distinguish between point estimation and interval estimation BTL -2 Understanding
11. Mention the properties of a good estimator. BTL -1 Remembering
12. Define confidence coefficient. BTL -1 Remembering
13. What is the level of significance in testing of hypothesis BTL -6 Creating
14. Define confidence limits for a parameter BTL -1 Remembering
15.
State the conditions under which a binomial distribution becomes a
normal distribution
BTL -4 Analyzing
16.
If the random sample comes from a normal population, what can
be said about the sampling distribution of the mean.
BTL -5 Evaluating
17.
An automobile repair shop has taken a random sample of 40
services that the average service time on an automobile is 130
minutes with a standard deviation of 26 minutes. Compute the
standard error of the mean.
BTL -6 Creating
7
18. What is a random number? How it is useful in sampling? BTL -6 Creating
19.
A population has the numbers: 12, 8, 10, 30, 12, 16, 40, 5, 16, 24,
22, 31, 30, 16, 15. Draw a systematic sample of size 5. Find out its
mean.
BTL -3 Applying
20. How large sample is useful in estimation and testing BTL -4 Analyzing
PART -B
1(a).
A random sample of 700 units from a large consignment showed
that 200 were damaged. Find (i) 95% (ii) 99% confidence limits
for the proportion of damaged units in the consignment.
BTL -3 Applying
1(b).
A random sample of size 9 is obtained from a Normal population
with mean 25 and if the variance 100 find the probability that the
sample mean exceeds 31.2.
BTL -4 Analyzing
2(a).
In a normally distributed population, average income per
household is Rs.20,000 with a standard deviation of Rs. 1,600.
Find the probability that the sample mean will be between
Rs.19,600 and Rs.20,200 in a survey of a random sample of 100
households.
BTL -6 Creating
2(b).
A university wants to determine the percentage of students who
would accept proposed fees hike for improving facilities. The
university wants to be 90% confident that the percentage is
within2% of the true value. Find the sample size to achieve the
accuracy regardless of the true percentage assuming the percentage
of students accepting the increase in tuition fees to be 0.5.
BTL -6 Creating
3(a).
A bank has kept records of the checking balances of its customers
and determined that the average daily balances of its customers is
Rs.300 with a standard deviation of Rs. 48. A random sample of
144 checking accounts is selected.
(i) What is the probability that the sample mean will be more
than Rs. 306.60?
(ii) What is the probability that the sample mean will be less
than Rs. 308?
BTL -6 Creating
3(b).
From the question 3(a)
(i) What is probability that the sample mean will between Rs.
302 and Rs. 308?
(ii) What is probability that the sample mean will be atleast
Rs. 296?
BTL -6 Creating
4(a).
Explain Stratified sampling technique and discuss how it is better
than simple random sampling in a particular situation.
BTL -4
Analyzing
4(b). Discuss the standard error of proportion BTL-2 Understanding
5.
Explain the methods of drawing simple random sample from a
finite population.
BTL -4 Analyzing
8
6(a).
In a sample of 1000 citizens of India, 540 are wheat eaters and the
rest are rice eaters. Can we assume that both rice and wheat
equally popular in India at 1 % level of significance?
BTL-5
Evaluating
6(b).
A simple random sample of 144 items resulted in a sample mean
of 1257.85 and standard deviation of 480. Develop a 95%
confidence interval for the population mean
BTL -6
Creating
7(a).
A car dealer wants to estimate the proportion of customers who
still own the cars they purchased 5 years earlier. A random sample
of 500 customers selected from the dealer?s records indicate that
315 customers still own cars that they were purchased 5 years
earlier. Set up 95% confidence interval estimation of the
population proportion of all the customers who still own the cars 5
years after they were purchased.
BTL-2
Understanding
7(b).
A movie maker sampled 55 fans who viewed his master piece
movie and asked them whether they had planned to see it again.
Only 10 of them believed that the movie was worthy of a second
look. Find the standard error of the population of fans who will
view the film a second time. Construct a 90% confidence interval
for this population.
BTL -5 Evaluating
8(a).
From a population of size 600, a sample of 60 individuals revealed
mean and standard deviation as 6.2 and 1.45 respectively. (i) Find
the estimated standard error (ii) Construct 96% confidence
interval for the mean.
BTL -3 Applying
8(b).
The age of employees in a company follows normal distribution
with its mean and variance as 40 years and 121 years respectively.
If a random sample of 36 employees is taken from a finite normal
population of size 1000, what is the probability that the sample
mean is
(i) less than 45
(ii) greater than 42 and
(iii) between 40 and 42?
BTL -6
Creating
9(a).
A firm wishes to estimate with an error of not more than 0.03 and
a level of confidence of 98%, the proportion of consumers that
prefer its brand of household detergent. Sales report indicate the
about 0.20 of all consumers prefer the firm?s brand. What is the
requisite sample size?
BTL -5 Evaluating
9(b).
A random sample of 700 units from a large consignment should
that 200 were damaged.
Find (i) 95%
(ii) 99% confidence limits for the proportion of damaged
units in the consignment
BTL -3 Applying
10(a).
From a population of 500 items with a mean of 100 gms and
standard deviation of 12.5 gms, 65 items were chosen. (i) What is
the standard error? (ii) Find P(99.5 < X < 101.5).
BTL -6 Creating
10(b).
A non-normal distribution representing the number of trips
BTL -6 Creating
9
performed by lorries per week in a coal field has a mean of 100
trips and variance of 121 trips. A random sample of 36 lorries is
taken from the non-normal population. What is the probability that
the sample mean is
(i) greater than 105
(ii) less than 102
(iii) between 101 and 103 trips?
11.
Test the significance of the difference between the means of the
sample from the following data
Size of sample Mean SD
Sample A 100 61 4
Sample B 200 63 6
BTL -4 Analyzing
12(a).
A cigarete manufacturing firm claims that its brand. A outsells
brand B by 8%. If it is found that 42 out of a sample of 200
smokers prefer brand a and 18 out of another sample of 100
smokers prefer brand B, test whether the 8% difference is a valid
claim(use 5% level of significance).
BTL -4
Analyzing
12(b).
In an automotive safety test conducted by the North Carolina
Highway Safety Research center, the average tyre pressure in a
sample of 62 tyres was found to be 24 pounds per square inch, and
the standard deviation was 2.1 pounds per square inch.
(i) What is the estimated population standard deviation for this
population
(ii) Calculate the estimated standard error of the mean
(iii) Construct a 95% confidence interval for the population mean.
BTL -3 Applying
13(a).
The manager of a shop selling beverages wants to estimate the
actual amount of beverages in one litre bottles from a nationally
known manufacturer. As per manufacturer?s specifications, the
standard deviation of the volume of the beverage is 0.02 litre. The
average amount of beverage per 1 litre bottle is found to be 0.995
litre on checking 50 bottles. Setup 99% confidence interval
estimate of the true population average amount of beverage in a 1
liter bottle. Check whether the manufacturer is genuine in filling
the beverage.
BTL -6
Creating
13(b).
In a batch chemical process used for etching printed circuit boards,
two different catalysts are being compared to determine whether
they require different emersion times for removal of identical
quantities of photo resist material. Twelve batch were run with
catalyst 1, resulting in a sample mean emersion time of 24.6
minutes and sample standard deviation of 0.85 minutes. Fifteen
batches were run with catalyst 2, resulting in a mean emersion time
of 22.1 minutes and a standard deviation of 0.98 minutes. Find a
95% confidence interval on the difference in means, assuming that
2
2
2
1
? ? ? .
BTL -3 Applying
10
14.
In a random sample of 75 axle shafts. 12 have a surface finish that
is rougher than the specifications will allow. Suppose that a
modification is made in the surface finishing process and
subsequently a second random sample of 85 axle shafts is
obtained. The number of defective shafts in this second sample is
10. Obtain an approximate 95% confidence interval on the
difference in the proportions of defectives produced under the two
processes
BTL -5 Evaluating
PART-C
1.
In a sample of 25 observations from a Normal distribution with
mean 98.6 and standard deviation 17.2.
(i)What is P(92<102)
(ii)Find the corresponding probability given a sample of 36.
BTL -6 Creating
2.
Mary, an auditor for a large credit card company, knows that, on
average, the monthly balance of any customer is Rs.112, and the
standard deviation is Rs.56. If Mary audits 50 randomly selected
accounts, What is the probability that the sample average balance
is
(i) Below Rs. 100
(ii)Between Rs.100 and Rs.130
BTL -6 Creating
3(a).
Write the type of sampling methods and the uses of standard error?
BTL -1 Remembering
3(b).
From a population of 540, a sample of 60 individual is taken. From
this sample, the mean is found to 6.2 and the standard deviation
1.368
(i) Find the estimated standard error of the mean.
(ii) Construct a 96 % confidence interval for the mean.
BTL-2 Understanding
4(a).
Explain the properties of good point estimator.
BTL -4 Analyzing
4(b).
What do you mean by interval estimation? Give examples
BTL-6 Creating
UNIT III - TESTS OF HYPOTHESIS- PARAMETRIC TESTS
SYLLABUS: Hypothesis testing: one sample and two sample tests for means and proportions of large samples (z-test),
one sample and two sample tests for means of small samples (t-test), F-test for two sample standard deviations. ANOVA
one and two way.
PART-A
Q.
No.
Question
Bloom?s
Taxonomy
Level
Domain
1. Define Test of Significance. BTL-1 Remembering
2. What are the Type I and Type II errors? BTL-6 Creating
3. What do you mean by one tail test? BTL-6 Creating
4. State the applications of Z-test and t-test. BTL-4 Analyzing
5. Define critical region BTL-1 Remembering
6. Distinguish between one tail and two tail tests BTL-2 Understanding
7. What is the aim of design of experiments? BTL-6 Creating
8. Distinguish between one-way and two-way analysis of variance. BTL-2 Understanding
9. When does the Z-test apply? BTL-1 Remembering
10. Explain SSB , SSW and SSY
and relationship in ANOVA. BTL-4 Analyzing
11
11. Describe any two applications of t-distribution BTL-1 Remembering
12. Write the uses of F-test? BTL-6 Creating
13. Define the level of significance. BTL-1 Remembering
14. Write the properties of t-distribution? BTL-6 Creating
15. What is the role of standard error? BTL-6 Creating
16. Mention any four applications of t-distribution in tests of hypothesis. BTL-1 Remembering
17. Mention any four uses of Chi-square distribution in test of hypothesis. BTL-1 Remembering
18. Define null hypothesis ? Explain. BTL-6 Creating
19.
Estimate the standard error of difference between two proportion if
p
1
=0.10,p
2=
0.133 and n
1
=50,n
2
=75.
BTL-6 Creating
20.
Mention any two assumptions made in analysis of variance
techniques.
BTL-1 Remembering
PART-B
1(a).
A study compares the effect of four 1-month point-of-purchase
promotions on sales. The unit sales for five stores using all four
promotions in different months follow.
Free Sample
78 87 81 89 58
One-pack gift
94 91 87 90 88
Cents off
73 73 78 69 83
76Refund by mail
79 83 78 69 81
(i)Compute the mean unit sales for each promotion and then
determine the grand mean.
(ii)Estimate the population variance using the between column
variance.
BTL-5 Evaluating
1(b).
From the question 1(a)
(i)Estimate the population variance using the within-column variance
computed from the variance within the samples.
(ii)Calculate the F ratio. At the 0.01 level of significance, do the
promotions produce different effects on sales.
BTL-2 Understanding
2(a).
In a low cost Toy production system, the molding machine has been
set with standard of 1% defective. The 80 sample units produced from
this machine shows defective of one unit. Is it necessary to stop the
product for corrective mechanism? Test at 5% level of significance
BTL-5 Evaluating
2(b).
Block Enterprises, a manufacturer of chips for computers. Is in the
process of deciding whether to replace its current semi automated
assembly line with a fully automated assembly line. Block has
gathered some preliminary test data about hourly chip production,
which is summarized in the following table, and it would like to know
whether it should upgrade its assembly line. State (and test at a =0.02)
appropriate hypothesis to help Block decide.
BTL-5 Evaluating
3(a).
Three samples below have been obtained from normal population
with equal variance. Test the hypothesis that the means are equal.
Sample I : 10 12 18 15 16
Sample II : 7 15 10 12 8
Sample III : 12 8 15 16 15
BTL-5 Evaluating
3(b). The I.Q.s of 16 students from one class of an showed a BTL-2 Understanding
12
mean of 107 with a standard deviation of 10, while the I.Q.s of 14
students from another class showed a mean of 112 with a standard
deviation of 8. Check whether there is an appreciable difference
between the I.Q.s of the two groups at (i) 0.01and (ii) 0.05 level of
significance
4(a).
The following is the information obtained from a random sample of 5
observations. Assume the population has a normal distribution.
30 31 27 32 28
To test if the sample was drawn from a normal distribution with mean
less than 30, (i)State the null and alternative hypotheses
(ii)Compute the standard error.
BTL-2 Understanding
4(b).
From the question 4(a)
(i)Determine the test statistic.
(ii)Decide at 10% level whether or not the mean value could be
greater than 30
BTL-2 Understanding
5.
The following data relate to the number of units produced per week by
three methods.
Method 1 : 170 192 190 120
Method 2 : 160 165 170 172
Method 3 : 182 190 170 178 185
Prepare ANOVA table and write your comments
BTL-6 Creating
6(a).
Test if the following samples could have come from two populations
with the same means, assuming the population variances are equal.
Sample I Sample II
Sample size 12 10
Sample Mean 40.5 43.8
Sample variance 2.6 3.2
BTL-5 Evaluating
6(b).
The weights of 10 people of a locality are found to be
70,67,62,68,61,68,70,64,64,66 kilograms. Is it reasonable to believe
that the average weights of the people of locality is greater than 64
kg? Test at 5%level of significance.
BTL-5 Evaluating
7(a).
In Town A, there were 850 birds of which 52% was males, while in
Town A and Town B combined, the proportion of males in a total of
1200 birds was 0.49. Is there any significance difference in the
proportions of male birds in the two Towns?
BTL-2
Understanding
7(b).
IQ test result of randomly selected five employees in an organization
is given below. Test whether minimum requirement of average IQ
level 87 is maintained in that company or not.
Employee code 234 232 121 343 111
IQ test 85 95 90 93 87
BTL-4 Analyzing
8(a).
The weights of 8 persons are found to be 60, 65, 70, 68, 62, 63, 60,
and 66 kgs. The weights of another group of 12 persons are found to
be 70, 60, 58, 56, 50, 48, 52, 56, 52, 50, 54, and 50. Can we conclude
that both samples have come from populations with same variances?
BTL -4 Analyzing
FirstRanker.com - FirstRanker's Choice
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(An
Ka ttankulathur ?
DEPARTMENT OF MATHEMATICS
QUESTION BANK
I SEMESTER
1918108 ? STATISTICS FOR MANAGEMENT
Regulation ? 2019
Academic Year 2019 - 2020
Prepared by
Ms. B. Vasuki, Assistant Professor/Mathematics
Ms.B.Elakkiavani, Assistant Professor/Mathematics
2
(An
? .
DEPARTMENT OF MATHEMATICS
QUESTION BANK
SUBJECT : 1918108 ? STATISTICS FOR MANAGEMENT
SEM / YEAR : I Semester / I Year
UNIT I - INTRODUCTION
SYLLABUS: Basic definitions and rules for probability, conditional probability independence of events, Baye?s
theorem, and random variables, Probability distributions: Binomial, Poisson, Uniform and Normal distributions.
PART- A
S.NO QUESTIONS
BT Level
COMPETENCE
PART ? A
1. Define Statistics. BTL -6 Creating
2. What is the addition and multiplication theorem on probability. BTL -1 Remembering
3. Distinguish between a priori and posterior probability?. BTL -6 Creating
4.
The price of the selected stock over a five day period shown as 170, 110,
130, 170 and 160. Compute mean , median and mode.
BTL -6 Creating
5.
A car travels 25 miles at 25 mph, 25 miles at 50 mph and 25 miles at 75
mph. Find the harmonic of three velocities?
BTL -4 Analyse
6.
A ball is drawn at random from a box containg 6 red balls, 4 white balls
and 5 blue balls. Find the probability that the ball drawn is not red.
BTL -4 Analyse
7.
Find the median and mode for the weights (kgs) of 15 persons given as
68, 85, 70, 65, 71, 67, 65, 55, 80, 62, 65, 64, 70, 60, 56.
BTL -3 Applying
8. Name few measures of dispersion. BTL -1 Remembering
9. write the common measures of central tendency? BTL -1 Remembering
10. Define continuous and discrete variables examples. BTL -1 Remembering
11.
Let X be the lifetime in years of a mechanical part. Assume that X has
the cdf F(x) = 1- e
-x
, x ? 0. Find P[1< X ? 3].
BTL -1 Remembering
12. Define independent events. BTL -1 Remembering
13. State the theorem of total probability BTL -1 Remembering
14. What is the use of Baye?s theorem? BTL -6 Creating
15. Mention the properties of a discrete probability distribution. BTL -1 Remembering
16. Define a Poisson distribution and mention its mean and variance. BTL -1 Remembering
17. If the mean and variance of a binomial distribution are respectively 6 BTL -3 Applying
3
and 2.4, find P(x=2).
18.
If x is a Poisson distribution such that P(x=1)=4P(x=2). Find its
mean and variance.
BTL -3 Applying
19.
Suppose that X has a Poisson distribution with parameter ? = 2.
Compute P[X ? 1].
BTL -1 Remembering
20. Define mutually exclusive events. BTL -1 Remembering
PART-B
1(a).
Calculate the mean and standard deviation for the following table
giving the age distribution of 542 members.
Age
20-30 30-40 40-50 50-60 60-70 70-80 80-90
No 3 61 132 153 140 51 2
BTL-2 Understanding
1(b).
Find the geometric mean for the following data:
Group
2-4 4-6 6-8 8-10
Frequency 200 400 300 100
BTL-2
Understanding
2(a).
Find the mean, median and modal ages of married women at first
child birth
Age at the
birth of
first child
13
14
15
16
17
18
19
20
21
22
23
24
25
No of
married
women
37
162
343
390
256
433
161
355
65
85
49
46
40
BTL -6 Creating
2(b).
If A and B are independent event with P(A)=2/5, and P(B)=3/5,
find P(A ?B). Let S= {1,2,3,4,5,6} if A = {2,4,6} then find the
probability of A complement.
BTL -3 Applying
3(a).
Given: The probabilities of three events A, B and C occurring are
P(A) = 0.35, P(B) = 0.45 and P(C) = 0.2. Assuming that A, B, or
C has occurred, the probabilities of another event X occurring are
P(X/A) = 0.8, P(X/B) = 0.65 and P(X/C) = 0.3. Find P(A/X),
P(B/X) and P(C/X).
BTL -6 Creating
3(b).
4 cards are drawn from a well shuffled pack of cards. Find the
probability that
(i) All the four are queens
(ii) There is one card from each suit.
(iii) Two cards are diamonds and two are spades
All the four cards are hearts and one of them is jack
BTL -6 Creating
4(a).
Three machines all turn out non ferrous castings. Machine A
produces 1% defective and Machine B- 2% and machine C ? 5%.
Each machine produces 1/3 of the output. An inspector examines
a single casting, which he determines as non defective. Estimate
the probabilities of its having been produced by each machine.
BTL -6 Creating
4(b).
If the random variable X takes values 1, 2, 3, 4 such that
2P(X = 1) = 3P(X = 2) = P( X=3) = 5P(X = 4), find the
probability distribution and cumulative distribution of X.
BTL-2 Understanding
5(a).
Two dice are thrown together once. Find the probabilities for
BTL -3 Applying
4
getting the sum of the two numbers (i) equal to 5, (ii) multiple of
3, (iii) divisible by 4.
5(b).
Given ? = 4.2, for a poisson distribution. Find (a) P(X ? 2) (b)
P(X ? 5) (c) P(X = 8).
BTL -6 Creating
6(a).
An urn contains 5 balls. Two balls are drawn and found to be
white. What is the probability that all the balls are white?
BTL-1 Remembering
6(b).
The contents of urns I, II, III are as follows:
1 white, 2 black and 3 red balls;
2 white, 1 black and 1 red balls;
4 white, 5 black and 3 red balls;
One urn is chosen at random and two balls drawn. They happen to
be white and red. What is the probability that they come from
urns I, II, III?
BTL -3 Applying
7(a).
In 1989, there were three candidates for the position of principal
Mr. Chatterji, Mr. Ayangar and Dr. Singh. Whose chances of
getting the appointment are in the proportion 4:2:3 respectively.
The probability that Mr. Chatterji is selected, would introduce co-
education in the is 0.3. The probabilities of Mr. Ayangar
and Dr. Singh doing the same are respectively 0.5 and .08. What
is the probability that there was co-education in the in
1990?
BTL -3
Applying
7(b).
Find the probability that atmost 5 defective bolts will be found in
a box of 200 bolts, if it is known that 2% of such bolts are
expected to be defective. (e
-4
= 0.0183)
BTL -6 Creating
8(a).
A coin is tossed 6 times what is the probability of obtaining (a) 4
heads (b) 5 heads (c) 6 heads (d) getting 4 or more heads.
BTL -3 Applying
8(b).
In a bolt factory machines A, B, C manufacture respectively 25%,
35% and 40% of the total of their output 5, 4, 2 percent are
defective bolts. If A bolt is drawn at random from the product and
is found to be defective, what are the probabilities that is was
manufactured by machines A, B and C?
BTL -6 Creating
9(a).
In a test of 2000 electric blubs it was found that the life of a
particular make was normally distributed with an average life of
2040 hours and S. D. of 60 hours. Estimate the number of blubs
likely to burn for
(1) More than 2150 hours
(2) Less than 1950 hours
(3) More than 1920 hours but less than 2160 hours.
BTL -3 Applying
9(b).
The latest nationwide political poll indicates that for Americans
who are randomly selected, the probability that they are
conservative is 0.55, the probability that they are liberal is 0.30
and the probability that they are middle of the road is 0.15.
Assuming these probabilities are accurate, answer the following
BTL -4 Analyzing
5
questions from a randomly chosen group of 10 Americans
(a) What the probability that 4 are liberal?
(b) What the probability that none are conservative
(c) What the probability that two are middle of the road
(d) What the probability that a least 8 are liberal
10.
If X follows a normal distribution with mean 12 and variance 16
cm, find the probabilities for (i) X ? 20 (ii) X ? 20, and (iii) 0 ? X
? 12.
BTL -3 Applying
11.
A discerete random variable X has the probability function given
below:
Value of X=x: 0 1 2 3 4 5 6 7
P(X=x) : 0 k 2k 2k 3k k
2
2k
2
7k
2
+k
Find (1) The value of k
(2) P(1.5 < X < 4.5 / X > 2)
(3) P(X < 6), P(X ? 5), P( 0 < X < 4)
(4) The distribution of X.
BTL -3 Applying
12.
X is a normal variable with mean 30 and standard deviation of 5.
Find (i) P[26 ? X ? 40] (ii) P [X?45] (iii) P [ ?X - 30 ?> 5] use
normal distribution tables
BTL -4 Analyzing
13.
In an intelligence test administered on 1000 students, the average
was 42 and standard deviation 24, find (i) the number of students
exceeding a score 50. (ii) the number of students lying between
30 and 54(iii) the value of score exceeded by top 100 students.
BTL -4 Analyzing
14(a).
The probability that an entering student will graduate is 0.4
Determine the probability that out of 5 students atleast one will
graduate.
BTL-5
Evaluating
14(b).
Fit a Poisson Distribution to the following data which gives the
number of doddens in a sample of clover seeds
No 0 1 2 3 4 5 6 7 8
f 56 156 132 92 37 22 4 0 1
.
BTL -4 Analyzing
PART-C
1(a).
A disciplinary committee is formed from the staff of XYZ
Company which has three departments Marketing, Finance and
Production of the 10,5,20 members respectively. All departments
have two female staff each. A department is selected at random
and from which two matters are selected for the committee,
What is the probability that both the team members are female?
BTL-6 Creating
6
1(b).
In a bolt factory machines A, B, C manufacture respectively 25,
35 and 40 percent of the total. Of their output 5, 4 and 2 percent
are defective bolts respectively. A bolt is drawn at random from
the product and is found o be defective. What are the probabilities
that it was manufactured by machines A, B or C?
BTL-2
Understanding
2(a). State Bayes theorem and brief about its applications. BTL-2 Understanding
2(b).
Out of 800 families with 4 children each, how many families
would be expected to have (i) 2 boys and 2 girls (ii) at least 1 boy
(iii) at most 2 girls (iv) children of both sexes? Assume equal
probabilities for boys and girls.
BTL-1 Remembering
3. Describe the classifications of probability ? BTL-1 Remembering
4. What are the applications of Normal distribution in statistics? BTL-6 Creating
UNIT ?II- SAMPLING DISTRIBUTION & ESTIMATION.
SYLLABUS: Introduction to sampling distributions, sampling distribution of mean and proportion, application of central
limit theorem, sampling techniques. Estimation: Point and Interval estimates for population parameters of large sample and
small samples, determining the sample size.
PART - A
S.N
O
QUESTIONS
BT Level
COMPETENCE
1. Define Sampling distribution of proportion. BTL -1 Remembering
2. Define Probable standard error. BTL -1 Remembering
3. Define standard error and mention its importance BTL -1 Remembering
4. Define central limit theorem BTL -1 Remembering
5.
What is the role of central limit theorem in estimation and testing
problems
BTL -6 Creating
6. Define stratified sampling technique BTL -1 Remembering
7. Briefly describe the significance level. BTL -1 Remembering
8. Distinguish between parameter and statistic. BTL -2 Understanding
9. Define estimator, estimate and estimation. BTL -1 Remembering
10. Distinguish between point estimation and interval estimation BTL -2 Understanding
11. Mention the properties of a good estimator. BTL -1 Remembering
12. Define confidence coefficient. BTL -1 Remembering
13. What is the level of significance in testing of hypothesis BTL -6 Creating
14. Define confidence limits for a parameter BTL -1 Remembering
15.
State the conditions under which a binomial distribution becomes a
normal distribution
BTL -4 Analyzing
16.
If the random sample comes from a normal population, what can
be said about the sampling distribution of the mean.
BTL -5 Evaluating
17.
An automobile repair shop has taken a random sample of 40
services that the average service time on an automobile is 130
minutes with a standard deviation of 26 minutes. Compute the
standard error of the mean.
BTL -6 Creating
7
18. What is a random number? How it is useful in sampling? BTL -6 Creating
19.
A population has the numbers: 12, 8, 10, 30, 12, 16, 40, 5, 16, 24,
22, 31, 30, 16, 15. Draw a systematic sample of size 5. Find out its
mean.
BTL -3 Applying
20. How large sample is useful in estimation and testing BTL -4 Analyzing
PART -B
1(a).
A random sample of 700 units from a large consignment showed
that 200 were damaged. Find (i) 95% (ii) 99% confidence limits
for the proportion of damaged units in the consignment.
BTL -3 Applying
1(b).
A random sample of size 9 is obtained from a Normal population
with mean 25 and if the variance 100 find the probability that the
sample mean exceeds 31.2.
BTL -4 Analyzing
2(a).
In a normally distributed population, average income per
household is Rs.20,000 with a standard deviation of Rs. 1,600.
Find the probability that the sample mean will be between
Rs.19,600 and Rs.20,200 in a survey of a random sample of 100
households.
BTL -6 Creating
2(b).
A university wants to determine the percentage of students who
would accept proposed fees hike for improving facilities. The
university wants to be 90% confident that the percentage is
within2% of the true value. Find the sample size to achieve the
accuracy regardless of the true percentage assuming the percentage
of students accepting the increase in tuition fees to be 0.5.
BTL -6 Creating
3(a).
A bank has kept records of the checking balances of its customers
and determined that the average daily balances of its customers is
Rs.300 with a standard deviation of Rs. 48. A random sample of
144 checking accounts is selected.
(i) What is the probability that the sample mean will be more
than Rs. 306.60?
(ii) What is the probability that the sample mean will be less
than Rs. 308?
BTL -6 Creating
3(b).
From the question 3(a)
(i) What is probability that the sample mean will between Rs.
302 and Rs. 308?
(ii) What is probability that the sample mean will be atleast
Rs. 296?
BTL -6 Creating
4(a).
Explain Stratified sampling technique and discuss how it is better
than simple random sampling in a particular situation.
BTL -4
Analyzing
4(b). Discuss the standard error of proportion BTL-2 Understanding
5.
Explain the methods of drawing simple random sample from a
finite population.
BTL -4 Analyzing
8
6(a).
In a sample of 1000 citizens of India, 540 are wheat eaters and the
rest are rice eaters. Can we assume that both rice and wheat
equally popular in India at 1 % level of significance?
BTL-5
Evaluating
6(b).
A simple random sample of 144 items resulted in a sample mean
of 1257.85 and standard deviation of 480. Develop a 95%
confidence interval for the population mean
BTL -6
Creating
7(a).
A car dealer wants to estimate the proportion of customers who
still own the cars they purchased 5 years earlier. A random sample
of 500 customers selected from the dealer?s records indicate that
315 customers still own cars that they were purchased 5 years
earlier. Set up 95% confidence interval estimation of the
population proportion of all the customers who still own the cars 5
years after they were purchased.
BTL-2
Understanding
7(b).
A movie maker sampled 55 fans who viewed his master piece
movie and asked them whether they had planned to see it again.
Only 10 of them believed that the movie was worthy of a second
look. Find the standard error of the population of fans who will
view the film a second time. Construct a 90% confidence interval
for this population.
BTL -5 Evaluating
8(a).
From a population of size 600, a sample of 60 individuals revealed
mean and standard deviation as 6.2 and 1.45 respectively. (i) Find
the estimated standard error (ii) Construct 96% confidence
interval for the mean.
BTL -3 Applying
8(b).
The age of employees in a company follows normal distribution
with its mean and variance as 40 years and 121 years respectively.
If a random sample of 36 employees is taken from a finite normal
population of size 1000, what is the probability that the sample
mean is
(i) less than 45
(ii) greater than 42 and
(iii) between 40 and 42?
BTL -6
Creating
9(a).
A firm wishes to estimate with an error of not more than 0.03 and
a level of confidence of 98%, the proportion of consumers that
prefer its brand of household detergent. Sales report indicate the
about 0.20 of all consumers prefer the firm?s brand. What is the
requisite sample size?
BTL -5 Evaluating
9(b).
A random sample of 700 units from a large consignment should
that 200 were damaged.
Find (i) 95%
(ii) 99% confidence limits for the proportion of damaged
units in the consignment
BTL -3 Applying
10(a).
From a population of 500 items with a mean of 100 gms and
standard deviation of 12.5 gms, 65 items were chosen. (i) What is
the standard error? (ii) Find P(99.5 < X < 101.5).
BTL -6 Creating
10(b).
A non-normal distribution representing the number of trips
BTL -6 Creating
9
performed by lorries per week in a coal field has a mean of 100
trips and variance of 121 trips. A random sample of 36 lorries is
taken from the non-normal population. What is the probability that
the sample mean is
(i) greater than 105
(ii) less than 102
(iii) between 101 and 103 trips?
11.
Test the significance of the difference between the means of the
sample from the following data
Size of sample Mean SD
Sample A 100 61 4
Sample B 200 63 6
BTL -4 Analyzing
12(a).
A cigarete manufacturing firm claims that its brand. A outsells
brand B by 8%. If it is found that 42 out of a sample of 200
smokers prefer brand a and 18 out of another sample of 100
smokers prefer brand B, test whether the 8% difference is a valid
claim(use 5% level of significance).
BTL -4
Analyzing
12(b).
In an automotive safety test conducted by the North Carolina
Highway Safety Research center, the average tyre pressure in a
sample of 62 tyres was found to be 24 pounds per square inch, and
the standard deviation was 2.1 pounds per square inch.
(i) What is the estimated population standard deviation for this
population
(ii) Calculate the estimated standard error of the mean
(iii) Construct a 95% confidence interval for the population mean.
BTL -3 Applying
13(a).
The manager of a shop selling beverages wants to estimate the
actual amount of beverages in one litre bottles from a nationally
known manufacturer. As per manufacturer?s specifications, the
standard deviation of the volume of the beverage is 0.02 litre. The
average amount of beverage per 1 litre bottle is found to be 0.995
litre on checking 50 bottles. Setup 99% confidence interval
estimate of the true population average amount of beverage in a 1
liter bottle. Check whether the manufacturer is genuine in filling
the beverage.
BTL -6
Creating
13(b).
In a batch chemical process used for etching printed circuit boards,
two different catalysts are being compared to determine whether
they require different emersion times for removal of identical
quantities of photo resist material. Twelve batch were run with
catalyst 1, resulting in a sample mean emersion time of 24.6
minutes and sample standard deviation of 0.85 minutes. Fifteen
batches were run with catalyst 2, resulting in a mean emersion time
of 22.1 minutes and a standard deviation of 0.98 minutes. Find a
95% confidence interval on the difference in means, assuming that
2
2
2
1
? ? ? .
BTL -3 Applying
10
14.
In a random sample of 75 axle shafts. 12 have a surface finish that
is rougher than the specifications will allow. Suppose that a
modification is made in the surface finishing process and
subsequently a second random sample of 85 axle shafts is
obtained. The number of defective shafts in this second sample is
10. Obtain an approximate 95% confidence interval on the
difference in the proportions of defectives produced under the two
processes
BTL -5 Evaluating
PART-C
1.
In a sample of 25 observations from a Normal distribution with
mean 98.6 and standard deviation 17.2.
(i)What is P(92<102)
(ii)Find the corresponding probability given a sample of 36.
BTL -6 Creating
2.
Mary, an auditor for a large credit card company, knows that, on
average, the monthly balance of any customer is Rs.112, and the
standard deviation is Rs.56. If Mary audits 50 randomly selected
accounts, What is the probability that the sample average balance
is
(i) Below Rs. 100
(ii)Between Rs.100 and Rs.130
BTL -6 Creating
3(a).
Write the type of sampling methods and the uses of standard error?
BTL -1 Remembering
3(b).
From a population of 540, a sample of 60 individual is taken. From
this sample, the mean is found to 6.2 and the standard deviation
1.368
(i) Find the estimated standard error of the mean.
(ii) Construct a 96 % confidence interval for the mean.
BTL-2 Understanding
4(a).
Explain the properties of good point estimator.
BTL -4 Analyzing
4(b).
What do you mean by interval estimation? Give examples
BTL-6 Creating
UNIT III - TESTS OF HYPOTHESIS- PARAMETRIC TESTS
SYLLABUS: Hypothesis testing: one sample and two sample tests for means and proportions of large samples (z-test),
one sample and two sample tests for means of small samples (t-test), F-test for two sample standard deviations. ANOVA
one and two way.
PART-A
Q.
No.
Question
Bloom?s
Taxonomy
Level
Domain
1. Define Test of Significance. BTL-1 Remembering
2. What are the Type I and Type II errors? BTL-6 Creating
3. What do you mean by one tail test? BTL-6 Creating
4. State the applications of Z-test and t-test. BTL-4 Analyzing
5. Define critical region BTL-1 Remembering
6. Distinguish between one tail and two tail tests BTL-2 Understanding
7. What is the aim of design of experiments? BTL-6 Creating
8. Distinguish between one-way and two-way analysis of variance. BTL-2 Understanding
9. When does the Z-test apply? BTL-1 Remembering
10. Explain SSB , SSW and SSY
and relationship in ANOVA. BTL-4 Analyzing
11
11. Describe any two applications of t-distribution BTL-1 Remembering
12. Write the uses of F-test? BTL-6 Creating
13. Define the level of significance. BTL-1 Remembering
14. Write the properties of t-distribution? BTL-6 Creating
15. What is the role of standard error? BTL-6 Creating
16. Mention any four applications of t-distribution in tests of hypothesis. BTL-1 Remembering
17. Mention any four uses of Chi-square distribution in test of hypothesis. BTL-1 Remembering
18. Define null hypothesis ? Explain. BTL-6 Creating
19.
Estimate the standard error of difference between two proportion if
p
1
=0.10,p
2=
0.133 and n
1
=50,n
2
=75.
BTL-6 Creating
20.
Mention any two assumptions made in analysis of variance
techniques.
BTL-1 Remembering
PART-B
1(a).
A study compares the effect of four 1-month point-of-purchase
promotions on sales. The unit sales for five stores using all four
promotions in different months follow.
Free Sample
78 87 81 89 58
One-pack gift
94 91 87 90 88
Cents off
73 73 78 69 83
76Refund by mail
79 83 78 69 81
(i)Compute the mean unit sales for each promotion and then
determine the grand mean.
(ii)Estimate the population variance using the between column
variance.
BTL-5 Evaluating
1(b).
From the question 1(a)
(i)Estimate the population variance using the within-column variance
computed from the variance within the samples.
(ii)Calculate the F ratio. At the 0.01 level of significance, do the
promotions produce different effects on sales.
BTL-2 Understanding
2(a).
In a low cost Toy production system, the molding machine has been
set with standard of 1% defective. The 80 sample units produced from
this machine shows defective of one unit. Is it necessary to stop the
product for corrective mechanism? Test at 5% level of significance
BTL-5 Evaluating
2(b).
Block Enterprises, a manufacturer of chips for computers. Is in the
process of deciding whether to replace its current semi automated
assembly line with a fully automated assembly line. Block has
gathered some preliminary test data about hourly chip production,
which is summarized in the following table, and it would like to know
whether it should upgrade its assembly line. State (and test at a =0.02)
appropriate hypothesis to help Block decide.
BTL-5 Evaluating
3(a).
Three samples below have been obtained from normal population
with equal variance. Test the hypothesis that the means are equal.
Sample I : 10 12 18 15 16
Sample II : 7 15 10 12 8
Sample III : 12 8 15 16 15
BTL-5 Evaluating
3(b). The I.Q.s of 16 students from one class of an showed a BTL-2 Understanding
12
mean of 107 with a standard deviation of 10, while the I.Q.s of 14
students from another class showed a mean of 112 with a standard
deviation of 8. Check whether there is an appreciable difference
between the I.Q.s of the two groups at (i) 0.01and (ii) 0.05 level of
significance
4(a).
The following is the information obtained from a random sample of 5
observations. Assume the population has a normal distribution.
30 31 27 32 28
To test if the sample was drawn from a normal distribution with mean
less than 30, (i)State the null and alternative hypotheses
(ii)Compute the standard error.
BTL-2 Understanding
4(b).
From the question 4(a)
(i)Determine the test statistic.
(ii)Decide at 10% level whether or not the mean value could be
greater than 30
BTL-2 Understanding
5.
The following data relate to the number of units produced per week by
three methods.
Method 1 : 170 192 190 120
Method 2 : 160 165 170 172
Method 3 : 182 190 170 178 185
Prepare ANOVA table and write your comments
BTL-6 Creating
6(a).
Test if the following samples could have come from two populations
with the same means, assuming the population variances are equal.
Sample I Sample II
Sample size 12 10
Sample Mean 40.5 43.8
Sample variance 2.6 3.2
BTL-5 Evaluating
6(b).
The weights of 10 people of a locality are found to be
70,67,62,68,61,68,70,64,64,66 kilograms. Is it reasonable to believe
that the average weights of the people of locality is greater than 64
kg? Test at 5%level of significance.
BTL-5 Evaluating
7(a).
In Town A, there were 850 birds of which 52% was males, while in
Town A and Town B combined, the proportion of males in a total of
1200 birds was 0.49. Is there any significance difference in the
proportions of male birds in the two Towns?
BTL-2
Understanding
7(b).
IQ test result of randomly selected five employees in an organization
is given below. Test whether minimum requirement of average IQ
level 87 is maintained in that company or not.
Employee code 234 232 121 343 111
IQ test 85 95 90 93 87
BTL-4 Analyzing
8(a).
The weights of 8 persons are found to be 60, 65, 70, 68, 62, 63, 60,
and 66 kgs. The weights of another group of 12 persons are found to
be 70, 60, 58, 56, 50, 48, 52, 56, 52, 50, 54, and 50. Can we conclude
that both samples have come from populations with same variances?
BTL -4 Analyzing
13
8(b).
ATMs must be stocked with enough cash to meet the requirements of
customers over a week, but excess cash results in loss of income as
investment opportunities could not be utilized. In an ATM, the
average transaction per customer in a week is Rs.8000 with a standard
deviation of Rs.1500. If a random sample of 36 customer transactions
is examined and it is observed that the sample mean with drawl is
Rs.8600, check the belief that the true average withdrawal is no longer
Rs.8000. Assume 0.05 level of significance
BTL -3 Applying
9.
Apply ANOVA technique and write your comment regarding the
sales(in Rs. Lakhs)
Area
Representatives
1 2 3 4
A 12 16 20 18
B 15 10 12 16
C 10 08 16 15
BTL -3 Applying
10(a).
A farmer wishes to determine whether there is a difference in yields
between two different varieties of wheat I and II. The following data
shows the production of wheat per unit area using the two varieties.
Can the farmer conclude at significance levels of
(i) 0.05
(ii) 0.01 that a difference exists?
BTL -4 Analyzing
10(b).
Test if the samples could have come from equal population means.
Sample A Sample B
Size 200 400
Mean 154.8 164.3
Variance 15.2 18.2
BTL-5 Evaluating
11(a).
The number of accidents per week in a city are as follows:
12, 8, 20, 2, 14, 10, 15, 6, 9 and 4. Are these frequencies in agreement
with the belief that accident conditions were the same during this 10
weeks period?
BTL -4
Analyzing
11(b).
Two samples are drawn from two normal population. From the
following data, Test whether the two samples have the same variance
5% level of significance.
Sample 1 60 65 69 74 76 82 85 87
Sample 2 61 66 67 85 78 63 85 86 88 91
BTL -3 Applying
12(a).
Given a sample mean of 83, a sample standard deviation of 12.5 and a
sample size of 22, test the hypothesis that the value of the population
mean is 70 against alternative that it is more than 70. Use the 0.025
significance level.
BTL-2
Understanding
12(b).
The following table shows the lifetimes in hours of samples from
three different types of television tables manufactured by a company.
Determine whether there is a difference between the three types at
significance level of 0.01.
Table:
BTL-2
Understanding
FirstRanker.com - FirstRanker's Choice
1
(An
Ka ttankulathur ?
DEPARTMENT OF MATHEMATICS
QUESTION BANK
I SEMESTER
1918108 ? STATISTICS FOR MANAGEMENT
Regulation ? 2019
Academic Year 2019 - 2020
Prepared by
Ms. B. Vasuki, Assistant Professor/Mathematics
Ms.B.Elakkiavani, Assistant Professor/Mathematics
2
(An
? .
DEPARTMENT OF MATHEMATICS
QUESTION BANK
SUBJECT : 1918108 ? STATISTICS FOR MANAGEMENT
SEM / YEAR : I Semester / I Year
UNIT I - INTRODUCTION
SYLLABUS: Basic definitions and rules for probability, conditional probability independence of events, Baye?s
theorem, and random variables, Probability distributions: Binomial, Poisson, Uniform and Normal distributions.
PART- A
S.NO QUESTIONS
BT Level
COMPETENCE
PART ? A
1. Define Statistics. BTL -6 Creating
2. What is the addition and multiplication theorem on probability. BTL -1 Remembering
3. Distinguish between a priori and posterior probability?. BTL -6 Creating
4.
The price of the selected stock over a five day period shown as 170, 110,
130, 170 and 160. Compute mean , median and mode.
BTL -6 Creating
5.
A car travels 25 miles at 25 mph, 25 miles at 50 mph and 25 miles at 75
mph. Find the harmonic of three velocities?
BTL -4 Analyse
6.
A ball is drawn at random from a box containg 6 red balls, 4 white balls
and 5 blue balls. Find the probability that the ball drawn is not red.
BTL -4 Analyse
7.
Find the median and mode for the weights (kgs) of 15 persons given as
68, 85, 70, 65, 71, 67, 65, 55, 80, 62, 65, 64, 70, 60, 56.
BTL -3 Applying
8. Name few measures of dispersion. BTL -1 Remembering
9. write the common measures of central tendency? BTL -1 Remembering
10. Define continuous and discrete variables examples. BTL -1 Remembering
11.
Let X be the lifetime in years of a mechanical part. Assume that X has
the cdf F(x) = 1- e
-x
, x ? 0. Find P[1< X ? 3].
BTL -1 Remembering
12. Define independent events. BTL -1 Remembering
13. State the theorem of total probability BTL -1 Remembering
14. What is the use of Baye?s theorem? BTL -6 Creating
15. Mention the properties of a discrete probability distribution. BTL -1 Remembering
16. Define a Poisson distribution and mention its mean and variance. BTL -1 Remembering
17. If the mean and variance of a binomial distribution are respectively 6 BTL -3 Applying
3
and 2.4, find P(x=2).
18.
If x is a Poisson distribution such that P(x=1)=4P(x=2). Find its
mean and variance.
BTL -3 Applying
19.
Suppose that X has a Poisson distribution with parameter ? = 2.
Compute P[X ? 1].
BTL -1 Remembering
20. Define mutually exclusive events. BTL -1 Remembering
PART-B
1(a).
Calculate the mean and standard deviation for the following table
giving the age distribution of 542 members.
Age
20-30 30-40 40-50 50-60 60-70 70-80 80-90
No 3 61 132 153 140 51 2
BTL-2 Understanding
1(b).
Find the geometric mean for the following data:
Group
2-4 4-6 6-8 8-10
Frequency 200 400 300 100
BTL-2
Understanding
2(a).
Find the mean, median and modal ages of married women at first
child birth
Age at the
birth of
first child
13
14
15
16
17
18
19
20
21
22
23
24
25
No of
married
women
37
162
343
390
256
433
161
355
65
85
49
46
40
BTL -6 Creating
2(b).
If A and B are independent event with P(A)=2/5, and P(B)=3/5,
find P(A ?B). Let S= {1,2,3,4,5,6} if A = {2,4,6} then find the
probability of A complement.
BTL -3 Applying
3(a).
Given: The probabilities of three events A, B and C occurring are
P(A) = 0.35, P(B) = 0.45 and P(C) = 0.2. Assuming that A, B, or
C has occurred, the probabilities of another event X occurring are
P(X/A) = 0.8, P(X/B) = 0.65 and P(X/C) = 0.3. Find P(A/X),
P(B/X) and P(C/X).
BTL -6 Creating
3(b).
4 cards are drawn from a well shuffled pack of cards. Find the
probability that
(i) All the four are queens
(ii) There is one card from each suit.
(iii) Two cards are diamonds and two are spades
All the four cards are hearts and one of them is jack
BTL -6 Creating
4(a).
Three machines all turn out non ferrous castings. Machine A
produces 1% defective and Machine B- 2% and machine C ? 5%.
Each machine produces 1/3 of the output. An inspector examines
a single casting, which he determines as non defective. Estimate
the probabilities of its having been produced by each machine.
BTL -6 Creating
4(b).
If the random variable X takes values 1, 2, 3, 4 such that
2P(X = 1) = 3P(X = 2) = P( X=3) = 5P(X = 4), find the
probability distribution and cumulative distribution of X.
BTL-2 Understanding
5(a).
Two dice are thrown together once. Find the probabilities for
BTL -3 Applying
4
getting the sum of the two numbers (i) equal to 5, (ii) multiple of
3, (iii) divisible by 4.
5(b).
Given ? = 4.2, for a poisson distribution. Find (a) P(X ? 2) (b)
P(X ? 5) (c) P(X = 8).
BTL -6 Creating
6(a).
An urn contains 5 balls. Two balls are drawn and found to be
white. What is the probability that all the balls are white?
BTL-1 Remembering
6(b).
The contents of urns I, II, III are as follows:
1 white, 2 black and 3 red balls;
2 white, 1 black and 1 red balls;
4 white, 5 black and 3 red balls;
One urn is chosen at random and two balls drawn. They happen to
be white and red. What is the probability that they come from
urns I, II, III?
BTL -3 Applying
7(a).
In 1989, there were three candidates for the position of principal
Mr. Chatterji, Mr. Ayangar and Dr. Singh. Whose chances of
getting the appointment are in the proportion 4:2:3 respectively.
The probability that Mr. Chatterji is selected, would introduce co-
education in the is 0.3. The probabilities of Mr. Ayangar
and Dr. Singh doing the same are respectively 0.5 and .08. What
is the probability that there was co-education in the in
1990?
BTL -3
Applying
7(b).
Find the probability that atmost 5 defective bolts will be found in
a box of 200 bolts, if it is known that 2% of such bolts are
expected to be defective. (e
-4
= 0.0183)
BTL -6 Creating
8(a).
A coin is tossed 6 times what is the probability of obtaining (a) 4
heads (b) 5 heads (c) 6 heads (d) getting 4 or more heads.
BTL -3 Applying
8(b).
In a bolt factory machines A, B, C manufacture respectively 25%,
35% and 40% of the total of their output 5, 4, 2 percent are
defective bolts. If A bolt is drawn at random from the product and
is found to be defective, what are the probabilities that is was
manufactured by machines A, B and C?
BTL -6 Creating
9(a).
In a test of 2000 electric blubs it was found that the life of a
particular make was normally distributed with an average life of
2040 hours and S. D. of 60 hours. Estimate the number of blubs
likely to burn for
(1) More than 2150 hours
(2) Less than 1950 hours
(3) More than 1920 hours but less than 2160 hours.
BTL -3 Applying
9(b).
The latest nationwide political poll indicates that for Americans
who are randomly selected, the probability that they are
conservative is 0.55, the probability that they are liberal is 0.30
and the probability that they are middle of the road is 0.15.
Assuming these probabilities are accurate, answer the following
BTL -4 Analyzing
5
questions from a randomly chosen group of 10 Americans
(a) What the probability that 4 are liberal?
(b) What the probability that none are conservative
(c) What the probability that two are middle of the road
(d) What the probability that a least 8 are liberal
10.
If X follows a normal distribution with mean 12 and variance 16
cm, find the probabilities for (i) X ? 20 (ii) X ? 20, and (iii) 0 ? X
? 12.
BTL -3 Applying
11.
A discerete random variable X has the probability function given
below:
Value of X=x: 0 1 2 3 4 5 6 7
P(X=x) : 0 k 2k 2k 3k k
2
2k
2
7k
2
+k
Find (1) The value of k
(2) P(1.5 < X < 4.5 / X > 2)
(3) P(X < 6), P(X ? 5), P( 0 < X < 4)
(4) The distribution of X.
BTL -3 Applying
12.
X is a normal variable with mean 30 and standard deviation of 5.
Find (i) P[26 ? X ? 40] (ii) P [X?45] (iii) P [ ?X - 30 ?> 5] use
normal distribution tables
BTL -4 Analyzing
13.
In an intelligence test administered on 1000 students, the average
was 42 and standard deviation 24, find (i) the number of students
exceeding a score 50. (ii) the number of students lying between
30 and 54(iii) the value of score exceeded by top 100 students.
BTL -4 Analyzing
14(a).
The probability that an entering student will graduate is 0.4
Determine the probability that out of 5 students atleast one will
graduate.
BTL-5
Evaluating
14(b).
Fit a Poisson Distribution to the following data which gives the
number of doddens in a sample of clover seeds
No 0 1 2 3 4 5 6 7 8
f 56 156 132 92 37 22 4 0 1
.
BTL -4 Analyzing
PART-C
1(a).
A disciplinary committee is formed from the staff of XYZ
Company which has three departments Marketing, Finance and
Production of the 10,5,20 members respectively. All departments
have two female staff each. A department is selected at random
and from which two matters are selected for the committee,
What is the probability that both the team members are female?
BTL-6 Creating
6
1(b).
In a bolt factory machines A, B, C manufacture respectively 25,
35 and 40 percent of the total. Of their output 5, 4 and 2 percent
are defective bolts respectively. A bolt is drawn at random from
the product and is found o be defective. What are the probabilities
that it was manufactured by machines A, B or C?
BTL-2
Understanding
2(a). State Bayes theorem and brief about its applications. BTL-2 Understanding
2(b).
Out of 800 families with 4 children each, how many families
would be expected to have (i) 2 boys and 2 girls (ii) at least 1 boy
(iii) at most 2 girls (iv) children of both sexes? Assume equal
probabilities for boys and girls.
BTL-1 Remembering
3. Describe the classifications of probability ? BTL-1 Remembering
4. What are the applications of Normal distribution in statistics? BTL-6 Creating
UNIT ?II- SAMPLING DISTRIBUTION & ESTIMATION.
SYLLABUS: Introduction to sampling distributions, sampling distribution of mean and proportion, application of central
limit theorem, sampling techniques. Estimation: Point and Interval estimates for population parameters of large sample and
small samples, determining the sample size.
PART - A
S.N
O
QUESTIONS
BT Level
COMPETENCE
1. Define Sampling distribution of proportion. BTL -1 Remembering
2. Define Probable standard error. BTL -1 Remembering
3. Define standard error and mention its importance BTL -1 Remembering
4. Define central limit theorem BTL -1 Remembering
5.
What is the role of central limit theorem in estimation and testing
problems
BTL -6 Creating
6. Define stratified sampling technique BTL -1 Remembering
7. Briefly describe the significance level. BTL -1 Remembering
8. Distinguish between parameter and statistic. BTL -2 Understanding
9. Define estimator, estimate and estimation. BTL -1 Remembering
10. Distinguish between point estimation and interval estimation BTL -2 Understanding
11. Mention the properties of a good estimator. BTL -1 Remembering
12. Define confidence coefficient. BTL -1 Remembering
13. What is the level of significance in testing of hypothesis BTL -6 Creating
14. Define confidence limits for a parameter BTL -1 Remembering
15.
State the conditions under which a binomial distribution becomes a
normal distribution
BTL -4 Analyzing
16.
If the random sample comes from a normal population, what can
be said about the sampling distribution of the mean.
BTL -5 Evaluating
17.
An automobile repair shop has taken a random sample of 40
services that the average service time on an automobile is 130
minutes with a standard deviation of 26 minutes. Compute the
standard error of the mean.
BTL -6 Creating
7
18. What is a random number? How it is useful in sampling? BTL -6 Creating
19.
A population has the numbers: 12, 8, 10, 30, 12, 16, 40, 5, 16, 24,
22, 31, 30, 16, 15. Draw a systematic sample of size 5. Find out its
mean.
BTL -3 Applying
20. How large sample is useful in estimation and testing BTL -4 Analyzing
PART -B
1(a).
A random sample of 700 units from a large consignment showed
that 200 were damaged. Find (i) 95% (ii) 99% confidence limits
for the proportion of damaged units in the consignment.
BTL -3 Applying
1(b).
A random sample of size 9 is obtained from a Normal population
with mean 25 and if the variance 100 find the probability that the
sample mean exceeds 31.2.
BTL -4 Analyzing
2(a).
In a normally distributed population, average income per
household is Rs.20,000 with a standard deviation of Rs. 1,600.
Find the probability that the sample mean will be between
Rs.19,600 and Rs.20,200 in a survey of a random sample of 100
households.
BTL -6 Creating
2(b).
A university wants to determine the percentage of students who
would accept proposed fees hike for improving facilities. The
university wants to be 90% confident that the percentage is
within2% of the true value. Find the sample size to achieve the
accuracy regardless of the true percentage assuming the percentage
of students accepting the increase in tuition fees to be 0.5.
BTL -6 Creating
3(a).
A bank has kept records of the checking balances of its customers
and determined that the average daily balances of its customers is
Rs.300 with a standard deviation of Rs. 48. A random sample of
144 checking accounts is selected.
(i) What is the probability that the sample mean will be more
than Rs. 306.60?
(ii) What is the probability that the sample mean will be less
than Rs. 308?
BTL -6 Creating
3(b).
From the question 3(a)
(i) What is probability that the sample mean will between Rs.
302 and Rs. 308?
(ii) What is probability that the sample mean will be atleast
Rs. 296?
BTL -6 Creating
4(a).
Explain Stratified sampling technique and discuss how it is better
than simple random sampling in a particular situation.
BTL -4
Analyzing
4(b). Discuss the standard error of proportion BTL-2 Understanding
5.
Explain the methods of drawing simple random sample from a
finite population.
BTL -4 Analyzing
8
6(a).
In a sample of 1000 citizens of India, 540 are wheat eaters and the
rest are rice eaters. Can we assume that both rice and wheat
equally popular in India at 1 % level of significance?
BTL-5
Evaluating
6(b).
A simple random sample of 144 items resulted in a sample mean
of 1257.85 and standard deviation of 480. Develop a 95%
confidence interval for the population mean
BTL -6
Creating
7(a).
A car dealer wants to estimate the proportion of customers who
still own the cars they purchased 5 years earlier. A random sample
of 500 customers selected from the dealer?s records indicate that
315 customers still own cars that they were purchased 5 years
earlier. Set up 95% confidence interval estimation of the
population proportion of all the customers who still own the cars 5
years after they were purchased.
BTL-2
Understanding
7(b).
A movie maker sampled 55 fans who viewed his master piece
movie and asked them whether they had planned to see it again.
Only 10 of them believed that the movie was worthy of a second
look. Find the standard error of the population of fans who will
view the film a second time. Construct a 90% confidence interval
for this population.
BTL -5 Evaluating
8(a).
From a population of size 600, a sample of 60 individuals revealed
mean and standard deviation as 6.2 and 1.45 respectively. (i) Find
the estimated standard error (ii) Construct 96% confidence
interval for the mean.
BTL -3 Applying
8(b).
The age of employees in a company follows normal distribution
with its mean and variance as 40 years and 121 years respectively.
If a random sample of 36 employees is taken from a finite normal
population of size 1000, what is the probability that the sample
mean is
(i) less than 45
(ii) greater than 42 and
(iii) between 40 and 42?
BTL -6
Creating
9(a).
A firm wishes to estimate with an error of not more than 0.03 and
a level of confidence of 98%, the proportion of consumers that
prefer its brand of household detergent. Sales report indicate the
about 0.20 of all consumers prefer the firm?s brand. What is the
requisite sample size?
BTL -5 Evaluating
9(b).
A random sample of 700 units from a large consignment should
that 200 were damaged.
Find (i) 95%
(ii) 99% confidence limits for the proportion of damaged
units in the consignment
BTL -3 Applying
10(a).
From a population of 500 items with a mean of 100 gms and
standard deviation of 12.5 gms, 65 items were chosen. (i) What is
the standard error? (ii) Find P(99.5 < X < 101.5).
BTL -6 Creating
10(b).
A non-normal distribution representing the number of trips
BTL -6 Creating
9
performed by lorries per week in a coal field has a mean of 100
trips and variance of 121 trips. A random sample of 36 lorries is
taken from the non-normal population. What is the probability that
the sample mean is
(i) greater than 105
(ii) less than 102
(iii) between 101 and 103 trips?
11.
Test the significance of the difference between the means of the
sample from the following data
Size of sample Mean SD
Sample A 100 61 4
Sample B 200 63 6
BTL -4 Analyzing
12(a).
A cigarete manufacturing firm claims that its brand. A outsells
brand B by 8%. If it is found that 42 out of a sample of 200
smokers prefer brand a and 18 out of another sample of 100
smokers prefer brand B, test whether the 8% difference is a valid
claim(use 5% level of significance).
BTL -4
Analyzing
12(b).
In an automotive safety test conducted by the North Carolina
Highway Safety Research center, the average tyre pressure in a
sample of 62 tyres was found to be 24 pounds per square inch, and
the standard deviation was 2.1 pounds per square inch.
(i) What is the estimated population standard deviation for this
population
(ii) Calculate the estimated standard error of the mean
(iii) Construct a 95% confidence interval for the population mean.
BTL -3 Applying
13(a).
The manager of a shop selling beverages wants to estimate the
actual amount of beverages in one litre bottles from a nationally
known manufacturer. As per manufacturer?s specifications, the
standard deviation of the volume of the beverage is 0.02 litre. The
average amount of beverage per 1 litre bottle is found to be 0.995
litre on checking 50 bottles. Setup 99% confidence interval
estimate of the true population average amount of beverage in a 1
liter bottle. Check whether the manufacturer is genuine in filling
the beverage.
BTL -6
Creating
13(b).
In a batch chemical process used for etching printed circuit boards,
two different catalysts are being compared to determine whether
they require different emersion times for removal of identical
quantities of photo resist material. Twelve batch were run with
catalyst 1, resulting in a sample mean emersion time of 24.6
minutes and sample standard deviation of 0.85 minutes. Fifteen
batches were run with catalyst 2, resulting in a mean emersion time
of 22.1 minutes and a standard deviation of 0.98 minutes. Find a
95% confidence interval on the difference in means, assuming that
2
2
2
1
? ? ? .
BTL -3 Applying
10
14.
In a random sample of 75 axle shafts. 12 have a surface finish that
is rougher than the specifications will allow. Suppose that a
modification is made in the surface finishing process and
subsequently a second random sample of 85 axle shafts is
obtained. The number of defective shafts in this second sample is
10. Obtain an approximate 95% confidence interval on the
difference in the proportions of defectives produced under the two
processes
BTL -5 Evaluating
PART-C
1.
In a sample of 25 observations from a Normal distribution with
mean 98.6 and standard deviation 17.2.
(i)What is P(92<102)
(ii)Find the corresponding probability given a sample of 36.
BTL -6 Creating
2.
Mary, an auditor for a large credit card company, knows that, on
average, the monthly balance of any customer is Rs.112, and the
standard deviation is Rs.56. If Mary audits 50 randomly selected
accounts, What is the probability that the sample average balance
is
(i) Below Rs. 100
(ii)Between Rs.100 and Rs.130
BTL -6 Creating
3(a).
Write the type of sampling methods and the uses of standard error?
BTL -1 Remembering
3(b).
From a population of 540, a sample of 60 individual is taken. From
this sample, the mean is found to 6.2 and the standard deviation
1.368
(i) Find the estimated standard error of the mean.
(ii) Construct a 96 % confidence interval for the mean.
BTL-2 Understanding
4(a).
Explain the properties of good point estimator.
BTL -4 Analyzing
4(b).
What do you mean by interval estimation? Give examples
BTL-6 Creating
UNIT III - TESTS OF HYPOTHESIS- PARAMETRIC TESTS
SYLLABUS: Hypothesis testing: one sample and two sample tests for means and proportions of large samples (z-test),
one sample and two sample tests for means of small samples (t-test), F-test for two sample standard deviations. ANOVA
one and two way.
PART-A
Q.
No.
Question
Bloom?s
Taxonomy
Level
Domain
1. Define Test of Significance. BTL-1 Remembering
2. What are the Type I and Type II errors? BTL-6 Creating
3. What do you mean by one tail test? BTL-6 Creating
4. State the applications of Z-test and t-test. BTL-4 Analyzing
5. Define critical region BTL-1 Remembering
6. Distinguish between one tail and two tail tests BTL-2 Understanding
7. What is the aim of design of experiments? BTL-6 Creating
8. Distinguish between one-way and two-way analysis of variance. BTL-2 Understanding
9. When does the Z-test apply? BTL-1 Remembering
10. Explain SSB , SSW and SSY
and relationship in ANOVA. BTL-4 Analyzing
11
11. Describe any two applications of t-distribution BTL-1 Remembering
12. Write the uses of F-test? BTL-6 Creating
13. Define the level of significance. BTL-1 Remembering
14. Write the properties of t-distribution? BTL-6 Creating
15. What is the role of standard error? BTL-6 Creating
16. Mention any four applications of t-distribution in tests of hypothesis. BTL-1 Remembering
17. Mention any four uses of Chi-square distribution in test of hypothesis. BTL-1 Remembering
18. Define null hypothesis ? Explain. BTL-6 Creating
19.
Estimate the standard error of difference between two proportion if
p
1
=0.10,p
2=
0.133 and n
1
=50,n
2
=75.
BTL-6 Creating
20.
Mention any two assumptions made in analysis of variance
techniques.
BTL-1 Remembering
PART-B
1(a).
A study compares the effect of four 1-month point-of-purchase
promotions on sales. The unit sales for five stores using all four
promotions in different months follow.
Free Sample
78 87 81 89 58
One-pack gift
94 91 87 90 88
Cents off
73 73 78 69 83
76Refund by mail
79 83 78 69 81
(i)Compute the mean unit sales for each promotion and then
determine the grand mean.
(ii)Estimate the population variance using the between column
variance.
BTL-5 Evaluating
1(b).
From the question 1(a)
(i)Estimate the population variance using the within-column variance
computed from the variance within the samples.
(ii)Calculate the F ratio. At the 0.01 level of significance, do the
promotions produce different effects on sales.
BTL-2 Understanding
2(a).
In a low cost Toy production system, the molding machine has been
set with standard of 1% defective. The 80 sample units produced from
this machine shows defective of one unit. Is it necessary to stop the
product for corrective mechanism? Test at 5% level of significance
BTL-5 Evaluating
2(b).
Block Enterprises, a manufacturer of chips for computers. Is in the
process of deciding whether to replace its current semi automated
assembly line with a fully automated assembly line. Block has
gathered some preliminary test data about hourly chip production,
which is summarized in the following table, and it would like to know
whether it should upgrade its assembly line. State (and test at a =0.02)
appropriate hypothesis to help Block decide.
BTL-5 Evaluating
3(a).
Three samples below have been obtained from normal population
with equal variance. Test the hypothesis that the means are equal.
Sample I : 10 12 18 15 16
Sample II : 7 15 10 12 8
Sample III : 12 8 15 16 15
BTL-5 Evaluating
3(b). The I.Q.s of 16 students from one class of an showed a BTL-2 Understanding
12
mean of 107 with a standard deviation of 10, while the I.Q.s of 14
students from another class showed a mean of 112 with a standard
deviation of 8. Check whether there is an appreciable difference
between the I.Q.s of the two groups at (i) 0.01and (ii) 0.05 level of
significance
4(a).
The following is the information obtained from a random sample of 5
observations. Assume the population has a normal distribution.
30 31 27 32 28
To test if the sample was drawn from a normal distribution with mean
less than 30, (i)State the null and alternative hypotheses
(ii)Compute the standard error.
BTL-2 Understanding
4(b).
From the question 4(a)
(i)Determine the test statistic.
(ii)Decide at 10% level whether or not the mean value could be
greater than 30
BTL-2 Understanding
5.
The following data relate to the number of units produced per week by
three methods.
Method 1 : 170 192 190 120
Method 2 : 160 165 170 172
Method 3 : 182 190 170 178 185
Prepare ANOVA table and write your comments
BTL-6 Creating
6(a).
Test if the following samples could have come from two populations
with the same means, assuming the population variances are equal.
Sample I Sample II
Sample size 12 10
Sample Mean 40.5 43.8
Sample variance 2.6 3.2
BTL-5 Evaluating
6(b).
The weights of 10 people of a locality are found to be
70,67,62,68,61,68,70,64,64,66 kilograms. Is it reasonable to believe
that the average weights of the people of locality is greater than 64
kg? Test at 5%level of significance.
BTL-5 Evaluating
7(a).
In Town A, there were 850 birds of which 52% was males, while in
Town A and Town B combined, the proportion of males in a total of
1200 birds was 0.49. Is there any significance difference in the
proportions of male birds in the two Towns?
BTL-2
Understanding
7(b).
IQ test result of randomly selected five employees in an organization
is given below. Test whether minimum requirement of average IQ
level 87 is maintained in that company or not.
Employee code 234 232 121 343 111
IQ test 85 95 90 93 87
BTL-4 Analyzing
8(a).
The weights of 8 persons are found to be 60, 65, 70, 68, 62, 63, 60,
and 66 kgs. The weights of another group of 12 persons are found to
be 70, 60, 58, 56, 50, 48, 52, 56, 52, 50, 54, and 50. Can we conclude
that both samples have come from populations with same variances?
BTL -4 Analyzing
13
8(b).
ATMs must be stocked with enough cash to meet the requirements of
customers over a week, but excess cash results in loss of income as
investment opportunities could not be utilized. In an ATM, the
average transaction per customer in a week is Rs.8000 with a standard
deviation of Rs.1500. If a random sample of 36 customer transactions
is examined and it is observed that the sample mean with drawl is
Rs.8600, check the belief that the true average withdrawal is no longer
Rs.8000. Assume 0.05 level of significance
BTL -3 Applying
9.
Apply ANOVA technique and write your comment regarding the
sales(in Rs. Lakhs)
Area
Representatives
1 2 3 4
A 12 16 20 18
B 15 10 12 16
C 10 08 16 15
BTL -3 Applying
10(a).
A farmer wishes to determine whether there is a difference in yields
between two different varieties of wheat I and II. The following data
shows the production of wheat per unit area using the two varieties.
Can the farmer conclude at significance levels of
(i) 0.05
(ii) 0.01 that a difference exists?
BTL -4 Analyzing
10(b).
Test if the samples could have come from equal population means.
Sample A Sample B
Size 200 400
Mean 154.8 164.3
Variance 15.2 18.2
BTL-5 Evaluating
11(a).
The number of accidents per week in a city are as follows:
12, 8, 20, 2, 14, 10, 15, 6, 9 and 4. Are these frequencies in agreement
with the belief that accident conditions were the same during this 10
weeks period?
BTL -4
Analyzing
11(b).
Two samples are drawn from two normal population. From the
following data, Test whether the two samples have the same variance
5% level of significance.
Sample 1 60 65 69 74 76 82 85 87
Sample 2 61 66 67 85 78 63 85 86 88 91
BTL -3 Applying
12(a).
Given a sample mean of 83, a sample standard deviation of 12.5 and a
sample size of 22, test the hypothesis that the value of the population
mean is 70 against alternative that it is more than 70. Use the 0.025
significance level.
BTL-2
Understanding
12(b).
The following table shows the lifetimes in hours of samples from
three different types of television tables manufactured by a company.
Determine whether there is a difference between the three types at
significance level of 0.01.
Table:
BTL-2
Understanding
14
Sample 1 407 411 409
Sample 2 404 406 408 405 402
Sample 3 410 408 406 408
13.
The following table shows the yields per acre of hour different plants
crops grown on lots treated with three different types of fertilizer.
Determine at the 5% significance level whether there is a difference in
yield per acre.
(i) due to the fertilizers and
(ii) due to the crops
Table:
Crop -I Crop -II Crop -III Crop -IV
Fertilizer A 4.5 6.4 7.2 6.7
Fertilizer B 8.8 7.8 9.6 7.0
Fertilizer C 5.9 6.8 5.7 5.2
BTL-2
Understanding
14.
Time of 6 machine operator (in minute) in making product is given
below. Use paired t-test for training effectiveness.
Machine operator 1 2 3 4 5 6
Before training 12 23 4 5 16 17
After training 2 3 10 8 12 6
BTL -3 Applying
PART C
1(a).
What are non-parametric tests? Point out their advantages and
disadvantages?
BTL -6 Creating
1(b).
The success of a sales engineer in adopting the proven sales technique
was found to be 12 out of 30 occasions. Hence he tried a novel
technique and achieved success at a rate of 23 out of 40 occasions.
Check whether the novel technique is effective at 5% level of
significance.
BTL-2 Understanding
2(a).
The following are the final examination marks of three groups of
students who were taught computer by three difference methods.
First method: 94 88 91 74 87 97
Second method: 85 82 79 84 61 72 80
Third method: 89 67 72 76 69
BTL -5 Evaluating
2(b).
A consumer product manufacturing company was selling one of its
leading products through a large number of retail shops. Before a
heavy advertisement campaign, the average sale per week per shop
was 140 dozens. After the campaign, a sample of 26 shops was taken
and the mean sales improved to 147 dozens with a standard deviation
of 16. Check the effectiveness of the advertisement campaign at 5%
level of significance
BTL-2
Understanding
3.
Discuss the test procedure to test hypothesized population proportion
using single sample proportion.
BTL-1 Understanding
FirstRanker.com - FirstRanker's Choice
1
(An
Ka ttankulathur ?
DEPARTMENT OF MATHEMATICS
QUESTION BANK
I SEMESTER
1918108 ? STATISTICS FOR MANAGEMENT
Regulation ? 2019
Academic Year 2019 - 2020
Prepared by
Ms. B. Vasuki, Assistant Professor/Mathematics
Ms.B.Elakkiavani, Assistant Professor/Mathematics
2
(An
? .
DEPARTMENT OF MATHEMATICS
QUESTION BANK
SUBJECT : 1918108 ? STATISTICS FOR MANAGEMENT
SEM / YEAR : I Semester / I Year
UNIT I - INTRODUCTION
SYLLABUS: Basic definitions and rules for probability, conditional probability independence of events, Baye?s
theorem, and random variables, Probability distributions: Binomial, Poisson, Uniform and Normal distributions.
PART- A
S.NO QUESTIONS
BT Level
COMPETENCE
PART ? A
1. Define Statistics. BTL -6 Creating
2. What is the addition and multiplication theorem on probability. BTL -1 Remembering
3. Distinguish between a priori and posterior probability?. BTL -6 Creating
4.
The price of the selected stock over a five day period shown as 170, 110,
130, 170 and 160. Compute mean , median and mode.
BTL -6 Creating
5.
A car travels 25 miles at 25 mph, 25 miles at 50 mph and 25 miles at 75
mph. Find the harmonic of three velocities?
BTL -4 Analyse
6.
A ball is drawn at random from a box containg 6 red balls, 4 white balls
and 5 blue balls. Find the probability that the ball drawn is not red.
BTL -4 Analyse
7.
Find the median and mode for the weights (kgs) of 15 persons given as
68, 85, 70, 65, 71, 67, 65, 55, 80, 62, 65, 64, 70, 60, 56.
BTL -3 Applying
8. Name few measures of dispersion. BTL -1 Remembering
9. write the common measures of central tendency? BTL -1 Remembering
10. Define continuous and discrete variables examples. BTL -1 Remembering
11.
Let X be the lifetime in years of a mechanical part. Assume that X has
the cdf F(x) = 1- e
-x
, x ? 0. Find P[1< X ? 3].
BTL -1 Remembering
12. Define independent events. BTL -1 Remembering
13. State the theorem of total probability BTL -1 Remembering
14. What is the use of Baye?s theorem? BTL -6 Creating
15. Mention the properties of a discrete probability distribution. BTL -1 Remembering
16. Define a Poisson distribution and mention its mean and variance. BTL -1 Remembering
17. If the mean and variance of a binomial distribution are respectively 6 BTL -3 Applying
3
and 2.4, find P(x=2).
18.
If x is a Poisson distribution such that P(x=1)=4P(x=2). Find its
mean and variance.
BTL -3 Applying
19.
Suppose that X has a Poisson distribution with parameter ? = 2.
Compute P[X ? 1].
BTL -1 Remembering
20. Define mutually exclusive events. BTL -1 Remembering
PART-B
1(a).
Calculate the mean and standard deviation for the following table
giving the age distribution of 542 members.
Age
20-30 30-40 40-50 50-60 60-70 70-80 80-90
No 3 61 132 153 140 51 2
BTL-2 Understanding
1(b).
Find the geometric mean for the following data:
Group
2-4 4-6 6-8 8-10
Frequency 200 400 300 100
BTL-2
Understanding
2(a).
Find the mean, median and modal ages of married women at first
child birth
Age at the
birth of
first child
13
14
15
16
17
18
19
20
21
22
23
24
25
No of
married
women
37
162
343
390
256
433
161
355
65
85
49
46
40
BTL -6 Creating
2(b).
If A and B are independent event with P(A)=2/5, and P(B)=3/5,
find P(A ?B). Let S= {1,2,3,4,5,6} if A = {2,4,6} then find the
probability of A complement.
BTL -3 Applying
3(a).
Given: The probabilities of three events A, B and C occurring are
P(A) = 0.35, P(B) = 0.45 and P(C) = 0.2. Assuming that A, B, or
C has occurred, the probabilities of another event X occurring are
P(X/A) = 0.8, P(X/B) = 0.65 and P(X/C) = 0.3. Find P(A/X),
P(B/X) and P(C/X).
BTL -6 Creating
3(b).
4 cards are drawn from a well shuffled pack of cards. Find the
probability that
(i) All the four are queens
(ii) There is one card from each suit.
(iii) Two cards are diamonds and two are spades
All the four cards are hearts and one of them is jack
BTL -6 Creating
4(a).
Three machines all turn out non ferrous castings. Machine A
produces 1% defective and Machine B- 2% and machine C ? 5%.
Each machine produces 1/3 of the output. An inspector examines
a single casting, which he determines as non defective. Estimate
the probabilities of its having been produced by each machine.
BTL -6 Creating
4(b).
If the random variable X takes values 1, 2, 3, 4 such that
2P(X = 1) = 3P(X = 2) = P( X=3) = 5P(X = 4), find the
probability distribution and cumulative distribution of X.
BTL-2 Understanding
5(a).
Two dice are thrown together once. Find the probabilities for
BTL -3 Applying
4
getting the sum of the two numbers (i) equal to 5, (ii) multiple of
3, (iii) divisible by 4.
5(b).
Given ? = 4.2, for a poisson distribution. Find (a) P(X ? 2) (b)
P(X ? 5) (c) P(X = 8).
BTL -6 Creating
6(a).
An urn contains 5 balls. Two balls are drawn and found to be
white. What is the probability that all the balls are white?
BTL-1 Remembering
6(b).
The contents of urns I, II, III are as follows:
1 white, 2 black and 3 red balls;
2 white, 1 black and 1 red balls;
4 white, 5 black and 3 red balls;
One urn is chosen at random and two balls drawn. They happen to
be white and red. What is the probability that they come from
urns I, II, III?
BTL -3 Applying
7(a).
In 1989, there were three candidates for the position of principal
Mr. Chatterji, Mr. Ayangar and Dr. Singh. Whose chances of
getting the appointment are in the proportion 4:2:3 respectively.
The probability that Mr. Chatterji is selected, would introduce co-
education in the is 0.3. The probabilities of Mr. Ayangar
and Dr. Singh doing the same are respectively 0.5 and .08. What
is the probability that there was co-education in the in
1990?
BTL -3
Applying
7(b).
Find the probability that atmost 5 defective bolts will be found in
a box of 200 bolts, if it is known that 2% of such bolts are
expected to be defective. (e
-4
= 0.0183)
BTL -6 Creating
8(a).
A coin is tossed 6 times what is the probability of obtaining (a) 4
heads (b) 5 heads (c) 6 heads (d) getting 4 or more heads.
BTL -3 Applying
8(b).
In a bolt factory machines A, B, C manufacture respectively 25%,
35% and 40% of the total of their output 5, 4, 2 percent are
defective bolts. If A bolt is drawn at random from the product and
is found to be defective, what are the probabilities that is was
manufactured by machines A, B and C?
BTL -6 Creating
9(a).
In a test of 2000 electric blubs it was found that the life of a
particular make was normally distributed with an average life of
2040 hours and S. D. of 60 hours. Estimate the number of blubs
likely to burn for
(1) More than 2150 hours
(2) Less than 1950 hours
(3) More than 1920 hours but less than 2160 hours.
BTL -3 Applying
9(b).
The latest nationwide political poll indicates that for Americans
who are randomly selected, the probability that they are
conservative is 0.55, the probability that they are liberal is 0.30
and the probability that they are middle of the road is 0.15.
Assuming these probabilities are accurate, answer the following
BTL -4 Analyzing
5
questions from a randomly chosen group of 10 Americans
(a) What the probability that 4 are liberal?
(b) What the probability that none are conservative
(c) What the probability that two are middle of the road
(d) What the probability that a least 8 are liberal
10.
If X follows a normal distribution with mean 12 and variance 16
cm, find the probabilities for (i) X ? 20 (ii) X ? 20, and (iii) 0 ? X
? 12.
BTL -3 Applying
11.
A discerete random variable X has the probability function given
below:
Value of X=x: 0 1 2 3 4 5 6 7
P(X=x) : 0 k 2k 2k 3k k
2
2k
2
7k
2
+k
Find (1) The value of k
(2) P(1.5 < X < 4.5 / X > 2)
(3) P(X < 6), P(X ? 5), P( 0 < X < 4)
(4) The distribution of X.
BTL -3 Applying
12.
X is a normal variable with mean 30 and standard deviation of 5.
Find (i) P[26 ? X ? 40] (ii) P [X?45] (iii) P [ ?X - 30 ?> 5] use
normal distribution tables
BTL -4 Analyzing
13.
In an intelligence test administered on 1000 students, the average
was 42 and standard deviation 24, find (i) the number of students
exceeding a score 50. (ii) the number of students lying between
30 and 54(iii) the value of score exceeded by top 100 students.
BTL -4 Analyzing
14(a).
The probability that an entering student will graduate is 0.4
Determine the probability that out of 5 students atleast one will
graduate.
BTL-5
Evaluating
14(b).
Fit a Poisson Distribution to the following data which gives the
number of doddens in a sample of clover seeds
No 0 1 2 3 4 5 6 7 8
f 56 156 132 92 37 22 4 0 1
.
BTL -4 Analyzing
PART-C
1(a).
A disciplinary committee is formed from the staff of XYZ
Company which has three departments Marketing, Finance and
Production of the 10,5,20 members respectively. All departments
have two female staff each. A department is selected at random
and from which two matters are selected for the committee,
What is the probability that both the team members are female?
BTL-6 Creating
6
1(b).
In a bolt factory machines A, B, C manufacture respectively 25,
35 and 40 percent of the total. Of their output 5, 4 and 2 percent
are defective bolts respectively. A bolt is drawn at random from
the product and is found o be defective. What are the probabilities
that it was manufactured by machines A, B or C?
BTL-2
Understanding
2(a). State Bayes theorem and brief about its applications. BTL-2 Understanding
2(b).
Out of 800 families with 4 children each, how many families
would be expected to have (i) 2 boys and 2 girls (ii) at least 1 boy
(iii) at most 2 girls (iv) children of both sexes? Assume equal
probabilities for boys and girls.
BTL-1 Remembering
3. Describe the classifications of probability ? BTL-1 Remembering
4. What are the applications of Normal distribution in statistics? BTL-6 Creating
UNIT ?II- SAMPLING DISTRIBUTION & ESTIMATION.
SYLLABUS: Introduction to sampling distributions, sampling distribution of mean and proportion, application of central
limit theorem, sampling techniques. Estimation: Point and Interval estimates for population parameters of large sample and
small samples, determining the sample size.
PART - A
S.N
O
QUESTIONS
BT Level
COMPETENCE
1. Define Sampling distribution of proportion. BTL -1 Remembering
2. Define Probable standard error. BTL -1 Remembering
3. Define standard error and mention its importance BTL -1 Remembering
4. Define central limit theorem BTL -1 Remembering
5.
What is the role of central limit theorem in estimation and testing
problems
BTL -6 Creating
6. Define stratified sampling technique BTL -1 Remembering
7. Briefly describe the significance level. BTL -1 Remembering
8. Distinguish between parameter and statistic. BTL -2 Understanding
9. Define estimator, estimate and estimation. BTL -1 Remembering
10. Distinguish between point estimation and interval estimation BTL -2 Understanding
11. Mention the properties of a good estimator. BTL -1 Remembering
12. Define confidence coefficient. BTL -1 Remembering
13. What is the level of significance in testing of hypothesis BTL -6 Creating
14. Define confidence limits for a parameter BTL -1 Remembering
15.
State the conditions under which a binomial distribution becomes a
normal distribution
BTL -4 Analyzing
16.
If the random sample comes from a normal population, what can
be said about the sampling distribution of the mean.
BTL -5 Evaluating
17.
An automobile repair shop has taken a random sample of 40
services that the average service time on an automobile is 130
minutes with a standard deviation of 26 minutes. Compute the
standard error of the mean.
BTL -6 Creating
7
18. What is a random number? How it is useful in sampling? BTL -6 Creating
19.
A population has the numbers: 12, 8, 10, 30, 12, 16, 40, 5, 16, 24,
22, 31, 30, 16, 15. Draw a systematic sample of size 5. Find out its
mean.
BTL -3 Applying
20. How large sample is useful in estimation and testing BTL -4 Analyzing
PART -B
1(a).
A random sample of 700 units from a large consignment showed
that 200 were damaged. Find (i) 95% (ii) 99% confidence limits
for the proportion of damaged units in the consignment.
BTL -3 Applying
1(b).
A random sample of size 9 is obtained from a Normal population
with mean 25 and if the variance 100 find the probability that the
sample mean exceeds 31.2.
BTL -4 Analyzing
2(a).
In a normally distributed population, average income per
household is Rs.20,000 with a standard deviation of Rs. 1,600.
Find the probability that the sample mean will be between
Rs.19,600 and Rs.20,200 in a survey of a random sample of 100
households.
BTL -6 Creating
2(b).
A university wants to determine the percentage of students who
would accept proposed fees hike for improving facilities. The
university wants to be 90% confident that the percentage is
within2% of the true value. Find the sample size to achieve the
accuracy regardless of the true percentage assuming the percentage
of students accepting the increase in tuition fees to be 0.5.
BTL -6 Creating
3(a).
A bank has kept records of the checking balances of its customers
and determined that the average daily balances of its customers is
Rs.300 with a standard deviation of Rs. 48. A random sample of
144 checking accounts is selected.
(i) What is the probability that the sample mean will be more
than Rs. 306.60?
(ii) What is the probability that the sample mean will be less
than Rs. 308?
BTL -6 Creating
3(b).
From the question 3(a)
(i) What is probability that the sample mean will between Rs.
302 and Rs. 308?
(ii) What is probability that the sample mean will be atleast
Rs. 296?
BTL -6 Creating
4(a).
Explain Stratified sampling technique and discuss how it is better
than simple random sampling in a particular situation.
BTL -4
Analyzing
4(b). Discuss the standard error of proportion BTL-2 Understanding
5.
Explain the methods of drawing simple random sample from a
finite population.
BTL -4 Analyzing
8
6(a).
In a sample of 1000 citizens of India, 540 are wheat eaters and the
rest are rice eaters. Can we assume that both rice and wheat
equally popular in India at 1 % level of significance?
BTL-5
Evaluating
6(b).
A simple random sample of 144 items resulted in a sample mean
of 1257.85 and standard deviation of 480. Develop a 95%
confidence interval for the population mean
BTL -6
Creating
7(a).
A car dealer wants to estimate the proportion of customers who
still own the cars they purchased 5 years earlier. A random sample
of 500 customers selected from the dealer?s records indicate that
315 customers still own cars that they were purchased 5 years
earlier. Set up 95% confidence interval estimation of the
population proportion of all the customers who still own the cars 5
years after they were purchased.
BTL-2
Understanding
7(b).
A movie maker sampled 55 fans who viewed his master piece
movie and asked them whether they had planned to see it again.
Only 10 of them believed that the movie was worthy of a second
look. Find the standard error of the population of fans who will
view the film a second time. Construct a 90% confidence interval
for this population.
BTL -5 Evaluating
8(a).
From a population of size 600, a sample of 60 individuals revealed
mean and standard deviation as 6.2 and 1.45 respectively. (i) Find
the estimated standard error (ii) Construct 96% confidence
interval for the mean.
BTL -3 Applying
8(b).
The age of employees in a company follows normal distribution
with its mean and variance as 40 years and 121 years respectively.
If a random sample of 36 employees is taken from a finite normal
population of size 1000, what is the probability that the sample
mean is
(i) less than 45
(ii) greater than 42 and
(iii) between 40 and 42?
BTL -6
Creating
9(a).
A firm wishes to estimate with an error of not more than 0.03 and
a level of confidence of 98%, the proportion of consumers that
prefer its brand of household detergent. Sales report indicate the
about 0.20 of all consumers prefer the firm?s brand. What is the
requisite sample size?
BTL -5 Evaluating
9(b).
A random sample of 700 units from a large consignment should
that 200 were damaged.
Find (i) 95%
(ii) 99% confidence limits for the proportion of damaged
units in the consignment
BTL -3 Applying
10(a).
From a population of 500 items with a mean of 100 gms and
standard deviation of 12.5 gms, 65 items were chosen. (i) What is
the standard error? (ii) Find P(99.5 < X < 101.5).
BTL -6 Creating
10(b).
A non-normal distribution representing the number of trips
BTL -6 Creating
9
performed by lorries per week in a coal field has a mean of 100
trips and variance of 121 trips. A random sample of 36 lorries is
taken from the non-normal population. What is the probability that
the sample mean is
(i) greater than 105
(ii) less than 102
(iii) between 101 and 103 trips?
11.
Test the significance of the difference between the means of the
sample from the following data
Size of sample Mean SD
Sample A 100 61 4
Sample B 200 63 6
BTL -4 Analyzing
12(a).
A cigarete manufacturing firm claims that its brand. A outsells
brand B by 8%. If it is found that 42 out of a sample of 200
smokers prefer brand a and 18 out of another sample of 100
smokers prefer brand B, test whether the 8% difference is a valid
claim(use 5% level of significance).
BTL -4
Analyzing
12(b).
In an automotive safety test conducted by the North Carolina
Highway Safety Research center, the average tyre pressure in a
sample of 62 tyres was found to be 24 pounds per square inch, and
the standard deviation was 2.1 pounds per square inch.
(i) What is the estimated population standard deviation for this
population
(ii) Calculate the estimated standard error of the mean
(iii) Construct a 95% confidence interval for the population mean.
BTL -3 Applying
13(a).
The manager of a shop selling beverages wants to estimate the
actual amount of beverages in one litre bottles from a nationally
known manufacturer. As per manufacturer?s specifications, the
standard deviation of the volume of the beverage is 0.02 litre. The
average amount of beverage per 1 litre bottle is found to be 0.995
litre on checking 50 bottles. Setup 99% confidence interval
estimate of the true population average amount of beverage in a 1
liter bottle. Check whether the manufacturer is genuine in filling
the beverage.
BTL -6
Creating
13(b).
In a batch chemical process used for etching printed circuit boards,
two different catalysts are being compared to determine whether
they require different emersion times for removal of identical
quantities of photo resist material. Twelve batch were run with
catalyst 1, resulting in a sample mean emersion time of 24.6
minutes and sample standard deviation of 0.85 minutes. Fifteen
batches were run with catalyst 2, resulting in a mean emersion time
of 22.1 minutes and a standard deviation of 0.98 minutes. Find a
95% confidence interval on the difference in means, assuming that
2
2
2
1
? ? ? .
BTL -3 Applying
10
14.
In a random sample of 75 axle shafts. 12 have a surface finish that
is rougher than the specifications will allow. Suppose that a
modification is made in the surface finishing process and
subsequently a second random sample of 85 axle shafts is
obtained. The number of defective shafts in this second sample is
10. Obtain an approximate 95% confidence interval on the
difference in the proportions of defectives produced under the two
processes
BTL -5 Evaluating
PART-C
1.
In a sample of 25 observations from a Normal distribution with
mean 98.6 and standard deviation 17.2.
(i)What is P(92<102)
(ii)Find the corresponding probability given a sample of 36.
BTL -6 Creating
2.
Mary, an auditor for a large credit card company, knows that, on
average, the monthly balance of any customer is Rs.112, and the
standard deviation is Rs.56. If Mary audits 50 randomly selected
accounts, What is the probability that the sample average balance
is
(i) Below Rs. 100
(ii)Between Rs.100 and Rs.130
BTL -6 Creating
3(a).
Write the type of sampling methods and the uses of standard error?
BTL -1 Remembering
3(b).
From a population of 540, a sample of 60 individual is taken. From
this sample, the mean is found to 6.2 and the standard deviation
1.368
(i) Find the estimated standard error of the mean.
(ii) Construct a 96 % confidence interval for the mean.
BTL-2 Understanding
4(a).
Explain the properties of good point estimator.
BTL -4 Analyzing
4(b).
What do you mean by interval estimation? Give examples
BTL-6 Creating
UNIT III - TESTS OF HYPOTHESIS- PARAMETRIC TESTS
SYLLABUS: Hypothesis testing: one sample and two sample tests for means and proportions of large samples (z-test),
one sample and two sample tests for means of small samples (t-test), F-test for two sample standard deviations. ANOVA
one and two way.
PART-A
Q.
No.
Question
Bloom?s
Taxonomy
Level
Domain
1. Define Test of Significance. BTL-1 Remembering
2. What are the Type I and Type II errors? BTL-6 Creating
3. What do you mean by one tail test? BTL-6 Creating
4. State the applications of Z-test and t-test. BTL-4 Analyzing
5. Define critical region BTL-1 Remembering
6. Distinguish between one tail and two tail tests BTL-2 Understanding
7. What is the aim of design of experiments? BTL-6 Creating
8. Distinguish between one-way and two-way analysis of variance. BTL-2 Understanding
9. When does the Z-test apply? BTL-1 Remembering
10. Explain SSB , SSW and SSY
and relationship in ANOVA. BTL-4 Analyzing
11
11. Describe any two applications of t-distribution BTL-1 Remembering
12. Write the uses of F-test? BTL-6 Creating
13. Define the level of significance. BTL-1 Remembering
14. Write the properties of t-distribution? BTL-6 Creating
15. What is the role of standard error? BTL-6 Creating
16. Mention any four applications of t-distribution in tests of hypothesis. BTL-1 Remembering
17. Mention any four uses of Chi-square distribution in test of hypothesis. BTL-1 Remembering
18. Define null hypothesis ? Explain. BTL-6 Creating
19.
Estimate the standard error of difference between two proportion if
p
1
=0.10,p
2=
0.133 and n
1
=50,n
2
=75.
BTL-6 Creating
20.
Mention any two assumptions made in analysis of variance
techniques.
BTL-1 Remembering
PART-B
1(a).
A study compares the effect of four 1-month point-of-purchase
promotions on sales. The unit sales for five stores using all four
promotions in different months follow.
Free Sample
78 87 81 89 58
One-pack gift
94 91 87 90 88
Cents off
73 73 78 69 83
76Refund by mail
79 83 78 69 81
(i)Compute the mean unit sales for each promotion and then
determine the grand mean.
(ii)Estimate the population variance using the between column
variance.
BTL-5 Evaluating
1(b).
From the question 1(a)
(i)Estimate the population variance using the within-column variance
computed from the variance within the samples.
(ii)Calculate the F ratio. At the 0.01 level of significance, do the
promotions produce different effects on sales.
BTL-2 Understanding
2(a).
In a low cost Toy production system, the molding machine has been
set with standard of 1% defective. The 80 sample units produced from
this machine shows defective of one unit. Is it necessary to stop the
product for corrective mechanism? Test at 5% level of significance
BTL-5 Evaluating
2(b).
Block Enterprises, a manufacturer of chips for computers. Is in the
process of deciding whether to replace its current semi automated
assembly line with a fully automated assembly line. Block has
gathered some preliminary test data about hourly chip production,
which is summarized in the following table, and it would like to know
whether it should upgrade its assembly line. State (and test at a =0.02)
appropriate hypothesis to help Block decide.
BTL-5 Evaluating
3(a).
Three samples below have been obtained from normal population
with equal variance. Test the hypothesis that the means are equal.
Sample I : 10 12 18 15 16
Sample II : 7 15 10 12 8
Sample III : 12 8 15 16 15
BTL-5 Evaluating
3(b). The I.Q.s of 16 students from one class of an showed a BTL-2 Understanding
12
mean of 107 with a standard deviation of 10, while the I.Q.s of 14
students from another class showed a mean of 112 with a standard
deviation of 8. Check whether there is an appreciable difference
between the I.Q.s of the two groups at (i) 0.01and (ii) 0.05 level of
significance
4(a).
The following is the information obtained from a random sample of 5
observations. Assume the population has a normal distribution.
30 31 27 32 28
To test if the sample was drawn from a normal distribution with mean
less than 30, (i)State the null and alternative hypotheses
(ii)Compute the standard error.
BTL-2 Understanding
4(b).
From the question 4(a)
(i)Determine the test statistic.
(ii)Decide at 10% level whether or not the mean value could be
greater than 30
BTL-2 Understanding
5.
The following data relate to the number of units produced per week by
three methods.
Method 1 : 170 192 190 120
Method 2 : 160 165 170 172
Method 3 : 182 190 170 178 185
Prepare ANOVA table and write your comments
BTL-6 Creating
6(a).
Test if the following samples could have come from two populations
with the same means, assuming the population variances are equal.
Sample I Sample II
Sample size 12 10
Sample Mean 40.5 43.8
Sample variance 2.6 3.2
BTL-5 Evaluating
6(b).
The weights of 10 people of a locality are found to be
70,67,62,68,61,68,70,64,64,66 kilograms. Is it reasonable to believe
that the average weights of the people of locality is greater than 64
kg? Test at 5%level of significance.
BTL-5 Evaluating
7(a).
In Town A, there were 850 birds of which 52% was males, while in
Town A and Town B combined, the proportion of males in a total of
1200 birds was 0.49. Is there any significance difference in the
proportions of male birds in the two Towns?
BTL-2
Understanding
7(b).
IQ test result of randomly selected five employees in an organization
is given below. Test whether minimum requirement of average IQ
level 87 is maintained in that company or not.
Employee code 234 232 121 343 111
IQ test 85 95 90 93 87
BTL-4 Analyzing
8(a).
The weights of 8 persons are found to be 60, 65, 70, 68, 62, 63, 60,
and 66 kgs. The weights of another group of 12 persons are found to
be 70, 60, 58, 56, 50, 48, 52, 56, 52, 50, 54, and 50. Can we conclude
that both samples have come from populations with same variances?
BTL -4 Analyzing
13
8(b).
ATMs must be stocked with enough cash to meet the requirements of
customers over a week, but excess cash results in loss of income as
investment opportunities could not be utilized. In an ATM, the
average transaction per customer in a week is Rs.8000 with a standard
deviation of Rs.1500. If a random sample of 36 customer transactions
is examined and it is observed that the sample mean with drawl is
Rs.8600, check the belief that the true average withdrawal is no longer
Rs.8000. Assume 0.05 level of significance
BTL -3 Applying
9.
Apply ANOVA technique and write your comment regarding the
sales(in Rs. Lakhs)
Area
Representatives
1 2 3 4
A 12 16 20 18
B 15 10 12 16
C 10 08 16 15
BTL -3 Applying
10(a).
A farmer wishes to determine whether there is a difference in yields
between two different varieties of wheat I and II. The following data
shows the production of wheat per unit area using the two varieties.
Can the farmer conclude at significance levels of
(i) 0.05
(ii) 0.01 that a difference exists?
BTL -4 Analyzing
10(b).
Test if the samples could have come from equal population means.
Sample A Sample B
Size 200 400
Mean 154.8 164.3
Variance 15.2 18.2
BTL-5 Evaluating
11(a).
The number of accidents per week in a city are as follows:
12, 8, 20, 2, 14, 10, 15, 6, 9 and 4. Are these frequencies in agreement
with the belief that accident conditions were the same during this 10
weeks period?
BTL -4
Analyzing
11(b).
Two samples are drawn from two normal population. From the
following data, Test whether the two samples have the same variance
5% level of significance.
Sample 1 60 65 69 74 76 82 85 87
Sample 2 61 66 67 85 78 63 85 86 88 91
BTL -3 Applying
12(a).
Given a sample mean of 83, a sample standard deviation of 12.5 and a
sample size of 22, test the hypothesis that the value of the population
mean is 70 against alternative that it is more than 70. Use the 0.025
significance level.
BTL-2
Understanding
12(b).
The following table shows the lifetimes in hours of samples from
three different types of television tables manufactured by a company.
Determine whether there is a difference between the three types at
significance level of 0.01.
Table:
BTL-2
Understanding
14
Sample 1 407 411 409
Sample 2 404 406 408 405 402
Sample 3 410 408 406 408
13.
The following table shows the yields per acre of hour different plants
crops grown on lots treated with three different types of fertilizer.
Determine at the 5% significance level whether there is a difference in
yield per acre.
(i) due to the fertilizers and
(ii) due to the crops
Table:
Crop -I Crop -II Crop -III Crop -IV
Fertilizer A 4.5 6.4 7.2 6.7
Fertilizer B 8.8 7.8 9.6 7.0
Fertilizer C 5.9 6.8 5.7 5.2
BTL-2
Understanding
14.
Time of 6 machine operator (in minute) in making product is given
below. Use paired t-test for training effectiveness.
Machine operator 1 2 3 4 5 6
Before training 12 23 4 5 16 17
After training 2 3 10 8 12 6
BTL -3 Applying
PART C
1(a).
What are non-parametric tests? Point out their advantages and
disadvantages?
BTL -6 Creating
1(b).
The success of a sales engineer in adopting the proven sales technique
was found to be 12 out of 30 occasions. Hence he tried a novel
technique and achieved success at a rate of 23 out of 40 occasions.
Check whether the novel technique is effective at 5% level of
significance.
BTL-2 Understanding
2(a).
The following are the final examination marks of three groups of
students who were taught computer by three difference methods.
First method: 94 88 91 74 87 97
Second method: 85 82 79 84 61 72 80
Third method: 89 67 72 76 69
BTL -5 Evaluating
2(b).
A consumer product manufacturing company was selling one of its
leading products through a large number of retail shops. Before a
heavy advertisement campaign, the average sale per week per shop
was 140 dozens. After the campaign, a sample of 26 shops was taken
and the mean sales improved to 147 dozens with a standard deviation
of 16. Check the effectiveness of the advertisement campaign at 5%
level of significance
BTL-2
Understanding
3.
Discuss the test procedure to test hypothesized population proportion
using single sample proportion.
BTL-1 Understanding
15
4.
(i)Write the application testing of hypothesis in statistics. (ii)What is
t-test? When should we apply a t-test?
BTL -3 Applying
UNIT IV: NON-PARAMETRIC TESTS
SYLLABUS: Chi-square test for single sample standard deviation. Chi-square tests for independence ofattributes and
goodness of fit. Sign test for paired data. Rank sum test. Kolmogorov-Smirnov ? test for goodness of fit, comparing two
populations. Mann ? Whitney U test and Kruskal Wallis test. One sample run test.
PART-A
Q.
No.
Question
Bloom?s
Taxonomy
Level
Domain
1. Define Rank Correlation test. BTL-1 Remembering
2. Write the formula in chi square test and any two uses. BTL-1 Remembering
3. Define Rank-Sum test. BTL-1 Remembering
4. Mention the advantages of Nonparametric Tests. BTL-1 Remembering
5. What is the other name or non-parametric test? Why? BTL-6 Creating
6. When are non parametric tests used? BTL-1 Remembering
7. What is the null hypothesis framed in Mann-Whitney test? BTL-6 Creating
8.
Write down the working rule for Mann-Whitney U-test and Kruskal-
Wallis test.
BTL-1 Remembering
9. Explain sign test. BTL-4 Analyzing
10. Define one sample run test? BTL-1 Remembering
11. When is Krushkal-Wallis test used? BTL-1 Remembering
12. Distinguish between Mann-Whitney U-test and Krushkal-Wallis test. BTL-2 Understanding
13. Write the contingency 2*2 table for
test. BTL-5 Evaluating
14.
Write down the formula to calculate rank correlation coefficient
(including tie values).
BTL-1 Remembering
15.
Two HR managers (A and B) ranked five candidates for a new
position. Their rankings of the candidates are show below:
Candidate Rank by A Rank by B
Nancy 2 1
Mary 1 3
John 3 4
Lynda 5 5
Steve 4 2
Compute the Spearman rank correlation.
BTL-6 Creating
16. Define rank correlation co-efficient. BTL-1 Remembering
17.
The following are the ranks obtained by 10 students in Statistics and
Mathematics. Find out the rank correlation coefficient.
Statistics 1 2 3 4 5 6 7
Mathematics 2 5 1 6 7 4 3
BTL-4 Analyzing
18. Explain Kolmogorov-Smirnov Test for one sample problem. BTL-4 Analyzing
19. What adjustment is to be done for tie values to find rank correlation. BTL-6 Creating
20. Mention the properties of linear coefficient of correlation. BTL-1 Remembering
PART -B
1(a).
The scores of a written examination of 24 students, who were trained
by using three different methods, are given below.
Video cassette A 74 88 82 93 55 70 65
BTL-3 Applying
FirstRanker.com - FirstRanker's Choice
1
(An
Ka ttankulathur ?
DEPARTMENT OF MATHEMATICS
QUESTION BANK
I SEMESTER
1918108 ? STATISTICS FOR MANAGEMENT
Regulation ? 2019
Academic Year 2019 - 2020
Prepared by
Ms. B. Vasuki, Assistant Professor/Mathematics
Ms.B.Elakkiavani, Assistant Professor/Mathematics
2
(An
? .
DEPARTMENT OF MATHEMATICS
QUESTION BANK
SUBJECT : 1918108 ? STATISTICS FOR MANAGEMENT
SEM / YEAR : I Semester / I Year
UNIT I - INTRODUCTION
SYLLABUS: Basic definitions and rules for probability, conditional probability independence of events, Baye?s
theorem, and random variables, Probability distributions: Binomial, Poisson, Uniform and Normal distributions.
PART- A
S.NO QUESTIONS
BT Level
COMPETENCE
PART ? A
1. Define Statistics. BTL -6 Creating
2. What is the addition and multiplication theorem on probability. BTL -1 Remembering
3. Distinguish between a priori and posterior probability?. BTL -6 Creating
4.
The price of the selected stock over a five day period shown as 170, 110,
130, 170 and 160. Compute mean , median and mode.
BTL -6 Creating
5.
A car travels 25 miles at 25 mph, 25 miles at 50 mph and 25 miles at 75
mph. Find the harmonic of three velocities?
BTL -4 Analyse
6.
A ball is drawn at random from a box containg 6 red balls, 4 white balls
and 5 blue balls. Find the probability that the ball drawn is not red.
BTL -4 Analyse
7.
Find the median and mode for the weights (kgs) of 15 persons given as
68, 85, 70, 65, 71, 67, 65, 55, 80, 62, 65, 64, 70, 60, 56.
BTL -3 Applying
8. Name few measures of dispersion. BTL -1 Remembering
9. write the common measures of central tendency? BTL -1 Remembering
10. Define continuous and discrete variables examples. BTL -1 Remembering
11.
Let X be the lifetime in years of a mechanical part. Assume that X has
the cdf F(x) = 1- e
-x
, x ? 0. Find P[1< X ? 3].
BTL -1 Remembering
12. Define independent events. BTL -1 Remembering
13. State the theorem of total probability BTL -1 Remembering
14. What is the use of Baye?s theorem? BTL -6 Creating
15. Mention the properties of a discrete probability distribution. BTL -1 Remembering
16. Define a Poisson distribution and mention its mean and variance. BTL -1 Remembering
17. If the mean and variance of a binomial distribution are respectively 6 BTL -3 Applying
3
and 2.4, find P(x=2).
18.
If x is a Poisson distribution such that P(x=1)=4P(x=2). Find its
mean and variance.
BTL -3 Applying
19.
Suppose that X has a Poisson distribution with parameter ? = 2.
Compute P[X ? 1].
BTL -1 Remembering
20. Define mutually exclusive events. BTL -1 Remembering
PART-B
1(a).
Calculate the mean and standard deviation for the following table
giving the age distribution of 542 members.
Age
20-30 30-40 40-50 50-60 60-70 70-80 80-90
No 3 61 132 153 140 51 2
BTL-2 Understanding
1(b).
Find the geometric mean for the following data:
Group
2-4 4-6 6-8 8-10
Frequency 200 400 300 100
BTL-2
Understanding
2(a).
Find the mean, median and modal ages of married women at first
child birth
Age at the
birth of
first child
13
14
15
16
17
18
19
20
21
22
23
24
25
No of
married
women
37
162
343
390
256
433
161
355
65
85
49
46
40
BTL -6 Creating
2(b).
If A and B are independent event with P(A)=2/5, and P(B)=3/5,
find P(A ?B). Let S= {1,2,3,4,5,6} if A = {2,4,6} then find the
probability of A complement.
BTL -3 Applying
3(a).
Given: The probabilities of three events A, B and C occurring are
P(A) = 0.35, P(B) = 0.45 and P(C) = 0.2. Assuming that A, B, or
C has occurred, the probabilities of another event X occurring are
P(X/A) = 0.8, P(X/B) = 0.65 and P(X/C) = 0.3. Find P(A/X),
P(B/X) and P(C/X).
BTL -6 Creating
3(b).
4 cards are drawn from a well shuffled pack of cards. Find the
probability that
(i) All the four are queens
(ii) There is one card from each suit.
(iii) Two cards are diamonds and two are spades
All the four cards are hearts and one of them is jack
BTL -6 Creating
4(a).
Three machines all turn out non ferrous castings. Machine A
produces 1% defective and Machine B- 2% and machine C ? 5%.
Each machine produces 1/3 of the output. An inspector examines
a single casting, which he determines as non defective. Estimate
the probabilities of its having been produced by each machine.
BTL -6 Creating
4(b).
If the random variable X takes values 1, 2, 3, 4 such that
2P(X = 1) = 3P(X = 2) = P( X=3) = 5P(X = 4), find the
probability distribution and cumulative distribution of X.
BTL-2 Understanding
5(a).
Two dice are thrown together once. Find the probabilities for
BTL -3 Applying
4
getting the sum of the two numbers (i) equal to 5, (ii) multiple of
3, (iii) divisible by 4.
5(b).
Given ? = 4.2, for a poisson distribution. Find (a) P(X ? 2) (b)
P(X ? 5) (c) P(X = 8).
BTL -6 Creating
6(a).
An urn contains 5 balls. Two balls are drawn and found to be
white. What is the probability that all the balls are white?
BTL-1 Remembering
6(b).
The contents of urns I, II, III are as follows:
1 white, 2 black and 3 red balls;
2 white, 1 black and 1 red balls;
4 white, 5 black and 3 red balls;
One urn is chosen at random and two balls drawn. They happen to
be white and red. What is the probability that they come from
urns I, II, III?
BTL -3 Applying
7(a).
In 1989, there were three candidates for the position of principal
Mr. Chatterji, Mr. Ayangar and Dr. Singh. Whose chances of
getting the appointment are in the proportion 4:2:3 respectively.
The probability that Mr. Chatterji is selected, would introduce co-
education in the is 0.3. The probabilities of Mr. Ayangar
and Dr. Singh doing the same are respectively 0.5 and .08. What
is the probability that there was co-education in the in
1990?
BTL -3
Applying
7(b).
Find the probability that atmost 5 defective bolts will be found in
a box of 200 bolts, if it is known that 2% of such bolts are
expected to be defective. (e
-4
= 0.0183)
BTL -6 Creating
8(a).
A coin is tossed 6 times what is the probability of obtaining (a) 4
heads (b) 5 heads (c) 6 heads (d) getting 4 or more heads.
BTL -3 Applying
8(b).
In a bolt factory machines A, B, C manufacture respectively 25%,
35% and 40% of the total of their output 5, 4, 2 percent are
defective bolts. If A bolt is drawn at random from the product and
is found to be defective, what are the probabilities that is was
manufactured by machines A, B and C?
BTL -6 Creating
9(a).
In a test of 2000 electric blubs it was found that the life of a
particular make was normally distributed with an average life of
2040 hours and S. D. of 60 hours. Estimate the number of blubs
likely to burn for
(1) More than 2150 hours
(2) Less than 1950 hours
(3) More than 1920 hours but less than 2160 hours.
BTL -3 Applying
9(b).
The latest nationwide political poll indicates that for Americans
who are randomly selected, the probability that they are
conservative is 0.55, the probability that they are liberal is 0.30
and the probability that they are middle of the road is 0.15.
Assuming these probabilities are accurate, answer the following
BTL -4 Analyzing
5
questions from a randomly chosen group of 10 Americans
(a) What the probability that 4 are liberal?
(b) What the probability that none are conservative
(c) What the probability that two are middle of the road
(d) What the probability that a least 8 are liberal
10.
If X follows a normal distribution with mean 12 and variance 16
cm, find the probabilities for (i) X ? 20 (ii) X ? 20, and (iii) 0 ? X
? 12.
BTL -3 Applying
11.
A discerete random variable X has the probability function given
below:
Value of X=x: 0 1 2 3 4 5 6 7
P(X=x) : 0 k 2k 2k 3k k
2
2k
2
7k
2
+k
Find (1) The value of k
(2) P(1.5 < X < 4.5 / X > 2)
(3) P(X < 6), P(X ? 5), P( 0 < X < 4)
(4) The distribution of X.
BTL -3 Applying
12.
X is a normal variable with mean 30 and standard deviation of 5.
Find (i) P[26 ? X ? 40] (ii) P [X?45] (iii) P [ ?X - 30 ?> 5] use
normal distribution tables
BTL -4 Analyzing
13.
In an intelligence test administered on 1000 students, the average
was 42 and standard deviation 24, find (i) the number of students
exceeding a score 50. (ii) the number of students lying between
30 and 54(iii) the value of score exceeded by top 100 students.
BTL -4 Analyzing
14(a).
The probability that an entering student will graduate is 0.4
Determine the probability that out of 5 students atleast one will
graduate.
BTL-5
Evaluating
14(b).
Fit a Poisson Distribution to the following data which gives the
number of doddens in a sample of clover seeds
No 0 1 2 3 4 5 6 7 8
f 56 156 132 92 37 22 4 0 1
.
BTL -4 Analyzing
PART-C
1(a).
A disciplinary committee is formed from the staff of XYZ
Company which has three departments Marketing, Finance and
Production of the 10,5,20 members respectively. All departments
have two female staff each. A department is selected at random
and from which two matters are selected for the committee,
What is the probability that both the team members are female?
BTL-6 Creating
6
1(b).
In a bolt factory machines A, B, C manufacture respectively 25,
35 and 40 percent of the total. Of their output 5, 4 and 2 percent
are defective bolts respectively. A bolt is drawn at random from
the product and is found o be defective. What are the probabilities
that it was manufactured by machines A, B or C?
BTL-2
Understanding
2(a). State Bayes theorem and brief about its applications. BTL-2 Understanding
2(b).
Out of 800 families with 4 children each, how many families
would be expected to have (i) 2 boys and 2 girls (ii) at least 1 boy
(iii) at most 2 girls (iv) children of both sexes? Assume equal
probabilities for boys and girls.
BTL-1 Remembering
3. Describe the classifications of probability ? BTL-1 Remembering
4. What are the applications of Normal distribution in statistics? BTL-6 Creating
UNIT ?II- SAMPLING DISTRIBUTION & ESTIMATION.
SYLLABUS: Introduction to sampling distributions, sampling distribution of mean and proportion, application of central
limit theorem, sampling techniques. Estimation: Point and Interval estimates for population parameters of large sample and
small samples, determining the sample size.
PART - A
S.N
O
QUESTIONS
BT Level
COMPETENCE
1. Define Sampling distribution of proportion. BTL -1 Remembering
2. Define Probable standard error. BTL -1 Remembering
3. Define standard error and mention its importance BTL -1 Remembering
4. Define central limit theorem BTL -1 Remembering
5.
What is the role of central limit theorem in estimation and testing
problems
BTL -6 Creating
6. Define stratified sampling technique BTL -1 Remembering
7. Briefly describe the significance level. BTL -1 Remembering
8. Distinguish between parameter and statistic. BTL -2 Understanding
9. Define estimator, estimate and estimation. BTL -1 Remembering
10. Distinguish between point estimation and interval estimation BTL -2 Understanding
11. Mention the properties of a good estimator. BTL -1 Remembering
12. Define confidence coefficient. BTL -1 Remembering
13. What is the level of significance in testing of hypothesis BTL -6 Creating
14. Define confidence limits for a parameter BTL -1 Remembering
15.
State the conditions under which a binomial distribution becomes a
normal distribution
BTL -4 Analyzing
16.
If the random sample comes from a normal population, what can
be said about the sampling distribution of the mean.
BTL -5 Evaluating
17.
An automobile repair shop has taken a random sample of 40
services that the average service time on an automobile is 130
minutes with a standard deviation of 26 minutes. Compute the
standard error of the mean.
BTL -6 Creating
7
18. What is a random number? How it is useful in sampling? BTL -6 Creating
19.
A population has the numbers: 12, 8, 10, 30, 12, 16, 40, 5, 16, 24,
22, 31, 30, 16, 15. Draw a systematic sample of size 5. Find out its
mean.
BTL -3 Applying
20. How large sample is useful in estimation and testing BTL -4 Analyzing
PART -B
1(a).
A random sample of 700 units from a large consignment showed
that 200 were damaged. Find (i) 95% (ii) 99% confidence limits
for the proportion of damaged units in the consignment.
BTL -3 Applying
1(b).
A random sample of size 9 is obtained from a Normal population
with mean 25 and if the variance 100 find the probability that the
sample mean exceeds 31.2.
BTL -4 Analyzing
2(a).
In a normally distributed population, average income per
household is Rs.20,000 with a standard deviation of Rs. 1,600.
Find the probability that the sample mean will be between
Rs.19,600 and Rs.20,200 in a survey of a random sample of 100
households.
BTL -6 Creating
2(b).
A university wants to determine the percentage of students who
would accept proposed fees hike for improving facilities. The
university wants to be 90% confident that the percentage is
within2% of the true value. Find the sample size to achieve the
accuracy regardless of the true percentage assuming the percentage
of students accepting the increase in tuition fees to be 0.5.
BTL -6 Creating
3(a).
A bank has kept records of the checking balances of its customers
and determined that the average daily balances of its customers is
Rs.300 with a standard deviation of Rs. 48. A random sample of
144 checking accounts is selected.
(i) What is the probability that the sample mean will be more
than Rs. 306.60?
(ii) What is the probability that the sample mean will be less
than Rs. 308?
BTL -6 Creating
3(b).
From the question 3(a)
(i) What is probability that the sample mean will between Rs.
302 and Rs. 308?
(ii) What is probability that the sample mean will be atleast
Rs. 296?
BTL -6 Creating
4(a).
Explain Stratified sampling technique and discuss how it is better
than simple random sampling in a particular situation.
BTL -4
Analyzing
4(b). Discuss the standard error of proportion BTL-2 Understanding
5.
Explain the methods of drawing simple random sample from a
finite population.
BTL -4 Analyzing
8
6(a).
In a sample of 1000 citizens of India, 540 are wheat eaters and the
rest are rice eaters. Can we assume that both rice and wheat
equally popular in India at 1 % level of significance?
BTL-5
Evaluating
6(b).
A simple random sample of 144 items resulted in a sample mean
of 1257.85 and standard deviation of 480. Develop a 95%
confidence interval for the population mean
BTL -6
Creating
7(a).
A car dealer wants to estimate the proportion of customers who
still own the cars they purchased 5 years earlier. A random sample
of 500 customers selected from the dealer?s records indicate that
315 customers still own cars that they were purchased 5 years
earlier. Set up 95% confidence interval estimation of the
population proportion of all the customers who still own the cars 5
years after they were purchased.
BTL-2
Understanding
7(b).
A movie maker sampled 55 fans who viewed his master piece
movie and asked them whether they had planned to see it again.
Only 10 of them believed that the movie was worthy of a second
look. Find the standard error of the population of fans who will
view the film a second time. Construct a 90% confidence interval
for this population.
BTL -5 Evaluating
8(a).
From a population of size 600, a sample of 60 individuals revealed
mean and standard deviation as 6.2 and 1.45 respectively. (i) Find
the estimated standard error (ii) Construct 96% confidence
interval for the mean.
BTL -3 Applying
8(b).
The age of employees in a company follows normal distribution
with its mean and variance as 40 years and 121 years respectively.
If a random sample of 36 employees is taken from a finite normal
population of size 1000, what is the probability that the sample
mean is
(i) less than 45
(ii) greater than 42 and
(iii) between 40 and 42?
BTL -6
Creating
9(a).
A firm wishes to estimate with an error of not more than 0.03 and
a level of confidence of 98%, the proportion of consumers that
prefer its brand of household detergent. Sales report indicate the
about 0.20 of all consumers prefer the firm?s brand. What is the
requisite sample size?
BTL -5 Evaluating
9(b).
A random sample of 700 units from a large consignment should
that 200 were damaged.
Find (i) 95%
(ii) 99% confidence limits for the proportion of damaged
units in the consignment
BTL -3 Applying
10(a).
From a population of 500 items with a mean of 100 gms and
standard deviation of 12.5 gms, 65 items were chosen. (i) What is
the standard error? (ii) Find P(99.5 < X < 101.5).
BTL -6 Creating
10(b).
A non-normal distribution representing the number of trips
BTL -6 Creating
9
performed by lorries per week in a coal field has a mean of 100
trips and variance of 121 trips. A random sample of 36 lorries is
taken from the non-normal population. What is the probability that
the sample mean is
(i) greater than 105
(ii) less than 102
(iii) between 101 and 103 trips?
11.
Test the significance of the difference between the means of the
sample from the following data
Size of sample Mean SD
Sample A 100 61 4
Sample B 200 63 6
BTL -4 Analyzing
12(a).
A cigarete manufacturing firm claims that its brand. A outsells
brand B by 8%. If it is found that 42 out of a sample of 200
smokers prefer brand a and 18 out of another sample of 100
smokers prefer brand B, test whether the 8% difference is a valid
claim(use 5% level of significance).
BTL -4
Analyzing
12(b).
In an automotive safety test conducted by the North Carolina
Highway Safety Research center, the average tyre pressure in a
sample of 62 tyres was found to be 24 pounds per square inch, and
the standard deviation was 2.1 pounds per square inch.
(i) What is the estimated population standard deviation for this
population
(ii) Calculate the estimated standard error of the mean
(iii) Construct a 95% confidence interval for the population mean.
BTL -3 Applying
13(a).
The manager of a shop selling beverages wants to estimate the
actual amount of beverages in one litre bottles from a nationally
known manufacturer. As per manufacturer?s specifications, the
standard deviation of the volume of the beverage is 0.02 litre. The
average amount of beverage per 1 litre bottle is found to be 0.995
litre on checking 50 bottles. Setup 99% confidence interval
estimate of the true population average amount of beverage in a 1
liter bottle. Check whether the manufacturer is genuine in filling
the beverage.
BTL -6
Creating
13(b).
In a batch chemical process used for etching printed circuit boards,
two different catalysts are being compared to determine whether
they require different emersion times for removal of identical
quantities of photo resist material. Twelve batch were run with
catalyst 1, resulting in a sample mean emersion time of 24.6
minutes and sample standard deviation of 0.85 minutes. Fifteen
batches were run with catalyst 2, resulting in a mean emersion time
of 22.1 minutes and a standard deviation of 0.98 minutes. Find a
95% confidence interval on the difference in means, assuming that
2
2
2
1
? ? ? .
BTL -3 Applying
10
14.
In a random sample of 75 axle shafts. 12 have a surface finish that
is rougher than the specifications will allow. Suppose that a
modification is made in the surface finishing process and
subsequently a second random sample of 85 axle shafts is
obtained. The number of defective shafts in this second sample is
10. Obtain an approximate 95% confidence interval on the
difference in the proportions of defectives produced under the two
processes
BTL -5 Evaluating
PART-C
1.
In a sample of 25 observations from a Normal distribution with
mean 98.6 and standard deviation 17.2.
(i)What is P(92<102)
(ii)Find the corresponding probability given a sample of 36.
BTL -6 Creating
2.
Mary, an auditor for a large credit card company, knows that, on
average, the monthly balance of any customer is Rs.112, and the
standard deviation is Rs.56. If Mary audits 50 randomly selected
accounts, What is the probability that the sample average balance
is
(i) Below Rs. 100
(ii)Between Rs.100 and Rs.130
BTL -6 Creating
3(a).
Write the type of sampling methods and the uses of standard error?
BTL -1 Remembering
3(b).
From a population of 540, a sample of 60 individual is taken. From
this sample, the mean is found to 6.2 and the standard deviation
1.368
(i) Find the estimated standard error of the mean.
(ii) Construct a 96 % confidence interval for the mean.
BTL-2 Understanding
4(a).
Explain the properties of good point estimator.
BTL -4 Analyzing
4(b).
What do you mean by interval estimation? Give examples
BTL-6 Creating
UNIT III - TESTS OF HYPOTHESIS- PARAMETRIC TESTS
SYLLABUS: Hypothesis testing: one sample and two sample tests for means and proportions of large samples (z-test),
one sample and two sample tests for means of small samples (t-test), F-test for two sample standard deviations. ANOVA
one and two way.
PART-A
Q.
No.
Question
Bloom?s
Taxonomy
Level
Domain
1. Define Test of Significance. BTL-1 Remembering
2. What are the Type I and Type II errors? BTL-6 Creating
3. What do you mean by one tail test? BTL-6 Creating
4. State the applications of Z-test and t-test. BTL-4 Analyzing
5. Define critical region BTL-1 Remembering
6. Distinguish between one tail and two tail tests BTL-2 Understanding
7. What is the aim of design of experiments? BTL-6 Creating
8. Distinguish between one-way and two-way analysis of variance. BTL-2 Understanding
9. When does the Z-test apply? BTL-1 Remembering
10. Explain SSB , SSW and SSY
and relationship in ANOVA. BTL-4 Analyzing
11
11. Describe any two applications of t-distribution BTL-1 Remembering
12. Write the uses of F-test? BTL-6 Creating
13. Define the level of significance. BTL-1 Remembering
14. Write the properties of t-distribution? BTL-6 Creating
15. What is the role of standard error? BTL-6 Creating
16. Mention any four applications of t-distribution in tests of hypothesis. BTL-1 Remembering
17. Mention any four uses of Chi-square distribution in test of hypothesis. BTL-1 Remembering
18. Define null hypothesis ? Explain. BTL-6 Creating
19.
Estimate the standard error of difference between two proportion if
p
1
=0.10,p
2=
0.133 and n
1
=50,n
2
=75.
BTL-6 Creating
20.
Mention any two assumptions made in analysis of variance
techniques.
BTL-1 Remembering
PART-B
1(a).
A study compares the effect of four 1-month point-of-purchase
promotions on sales. The unit sales for five stores using all four
promotions in different months follow.
Free Sample
78 87 81 89 58
One-pack gift
94 91 87 90 88
Cents off
73 73 78 69 83
76Refund by mail
79 83 78 69 81
(i)Compute the mean unit sales for each promotion and then
determine the grand mean.
(ii)Estimate the population variance using the between column
variance.
BTL-5 Evaluating
1(b).
From the question 1(a)
(i)Estimate the population variance using the within-column variance
computed from the variance within the samples.
(ii)Calculate the F ratio. At the 0.01 level of significance, do the
promotions produce different effects on sales.
BTL-2 Understanding
2(a).
In a low cost Toy production system, the molding machine has been
set with standard of 1% defective. The 80 sample units produced from
this machine shows defective of one unit. Is it necessary to stop the
product for corrective mechanism? Test at 5% level of significance
BTL-5 Evaluating
2(b).
Block Enterprises, a manufacturer of chips for computers. Is in the
process of deciding whether to replace its current semi automated
assembly line with a fully automated assembly line. Block has
gathered some preliminary test data about hourly chip production,
which is summarized in the following table, and it would like to know
whether it should upgrade its assembly line. State (and test at a =0.02)
appropriate hypothesis to help Block decide.
BTL-5 Evaluating
3(a).
Three samples below have been obtained from normal population
with equal variance. Test the hypothesis that the means are equal.
Sample I : 10 12 18 15 16
Sample II : 7 15 10 12 8
Sample III : 12 8 15 16 15
BTL-5 Evaluating
3(b). The I.Q.s of 16 students from one class of an showed a BTL-2 Understanding
12
mean of 107 with a standard deviation of 10, while the I.Q.s of 14
students from another class showed a mean of 112 with a standard
deviation of 8. Check whether there is an appreciable difference
between the I.Q.s of the two groups at (i) 0.01and (ii) 0.05 level of
significance
4(a).
The following is the information obtained from a random sample of 5
observations. Assume the population has a normal distribution.
30 31 27 32 28
To test if the sample was drawn from a normal distribution with mean
less than 30, (i)State the null and alternative hypotheses
(ii)Compute the standard error.
BTL-2 Understanding
4(b).
From the question 4(a)
(i)Determine the test statistic.
(ii)Decide at 10% level whether or not the mean value could be
greater than 30
BTL-2 Understanding
5.
The following data relate to the number of units produced per week by
three methods.
Method 1 : 170 192 190 120
Method 2 : 160 165 170 172
Method 3 : 182 190 170 178 185
Prepare ANOVA table and write your comments
BTL-6 Creating
6(a).
Test if the following samples could have come from two populations
with the same means, assuming the population variances are equal.
Sample I Sample II
Sample size 12 10
Sample Mean 40.5 43.8
Sample variance 2.6 3.2
BTL-5 Evaluating
6(b).
The weights of 10 people of a locality are found to be
70,67,62,68,61,68,70,64,64,66 kilograms. Is it reasonable to believe
that the average weights of the people of locality is greater than 64
kg? Test at 5%level of significance.
BTL-5 Evaluating
7(a).
In Town A, there were 850 birds of which 52% was males, while in
Town A and Town B combined, the proportion of males in a total of
1200 birds was 0.49. Is there any significance difference in the
proportions of male birds in the two Towns?
BTL-2
Understanding
7(b).
IQ test result of randomly selected five employees in an organization
is given below. Test whether minimum requirement of average IQ
level 87 is maintained in that company or not.
Employee code 234 232 121 343 111
IQ test 85 95 90 93 87
BTL-4 Analyzing
8(a).
The weights of 8 persons are found to be 60, 65, 70, 68, 62, 63, 60,
and 66 kgs. The weights of another group of 12 persons are found to
be 70, 60, 58, 56, 50, 48, 52, 56, 52, 50, 54, and 50. Can we conclude
that both samples have come from populations with same variances?
BTL -4 Analyzing
13
8(b).
ATMs must be stocked with enough cash to meet the requirements of
customers over a week, but excess cash results in loss of income as
investment opportunities could not be utilized. In an ATM, the
average transaction per customer in a week is Rs.8000 with a standard
deviation of Rs.1500. If a random sample of 36 customer transactions
is examined and it is observed that the sample mean with drawl is
Rs.8600, check the belief that the true average withdrawal is no longer
Rs.8000. Assume 0.05 level of significance
BTL -3 Applying
9.
Apply ANOVA technique and write your comment regarding the
sales(in Rs. Lakhs)
Area
Representatives
1 2 3 4
A 12 16 20 18
B 15 10 12 16
C 10 08 16 15
BTL -3 Applying
10(a).
A farmer wishes to determine whether there is a difference in yields
between two different varieties of wheat I and II. The following data
shows the production of wheat per unit area using the two varieties.
Can the farmer conclude at significance levels of
(i) 0.05
(ii) 0.01 that a difference exists?
BTL -4 Analyzing
10(b).
Test if the samples could have come from equal population means.
Sample A Sample B
Size 200 400
Mean 154.8 164.3
Variance 15.2 18.2
BTL-5 Evaluating
11(a).
The number of accidents per week in a city are as follows:
12, 8, 20, 2, 14, 10, 15, 6, 9 and 4. Are these frequencies in agreement
with the belief that accident conditions were the same during this 10
weeks period?
BTL -4
Analyzing
11(b).
Two samples are drawn from two normal population. From the
following data, Test whether the two samples have the same variance
5% level of significance.
Sample 1 60 65 69 74 76 82 85 87
Sample 2 61 66 67 85 78 63 85 86 88 91
BTL -3 Applying
12(a).
Given a sample mean of 83, a sample standard deviation of 12.5 and a
sample size of 22, test the hypothesis that the value of the population
mean is 70 against alternative that it is more than 70. Use the 0.025
significance level.
BTL-2
Understanding
12(b).
The following table shows the lifetimes in hours of samples from
three different types of television tables manufactured by a company.
Determine whether there is a difference between the three types at
significance level of 0.01.
Table:
BTL-2
Understanding
14
Sample 1 407 411 409
Sample 2 404 406 408 405 402
Sample 3 410 408 406 408
13.
The following table shows the yields per acre of hour different plants
crops grown on lots treated with three different types of fertilizer.
Determine at the 5% significance level whether there is a difference in
yield per acre.
(i) due to the fertilizers and
(ii) due to the crops
Table:
Crop -I Crop -II Crop -III Crop -IV
Fertilizer A 4.5 6.4 7.2 6.7
Fertilizer B 8.8 7.8 9.6 7.0
Fertilizer C 5.9 6.8 5.7 5.2
BTL-2
Understanding
14.
Time of 6 machine operator (in minute) in making product is given
below. Use paired t-test for training effectiveness.
Machine operator 1 2 3 4 5 6
Before training 12 23 4 5 16 17
After training 2 3 10 8 12 6
BTL -3 Applying
PART C
1(a).
What are non-parametric tests? Point out their advantages and
disadvantages?
BTL -6 Creating
1(b).
The success of a sales engineer in adopting the proven sales technique
was found to be 12 out of 30 occasions. Hence he tried a novel
technique and achieved success at a rate of 23 out of 40 occasions.
Check whether the novel technique is effective at 5% level of
significance.
BTL-2 Understanding
2(a).
The following are the final examination marks of three groups of
students who were taught computer by three difference methods.
First method: 94 88 91 74 87 97
Second method: 85 82 79 84 61 72 80
Third method: 89 67 72 76 69
BTL -5 Evaluating
2(b).
A consumer product manufacturing company was selling one of its
leading products through a large number of retail shops. Before a
heavy advertisement campaign, the average sale per week per shop
was 140 dozens. After the campaign, a sample of 26 shops was taken
and the mean sales improved to 147 dozens with a standard deviation
of 16. Check the effectiveness of the advertisement campaign at 5%
level of significance
BTL-2
Understanding
3.
Discuss the test procedure to test hypothesized population proportion
using single sample proportion.
BTL-1 Understanding
15
4.
(i)Write the application testing of hypothesis in statistics. (ii)What is
t-test? When should we apply a t-test?
BTL -3 Applying
UNIT IV: NON-PARAMETRIC TESTS
SYLLABUS: Chi-square test for single sample standard deviation. Chi-square tests for independence ofattributes and
goodness of fit. Sign test for paired data. Rank sum test. Kolmogorov-Smirnov ? test for goodness of fit, comparing two
populations. Mann ? Whitney U test and Kruskal Wallis test. One sample run test.
PART-A
Q.
No.
Question
Bloom?s
Taxonomy
Level
Domain
1. Define Rank Correlation test. BTL-1 Remembering
2. Write the formula in chi square test and any two uses. BTL-1 Remembering
3. Define Rank-Sum test. BTL-1 Remembering
4. Mention the advantages of Nonparametric Tests. BTL-1 Remembering
5. What is the other name or non-parametric test? Why? BTL-6 Creating
6. When are non parametric tests used? BTL-1 Remembering
7. What is the null hypothesis framed in Mann-Whitney test? BTL-6 Creating
8.
Write down the working rule for Mann-Whitney U-test and Kruskal-
Wallis test.
BTL-1 Remembering
9. Explain sign test. BTL-4 Analyzing
10. Define one sample run test? BTL-1 Remembering
11. When is Krushkal-Wallis test used? BTL-1 Remembering
12. Distinguish between Mann-Whitney U-test and Krushkal-Wallis test. BTL-2 Understanding
13. Write the contingency 2*2 table for
test. BTL-5 Evaluating
14.
Write down the formula to calculate rank correlation coefficient
(including tie values).
BTL-1 Remembering
15.
Two HR managers (A and B) ranked five candidates for a new
position. Their rankings of the candidates are show below:
Candidate Rank by A Rank by B
Nancy 2 1
Mary 1 3
John 3 4
Lynda 5 5
Steve 4 2
Compute the Spearman rank correlation.
BTL-6 Creating
16. Define rank correlation co-efficient. BTL-1 Remembering
17.
The following are the ranks obtained by 10 students in Statistics and
Mathematics. Find out the rank correlation coefficient.
Statistics 1 2 3 4 5 6 7
Mathematics 2 5 1 6 7 4 3
BTL-4 Analyzing
18. Explain Kolmogorov-Smirnov Test for one sample problem. BTL-4 Analyzing
19. What adjustment is to be done for tie values to find rank correlation. BTL-6 Creating
20. Mention the properties of linear coefficient of correlation. BTL-1 Remembering
PART -B
1(a).
The scores of a written examination of 24 students, who were trained
by using three different methods, are given below.
Video cassette A 74 88 82 93 55 70 65
BTL-3 Applying
16
Audio cassette B 78 80 65 57 89 85 78 70
Class Room C 68 83 50 91 84 77 94 81 92
Use Krushkal-Wallis test at ? = 5% level of significance, whether the
three methods of training yield the same results.
1(b). Explain Rank sum tests and its applications
2(a).
The production volume of units assembled by three different
operators during 9 shifts is summarized below. Check whether there
is significant difference between the production volumes of units
assembled by the three operators using Krushkal-Wallis test at a
significant level of 0.05.
Operator I 29 34 34 20 32 45 42 24 35
Operator II 30 21 23 25 44 37 34 19 38
Operator III 26 36 41 48 27 39 28 46 15
BTL-3
Applying
2(b).
Two faculty members ranked 12 candidates for scholarships.
Calculate the spearman rank-correlation coefficient and test it for
significance. Use 0.02level of significance.
Candidate Rank by Professor A Rank by Professor B
1 6 5
2 10 11
3 2 6
4 1 3
5 5 4
6 11 12
7 4 2
8 3 1
9 7 7
10 12 10
11 9 8
12 8 9
BTL-3
Applying
3(a).
In a study of sedimentary rocks, the following data were obtained
from samples of 32 grains from two kinds of sand :
Apply Mann-Whitney U test with suitable null and alternative
hypotheses.
Sand I 63 17 35 49 18 43 12 20 47
? 136 51 45 84 32 40 44 25
Sand II 113 54 96 26 39 88 92 53 101
? 48 89 107 111 58 62
BTL -3 Applying
3(b).
The Molisa?s shop has 3 mall locations. She keeps a daily record for
each locations of the number of the customers who actually make a
purchase. A sample of these data follows. Using Kruskal- Wallis test
can you say that at 5% level of significance that her stores have the
same number of customers who buy.
Eastowin 99 64 101 85 79 88 97 95 90 100
Craborchard 83 102 125 61 91 96 94 89 93 75
Fair forest 89 98 56 105 87 90 87 101 76 89
BTL -3 Applying
4(a)
The following are the prices in Rs. per kg of a commodity from 2
random samples of shops from 2 cities A&B.
BTL -3 Applying
FirstRanker.com - FirstRanker's Choice
1
(An
Ka ttankulathur ?
DEPARTMENT OF MATHEMATICS
QUESTION BANK
I SEMESTER
1918108 ? STATISTICS FOR MANAGEMENT
Regulation ? 2019
Academic Year 2019 - 2020
Prepared by
Ms. B. Vasuki, Assistant Professor/Mathematics
Ms.B.Elakkiavani, Assistant Professor/Mathematics
2
(An
? .
DEPARTMENT OF MATHEMATICS
QUESTION BANK
SUBJECT : 1918108 ? STATISTICS FOR MANAGEMENT
SEM / YEAR : I Semester / I Year
UNIT I - INTRODUCTION
SYLLABUS: Basic definitions and rules for probability, conditional probability independence of events, Baye?s
theorem, and random variables, Probability distributions: Binomial, Poisson, Uniform and Normal distributions.
PART- A
S.NO QUESTIONS
BT Level
COMPETENCE
PART ? A
1. Define Statistics. BTL -6 Creating
2. What is the addition and multiplication theorem on probability. BTL -1 Remembering
3. Distinguish between a priori and posterior probability?. BTL -6 Creating
4.
The price of the selected stock over a five day period shown as 170, 110,
130, 170 and 160. Compute mean , median and mode.
BTL -6 Creating
5.
A car travels 25 miles at 25 mph, 25 miles at 50 mph and 25 miles at 75
mph. Find the harmonic of three velocities?
BTL -4 Analyse
6.
A ball is drawn at random from a box containg 6 red balls, 4 white balls
and 5 blue balls. Find the probability that the ball drawn is not red.
BTL -4 Analyse
7.
Find the median and mode for the weights (kgs) of 15 persons given as
68, 85, 70, 65, 71, 67, 65, 55, 80, 62, 65, 64, 70, 60, 56.
BTL -3 Applying
8. Name few measures of dispersion. BTL -1 Remembering
9. write the common measures of central tendency? BTL -1 Remembering
10. Define continuous and discrete variables examples. BTL -1 Remembering
11.
Let X be the lifetime in years of a mechanical part. Assume that X has
the cdf F(x) = 1- e
-x
, x ? 0. Find P[1< X ? 3].
BTL -1 Remembering
12. Define independent events. BTL -1 Remembering
13. State the theorem of total probability BTL -1 Remembering
14. What is the use of Baye?s theorem? BTL -6 Creating
15. Mention the properties of a discrete probability distribution. BTL -1 Remembering
16. Define a Poisson distribution and mention its mean and variance. BTL -1 Remembering
17. If the mean and variance of a binomial distribution are respectively 6 BTL -3 Applying
3
and 2.4, find P(x=2).
18.
If x is a Poisson distribution such that P(x=1)=4P(x=2). Find its
mean and variance.
BTL -3 Applying
19.
Suppose that X has a Poisson distribution with parameter ? = 2.
Compute P[X ? 1].
BTL -1 Remembering
20. Define mutually exclusive events. BTL -1 Remembering
PART-B
1(a).
Calculate the mean and standard deviation for the following table
giving the age distribution of 542 members.
Age
20-30 30-40 40-50 50-60 60-70 70-80 80-90
No 3 61 132 153 140 51 2
BTL-2 Understanding
1(b).
Find the geometric mean for the following data:
Group
2-4 4-6 6-8 8-10
Frequency 200 400 300 100
BTL-2
Understanding
2(a).
Find the mean, median and modal ages of married women at first
child birth
Age at the
birth of
first child
13
14
15
16
17
18
19
20
21
22
23
24
25
No of
married
women
37
162
343
390
256
433
161
355
65
85
49
46
40
BTL -6 Creating
2(b).
If A and B are independent event with P(A)=2/5, and P(B)=3/5,
find P(A ?B). Let S= {1,2,3,4,5,6} if A = {2,4,6} then find the
probability of A complement.
BTL -3 Applying
3(a).
Given: The probabilities of three events A, B and C occurring are
P(A) = 0.35, P(B) = 0.45 and P(C) = 0.2. Assuming that A, B, or
C has occurred, the probabilities of another event X occurring are
P(X/A) = 0.8, P(X/B) = 0.65 and P(X/C) = 0.3. Find P(A/X),
P(B/X) and P(C/X).
BTL -6 Creating
3(b).
4 cards are drawn from a well shuffled pack of cards. Find the
probability that
(i) All the four are queens
(ii) There is one card from each suit.
(iii) Two cards are diamonds and two are spades
All the four cards are hearts and one of them is jack
BTL -6 Creating
4(a).
Three machines all turn out non ferrous castings. Machine A
produces 1% defective and Machine B- 2% and machine C ? 5%.
Each machine produces 1/3 of the output. An inspector examines
a single casting, which he determines as non defective. Estimate
the probabilities of its having been produced by each machine.
BTL -6 Creating
4(b).
If the random variable X takes values 1, 2, 3, 4 such that
2P(X = 1) = 3P(X = 2) = P( X=3) = 5P(X = 4), find the
probability distribution and cumulative distribution of X.
BTL-2 Understanding
5(a).
Two dice are thrown together once. Find the probabilities for
BTL -3 Applying
4
getting the sum of the two numbers (i) equal to 5, (ii) multiple of
3, (iii) divisible by 4.
5(b).
Given ? = 4.2, for a poisson distribution. Find (a) P(X ? 2) (b)
P(X ? 5) (c) P(X = 8).
BTL -6 Creating
6(a).
An urn contains 5 balls. Two balls are drawn and found to be
white. What is the probability that all the balls are white?
BTL-1 Remembering
6(b).
The contents of urns I, II, III are as follows:
1 white, 2 black and 3 red balls;
2 white, 1 black and 1 red balls;
4 white, 5 black and 3 red balls;
One urn is chosen at random and two balls drawn. They happen to
be white and red. What is the probability that they come from
urns I, II, III?
BTL -3 Applying
7(a).
In 1989, there were three candidates for the position of principal
Mr. Chatterji, Mr. Ayangar and Dr. Singh. Whose chances of
getting the appointment are in the proportion 4:2:3 respectively.
The probability that Mr. Chatterji is selected, would introduce co-
education in the is 0.3. The probabilities of Mr. Ayangar
and Dr. Singh doing the same are respectively 0.5 and .08. What
is the probability that there was co-education in the in
1990?
BTL -3
Applying
7(b).
Find the probability that atmost 5 defective bolts will be found in
a box of 200 bolts, if it is known that 2% of such bolts are
expected to be defective. (e
-4
= 0.0183)
BTL -6 Creating
8(a).
A coin is tossed 6 times what is the probability of obtaining (a) 4
heads (b) 5 heads (c) 6 heads (d) getting 4 or more heads.
BTL -3 Applying
8(b).
In a bolt factory machines A, B, C manufacture respectively 25%,
35% and 40% of the total of their output 5, 4, 2 percent are
defective bolts. If A bolt is drawn at random from the product and
is found to be defective, what are the probabilities that is was
manufactured by machines A, B and C?
BTL -6 Creating
9(a).
In a test of 2000 electric blubs it was found that the life of a
particular make was normally distributed with an average life of
2040 hours and S. D. of 60 hours. Estimate the number of blubs
likely to burn for
(1) More than 2150 hours
(2) Less than 1950 hours
(3) More than 1920 hours but less than 2160 hours.
BTL -3 Applying
9(b).
The latest nationwide political poll indicates that for Americans
who are randomly selected, the probability that they are
conservative is 0.55, the probability that they are liberal is 0.30
and the probability that they are middle of the road is 0.15.
Assuming these probabilities are accurate, answer the following
BTL -4 Analyzing
5
questions from a randomly chosen group of 10 Americans
(a) What the probability that 4 are liberal?
(b) What the probability that none are conservative
(c) What the probability that two are middle of the road
(d) What the probability that a least 8 are liberal
10.
If X follows a normal distribution with mean 12 and variance 16
cm, find the probabilities for (i) X ? 20 (ii) X ? 20, and (iii) 0 ? X
? 12.
BTL -3 Applying
11.
A discerete random variable X has the probability function given
below:
Value of X=x: 0 1 2 3 4 5 6 7
P(X=x) : 0 k 2k 2k 3k k
2
2k
2
7k
2
+k
Find (1) The value of k
(2) P(1.5 < X < 4.5 / X > 2)
(3) P(X < 6), P(X ? 5), P( 0 < X < 4)
(4) The distribution of X.
BTL -3 Applying
12.
X is a normal variable with mean 30 and standard deviation of 5.
Find (i) P[26 ? X ? 40] (ii) P [X?45] (iii) P [ ?X - 30 ?> 5] use
normal distribution tables
BTL -4 Analyzing
13.
In an intelligence test administered on 1000 students, the average
was 42 and standard deviation 24, find (i) the number of students
exceeding a score 50. (ii) the number of students lying between
30 and 54(iii) the value of score exceeded by top 100 students.
BTL -4 Analyzing
14(a).
The probability that an entering student will graduate is 0.4
Determine the probability that out of 5 students atleast one will
graduate.
BTL-5
Evaluating
14(b).
Fit a Poisson Distribution to the following data which gives the
number of doddens in a sample of clover seeds
No 0 1 2 3 4 5 6 7 8
f 56 156 132 92 37 22 4 0 1
.
BTL -4 Analyzing
PART-C
1(a).
A disciplinary committee is formed from the staff of XYZ
Company which has three departments Marketing, Finance and
Production of the 10,5,20 members respectively. All departments
have two female staff each. A department is selected at random
and from which two matters are selected for the committee,
What is the probability that both the team members are female?
BTL-6 Creating
6
1(b).
In a bolt factory machines A, B, C manufacture respectively 25,
35 and 40 percent of the total. Of their output 5, 4 and 2 percent
are defective bolts respectively. A bolt is drawn at random from
the product and is found o be defective. What are the probabilities
that it was manufactured by machines A, B or C?
BTL-2
Understanding
2(a). State Bayes theorem and brief about its applications. BTL-2 Understanding
2(b).
Out of 800 families with 4 children each, how many families
would be expected to have (i) 2 boys and 2 girls (ii) at least 1 boy
(iii) at most 2 girls (iv) children of both sexes? Assume equal
probabilities for boys and girls.
BTL-1 Remembering
3. Describe the classifications of probability ? BTL-1 Remembering
4. What are the applications of Normal distribution in statistics? BTL-6 Creating
UNIT ?II- SAMPLING DISTRIBUTION & ESTIMATION.
SYLLABUS: Introduction to sampling distributions, sampling distribution of mean and proportion, application of central
limit theorem, sampling techniques. Estimation: Point and Interval estimates for population parameters of large sample and
small samples, determining the sample size.
PART - A
S.N
O
QUESTIONS
BT Level
COMPETENCE
1. Define Sampling distribution of proportion. BTL -1 Remembering
2. Define Probable standard error. BTL -1 Remembering
3. Define standard error and mention its importance BTL -1 Remembering
4. Define central limit theorem BTL -1 Remembering
5.
What is the role of central limit theorem in estimation and testing
problems
BTL -6 Creating
6. Define stratified sampling technique BTL -1 Remembering
7. Briefly describe the significance level. BTL -1 Remembering
8. Distinguish between parameter and statistic. BTL -2 Understanding
9. Define estimator, estimate and estimation. BTL -1 Remembering
10. Distinguish between point estimation and interval estimation BTL -2 Understanding
11. Mention the properties of a good estimator. BTL -1 Remembering
12. Define confidence coefficient. BTL -1 Remembering
13. What is the level of significance in testing of hypothesis BTL -6 Creating
14. Define confidence limits for a parameter BTL -1 Remembering
15.
State the conditions under which a binomial distribution becomes a
normal distribution
BTL -4 Analyzing
16.
If the random sample comes from a normal population, what can
be said about the sampling distribution of the mean.
BTL -5 Evaluating
17.
An automobile repair shop has taken a random sample of 40
services that the average service time on an automobile is 130
minutes with a standard deviation of 26 minutes. Compute the
standard error of the mean.
BTL -6 Creating
7
18. What is a random number? How it is useful in sampling? BTL -6 Creating
19.
A population has the numbers: 12, 8, 10, 30, 12, 16, 40, 5, 16, 24,
22, 31, 30, 16, 15. Draw a systematic sample of size 5. Find out its
mean.
BTL -3 Applying
20. How large sample is useful in estimation and testing BTL -4 Analyzing
PART -B
1(a).
A random sample of 700 units from a large consignment showed
that 200 were damaged. Find (i) 95% (ii) 99% confidence limits
for the proportion of damaged units in the consignment.
BTL -3 Applying
1(b).
A random sample of size 9 is obtained from a Normal population
with mean 25 and if the variance 100 find the probability that the
sample mean exceeds 31.2.
BTL -4 Analyzing
2(a).
In a normally distributed population, average income per
household is Rs.20,000 with a standard deviation of Rs. 1,600.
Find the probability that the sample mean will be between
Rs.19,600 and Rs.20,200 in a survey of a random sample of 100
households.
BTL -6 Creating
2(b).
A university wants to determine the percentage of students who
would accept proposed fees hike for improving facilities. The
university wants to be 90% confident that the percentage is
within2% of the true value. Find the sample size to achieve the
accuracy regardless of the true percentage assuming the percentage
of students accepting the increase in tuition fees to be 0.5.
BTL -6 Creating
3(a).
A bank has kept records of the checking balances of its customers
and determined that the average daily balances of its customers is
Rs.300 with a standard deviation of Rs. 48. A random sample of
144 checking accounts is selected.
(i) What is the probability that the sample mean will be more
than Rs. 306.60?
(ii) What is the probability that the sample mean will be less
than Rs. 308?
BTL -6 Creating
3(b).
From the question 3(a)
(i) What is probability that the sample mean will between Rs.
302 and Rs. 308?
(ii) What is probability that the sample mean will be atleast
Rs. 296?
BTL -6 Creating
4(a).
Explain Stratified sampling technique and discuss how it is better
than simple random sampling in a particular situation.
BTL -4
Analyzing
4(b). Discuss the standard error of proportion BTL-2 Understanding
5.
Explain the methods of drawing simple random sample from a
finite population.
BTL -4 Analyzing
8
6(a).
In a sample of 1000 citizens of India, 540 are wheat eaters and the
rest are rice eaters. Can we assume that both rice and wheat
equally popular in India at 1 % level of significance?
BTL-5
Evaluating
6(b).
A simple random sample of 144 items resulted in a sample mean
of 1257.85 and standard deviation of 480. Develop a 95%
confidence interval for the population mean
BTL -6
Creating
7(a).
A car dealer wants to estimate the proportion of customers who
still own the cars they purchased 5 years earlier. A random sample
of 500 customers selected from the dealer?s records indicate that
315 customers still own cars that they were purchased 5 years
earlier. Set up 95% confidence interval estimation of the
population proportion of all the customers who still own the cars 5
years after they were purchased.
BTL-2
Understanding
7(b).
A movie maker sampled 55 fans who viewed his master piece
movie and asked them whether they had planned to see it again.
Only 10 of them believed that the movie was worthy of a second
look. Find the standard error of the population of fans who will
view the film a second time. Construct a 90% confidence interval
for this population.
BTL -5 Evaluating
8(a).
From a population of size 600, a sample of 60 individuals revealed
mean and standard deviation as 6.2 and 1.45 respectively. (i) Find
the estimated standard error (ii) Construct 96% confidence
interval for the mean.
BTL -3 Applying
8(b).
The age of employees in a company follows normal distribution
with its mean and variance as 40 years and 121 years respectively.
If a random sample of 36 employees is taken from a finite normal
population of size 1000, what is the probability that the sample
mean is
(i) less than 45
(ii) greater than 42 and
(iii) between 40 and 42?
BTL -6
Creating
9(a).
A firm wishes to estimate with an error of not more than 0.03 and
a level of confidence of 98%, the proportion of consumers that
prefer its brand of household detergent. Sales report indicate the
about 0.20 of all consumers prefer the firm?s brand. What is the
requisite sample size?
BTL -5 Evaluating
9(b).
A random sample of 700 units from a large consignment should
that 200 were damaged.
Find (i) 95%
(ii) 99% confidence limits for the proportion of damaged
units in the consignment
BTL -3 Applying
10(a).
From a population of 500 items with a mean of 100 gms and
standard deviation of 12.5 gms, 65 items were chosen. (i) What is
the standard error? (ii) Find P(99.5 < X < 101.5).
BTL -6 Creating
10(b).
A non-normal distribution representing the number of trips
BTL -6 Creating
9
performed by lorries per week in a coal field has a mean of 100
trips and variance of 121 trips. A random sample of 36 lorries is
taken from the non-normal population. What is the probability that
the sample mean is
(i) greater than 105
(ii) less than 102
(iii) between 101 and 103 trips?
11.
Test the significance of the difference between the means of the
sample from the following data
Size of sample Mean SD
Sample A 100 61 4
Sample B 200 63 6
BTL -4 Analyzing
12(a).
A cigarete manufacturing firm claims that its brand. A outsells
brand B by 8%. If it is found that 42 out of a sample of 200
smokers prefer brand a and 18 out of another sample of 100
smokers prefer brand B, test whether the 8% difference is a valid
claim(use 5% level of significance).
BTL -4
Analyzing
12(b).
In an automotive safety test conducted by the North Carolina
Highway Safety Research center, the average tyre pressure in a
sample of 62 tyres was found to be 24 pounds per square inch, and
the standard deviation was 2.1 pounds per square inch.
(i) What is the estimated population standard deviation for this
population
(ii) Calculate the estimated standard error of the mean
(iii) Construct a 95% confidence interval for the population mean.
BTL -3 Applying
13(a).
The manager of a shop selling beverages wants to estimate the
actual amount of beverages in one litre bottles from a nationally
known manufacturer. As per manufacturer?s specifications, the
standard deviation of the volume of the beverage is 0.02 litre. The
average amount of beverage per 1 litre bottle is found to be 0.995
litre on checking 50 bottles. Setup 99% confidence interval
estimate of the true population average amount of beverage in a 1
liter bottle. Check whether the manufacturer is genuine in filling
the beverage.
BTL -6
Creating
13(b).
In a batch chemical process used for etching printed circuit boards,
two different catalysts are being compared to determine whether
they require different emersion times for removal of identical
quantities of photo resist material. Twelve batch were run with
catalyst 1, resulting in a sample mean emersion time of 24.6
minutes and sample standard deviation of 0.85 minutes. Fifteen
batches were run with catalyst 2, resulting in a mean emersion time
of 22.1 minutes and a standard deviation of 0.98 minutes. Find a
95% confidence interval on the difference in means, assuming that
2
2
2
1
? ? ? .
BTL -3 Applying
10
14.
In a random sample of 75 axle shafts. 12 have a surface finish that
is rougher than the specifications will allow. Suppose that a
modification is made in the surface finishing process and
subsequently a second random sample of 85 axle shafts is
obtained. The number of defective shafts in this second sample is
10. Obtain an approximate 95% confidence interval on the
difference in the proportions of defectives produced under the two
processes
BTL -5 Evaluating
PART-C
1.
In a sample of 25 observations from a Normal distribution with
mean 98.6 and standard deviation 17.2.
(i)What is P(92<102)
(ii)Find the corresponding probability given a sample of 36.
BTL -6 Creating
2.
Mary, an auditor for a large credit card company, knows that, on
average, the monthly balance of any customer is Rs.112, and the
standard deviation is Rs.56. If Mary audits 50 randomly selected
accounts, What is the probability that the sample average balance
is
(i) Below Rs. 100
(ii)Between Rs.100 and Rs.130
BTL -6 Creating
3(a).
Write the type of sampling methods and the uses of standard error?
BTL -1 Remembering
3(b).
From a population of 540, a sample of 60 individual is taken. From
this sample, the mean is found to 6.2 and the standard deviation
1.368
(i) Find the estimated standard error of the mean.
(ii) Construct a 96 % confidence interval for the mean.
BTL-2 Understanding
4(a).
Explain the properties of good point estimator.
BTL -4 Analyzing
4(b).
What do you mean by interval estimation? Give examples
BTL-6 Creating
UNIT III - TESTS OF HYPOTHESIS- PARAMETRIC TESTS
SYLLABUS: Hypothesis testing: one sample and two sample tests for means and proportions of large samples (z-test),
one sample and two sample tests for means of small samples (t-test), F-test for two sample standard deviations. ANOVA
one and two way.
PART-A
Q.
No.
Question
Bloom?s
Taxonomy
Level
Domain
1. Define Test of Significance. BTL-1 Remembering
2. What are the Type I and Type II errors? BTL-6 Creating
3. What do you mean by one tail test? BTL-6 Creating
4. State the applications of Z-test and t-test. BTL-4 Analyzing
5. Define critical region BTL-1 Remembering
6. Distinguish between one tail and two tail tests BTL-2 Understanding
7. What is the aim of design of experiments? BTL-6 Creating
8. Distinguish between one-way and two-way analysis of variance. BTL-2 Understanding
9. When does the Z-test apply? BTL-1 Remembering
10. Explain SSB , SSW and SSY
and relationship in ANOVA. BTL-4 Analyzing
11
11. Describe any two applications of t-distribution BTL-1 Remembering
12. Write the uses of F-test? BTL-6 Creating
13. Define the level of significance. BTL-1 Remembering
14. Write the properties of t-distribution? BTL-6 Creating
15. What is the role of standard error? BTL-6 Creating
16. Mention any four applications of t-distribution in tests of hypothesis. BTL-1 Remembering
17. Mention any four uses of Chi-square distribution in test of hypothesis. BTL-1 Remembering
18. Define null hypothesis ? Explain. BTL-6 Creating
19.
Estimate the standard error of difference between two proportion if
p
1
=0.10,p
2=
0.133 and n
1
=50,n
2
=75.
BTL-6 Creating
20.
Mention any two assumptions made in analysis of variance
techniques.
BTL-1 Remembering
PART-B
1(a).
A study compares the effect of four 1-month point-of-purchase
promotions on sales. The unit sales for five stores using all four
promotions in different months follow.
Free Sample
78 87 81 89 58
One-pack gift
94 91 87 90 88
Cents off
73 73 78 69 83
76Refund by mail
79 83 78 69 81
(i)Compute the mean unit sales for each promotion and then
determine the grand mean.
(ii)Estimate the population variance using the between column
variance.
BTL-5 Evaluating
1(b).
From the question 1(a)
(i)Estimate the population variance using the within-column variance
computed from the variance within the samples.
(ii)Calculate the F ratio. At the 0.01 level of significance, do the
promotions produce different effects on sales.
BTL-2 Understanding
2(a).
In a low cost Toy production system, the molding machine has been
set with standard of 1% defective. The 80 sample units produced from
this machine shows defective of one unit. Is it necessary to stop the
product for corrective mechanism? Test at 5% level of significance
BTL-5 Evaluating
2(b).
Block Enterprises, a manufacturer of chips for computers. Is in the
process of deciding whether to replace its current semi automated
assembly line with a fully automated assembly line. Block has
gathered some preliminary test data about hourly chip production,
which is summarized in the following table, and it would like to know
whether it should upgrade its assembly line. State (and test at a =0.02)
appropriate hypothesis to help Block decide.
BTL-5 Evaluating
3(a).
Three samples below have been obtained from normal population
with equal variance. Test the hypothesis that the means are equal.
Sample I : 10 12 18 15 16
Sample II : 7 15 10 12 8
Sample III : 12 8 15 16 15
BTL-5 Evaluating
3(b). The I.Q.s of 16 students from one class of an showed a BTL-2 Understanding
12
mean of 107 with a standard deviation of 10, while the I.Q.s of 14
students from another class showed a mean of 112 with a standard
deviation of 8. Check whether there is an appreciable difference
between the I.Q.s of the two groups at (i) 0.01and (ii) 0.05 level of
significance
4(a).
The following is the information obtained from a random sample of 5
observations. Assume the population has a normal distribution.
30 31 27 32 28
To test if the sample was drawn from a normal distribution with mean
less than 30, (i)State the null and alternative hypotheses
(ii)Compute the standard error.
BTL-2 Understanding
4(b).
From the question 4(a)
(i)Determine the test statistic.
(ii)Decide at 10% level whether or not the mean value could be
greater than 30
BTL-2 Understanding
5.
The following data relate to the number of units produced per week by
three methods.
Method 1 : 170 192 190 120
Method 2 : 160 165 170 172
Method 3 : 182 190 170 178 185
Prepare ANOVA table and write your comments
BTL-6 Creating
6(a).
Test if the following samples could have come from two populations
with the same means, assuming the population variances are equal.
Sample I Sample II
Sample size 12 10
Sample Mean 40.5 43.8
Sample variance 2.6 3.2
BTL-5 Evaluating
6(b).
The weights of 10 people of a locality are found to be
70,67,62,68,61,68,70,64,64,66 kilograms. Is it reasonable to believe
that the average weights of the people of locality is greater than 64
kg? Test at 5%level of significance.
BTL-5 Evaluating
7(a).
In Town A, there were 850 birds of which 52% was males, while in
Town A and Town B combined, the proportion of males in a total of
1200 birds was 0.49. Is there any significance difference in the
proportions of male birds in the two Towns?
BTL-2
Understanding
7(b).
IQ test result of randomly selected five employees in an organization
is given below. Test whether minimum requirement of average IQ
level 87 is maintained in that company or not.
Employee code 234 232 121 343 111
IQ test 85 95 90 93 87
BTL-4 Analyzing
8(a).
The weights of 8 persons are found to be 60, 65, 70, 68, 62, 63, 60,
and 66 kgs. The weights of another group of 12 persons are found to
be 70, 60, 58, 56, 50, 48, 52, 56, 52, 50, 54, and 50. Can we conclude
that both samples have come from populations with same variances?
BTL -4 Analyzing
13
8(b).
ATMs must be stocked with enough cash to meet the requirements of
customers over a week, but excess cash results in loss of income as
investment opportunities could not be utilized. In an ATM, the
average transaction per customer in a week is Rs.8000 with a standard
deviation of Rs.1500. If a random sample of 36 customer transactions
is examined and it is observed that the sample mean with drawl is
Rs.8600, check the belief that the true average withdrawal is no longer
Rs.8000. Assume 0.05 level of significance
BTL -3 Applying
9.
Apply ANOVA technique and write your comment regarding the
sales(in Rs. Lakhs)
Area
Representatives
1 2 3 4
A 12 16 20 18
B 15 10 12 16
C 10 08 16 15
BTL -3 Applying
10(a).
A farmer wishes to determine whether there is a difference in yields
between two different varieties of wheat I and II. The following data
shows the production of wheat per unit area using the two varieties.
Can the farmer conclude at significance levels of
(i) 0.05
(ii) 0.01 that a difference exists?
BTL -4 Analyzing
10(b).
Test if the samples could have come from equal population means.
Sample A Sample B
Size 200 400
Mean 154.8 164.3
Variance 15.2 18.2
BTL-5 Evaluating
11(a).
The number of accidents per week in a city are as follows:
12, 8, 20, 2, 14, 10, 15, 6, 9 and 4. Are these frequencies in agreement
with the belief that accident conditions were the same during this 10
weeks period?
BTL -4
Analyzing
11(b).
Two samples are drawn from two normal population. From the
following data, Test whether the two samples have the same variance
5% level of significance.
Sample 1 60 65 69 74 76 82 85 87
Sample 2 61 66 67 85 78 63 85 86 88 91
BTL -3 Applying
12(a).
Given a sample mean of 83, a sample standard deviation of 12.5 and a
sample size of 22, test the hypothesis that the value of the population
mean is 70 against alternative that it is more than 70. Use the 0.025
significance level.
BTL-2
Understanding
12(b).
The following table shows the lifetimes in hours of samples from
three different types of television tables manufactured by a company.
Determine whether there is a difference between the three types at
significance level of 0.01.
Table:
BTL-2
Understanding
14
Sample 1 407 411 409
Sample 2 404 406 408 405 402
Sample 3 410 408 406 408
13.
The following table shows the yields per acre of hour different plants
crops grown on lots treated with three different types of fertilizer.
Determine at the 5% significance level whether there is a difference in
yield per acre.
(i) due to the fertilizers and
(ii) due to the crops
Table:
Crop -I Crop -II Crop -III Crop -IV
Fertilizer A 4.5 6.4 7.2 6.7
Fertilizer B 8.8 7.8 9.6 7.0
Fertilizer C 5.9 6.8 5.7 5.2
BTL-2
Understanding
14.
Time of 6 machine operator (in minute) in making product is given
below. Use paired t-test for training effectiveness.
Machine operator 1 2 3 4 5 6
Before training 12 23 4 5 16 17
After training 2 3 10 8 12 6
BTL -3 Applying
PART C
1(a).
What are non-parametric tests? Point out their advantages and
disadvantages?
BTL -6 Creating
1(b).
The success of a sales engineer in adopting the proven sales technique
was found to be 12 out of 30 occasions. Hence he tried a novel
technique and achieved success at a rate of 23 out of 40 occasions.
Check whether the novel technique is effective at 5% level of
significance.
BTL-2 Understanding
2(a).
The following are the final examination marks of three groups of
students who were taught computer by three difference methods.
First method: 94 88 91 74 87 97
Second method: 85 82 79 84 61 72 80
Third method: 89 67 72 76 69
BTL -5 Evaluating
2(b).
A consumer product manufacturing company was selling one of its
leading products through a large number of retail shops. Before a
heavy advertisement campaign, the average sale per week per shop
was 140 dozens. After the campaign, a sample of 26 shops was taken
and the mean sales improved to 147 dozens with a standard deviation
of 16. Check the effectiveness of the advertisement campaign at 5%
level of significance
BTL-2
Understanding
3.
Discuss the test procedure to test hypothesized population proportion
using single sample proportion.
BTL-1 Understanding
15
4.
(i)Write the application testing of hypothesis in statistics. (ii)What is
t-test? When should we apply a t-test?
BTL -3 Applying
UNIT IV: NON-PARAMETRIC TESTS
SYLLABUS: Chi-square test for single sample standard deviation. Chi-square tests for independence ofattributes and
goodness of fit. Sign test for paired data. Rank sum test. Kolmogorov-Smirnov ? test for goodness of fit, comparing two
populations. Mann ? Whitney U test and Kruskal Wallis test. One sample run test.
PART-A
Q.
No.
Question
Bloom?s
Taxonomy
Level
Domain
1. Define Rank Correlation test. BTL-1 Remembering
2. Write the formula in chi square test and any two uses. BTL-1 Remembering
3. Define Rank-Sum test. BTL-1 Remembering
4. Mention the advantages of Nonparametric Tests. BTL-1 Remembering
5. What is the other name or non-parametric test? Why? BTL-6 Creating
6. When are non parametric tests used? BTL-1 Remembering
7. What is the null hypothesis framed in Mann-Whitney test? BTL-6 Creating
8.
Write down the working rule for Mann-Whitney U-test and Kruskal-
Wallis test.
BTL-1 Remembering
9. Explain sign test. BTL-4 Analyzing
10. Define one sample run test? BTL-1 Remembering
11. When is Krushkal-Wallis test used? BTL-1 Remembering
12. Distinguish between Mann-Whitney U-test and Krushkal-Wallis test. BTL-2 Understanding
13. Write the contingency 2*2 table for
test. BTL-5 Evaluating
14.
Write down the formula to calculate rank correlation coefficient
(including tie values).
BTL-1 Remembering
15.
Two HR managers (A and B) ranked five candidates for a new
position. Their rankings of the candidates are show below:
Candidate Rank by A Rank by B
Nancy 2 1
Mary 1 3
John 3 4
Lynda 5 5
Steve 4 2
Compute the Spearman rank correlation.
BTL-6 Creating
16. Define rank correlation co-efficient. BTL-1 Remembering
17.
The following are the ranks obtained by 10 students in Statistics and
Mathematics. Find out the rank correlation coefficient.
Statistics 1 2 3 4 5 6 7
Mathematics 2 5 1 6 7 4 3
BTL-4 Analyzing
18. Explain Kolmogorov-Smirnov Test for one sample problem. BTL-4 Analyzing
19. What adjustment is to be done for tie values to find rank correlation. BTL-6 Creating
20. Mention the properties of linear coefficient of correlation. BTL-1 Remembering
PART -B
1(a).
The scores of a written examination of 24 students, who were trained
by using three different methods, are given below.
Video cassette A 74 88 82 93 55 70 65
BTL-3 Applying
16
Audio cassette B 78 80 65 57 89 85 78 70
Class Room C 68 83 50 91 84 77 94 81 92
Use Krushkal-Wallis test at ? = 5% level of significance, whether the
three methods of training yield the same results.
1(b). Explain Rank sum tests and its applications
2(a).
The production volume of units assembled by three different
operators during 9 shifts is summarized below. Check whether there
is significant difference between the production volumes of units
assembled by the three operators using Krushkal-Wallis test at a
significant level of 0.05.
Operator I 29 34 34 20 32 45 42 24 35
Operator II 30 21 23 25 44 37 34 19 38
Operator III 26 36 41 48 27 39 28 46 15
BTL-3
Applying
2(b).
Two faculty members ranked 12 candidates for scholarships.
Calculate the spearman rank-correlation coefficient and test it for
significance. Use 0.02level of significance.
Candidate Rank by Professor A Rank by Professor B
1 6 5
2 10 11
3 2 6
4 1 3
5 5 4
6 11 12
7 4 2
8 3 1
9 7 7
10 12 10
11 9 8
12 8 9
BTL-3
Applying
3(a).
In a study of sedimentary rocks, the following data were obtained
from samples of 32 grains from two kinds of sand :
Apply Mann-Whitney U test with suitable null and alternative
hypotheses.
Sand I 63 17 35 49 18 43 12 20 47
? 136 51 45 84 32 40 44 25
Sand II 113 54 96 26 39 88 92 53 101
? 48 89 107 111 58 62
BTL -3 Applying
3(b).
The Molisa?s shop has 3 mall locations. She keeps a daily record for
each locations of the number of the customers who actually make a
purchase. A sample of these data follows. Using Kruskal- Wallis test
can you say that at 5% level of significance that her stores have the
same number of customers who buy.
Eastowin 99 64 101 85 79 88 97 95 90 100
Craborchard 83 102 125 61 91 96 94 89 93 75
Fair forest 89 98 56 105 87 90 87 101 76 89
BTL -3 Applying
4(a)
The following are the prices in Rs. per kg of a commodity from 2
random samples of shops from 2 cities A&B.
BTL -3 Applying
17
City A 2.7 3.8 4.3 3.2 4.7 3.6 3.8 4.1
2.7 2.8 3.2 3.4 3.8 4.4 4.9 3.9 4.7
City B 3.7 5.3 4.7 3.6 4.7 4.8 6.0 4.8 4.9
3.8 3.9 4.8 5.2 6.1 3.6 3.8
Apply the run test to examine whether the distribution of prices of
commodity in the two cities is the same.
4(b)
Distinguish Nonparametric methods over parametric methods.
BTL -2 Understanding
5(a)
From a poll of 800 television viewers, the following data have been
accumulated as to,their levels of education and their performance of
television stations. We are interested in determining if the selection
of Tv station is independent of the level of education.
Education Level
High school Bachelor graduate Total
Public Broadcasting 50 150 80 280
Commercial
stations
150 250 120 520
Total 200 400 200 800
(i) State the null and alternative hypothesis.
(ii) Show the contingency table of the expected
frequencies
BTL -3 Applying
5(b)
From the question 5(a)
(i)Compute the test static
(ii)The null hypothesis to be tested at 95% confidence Determine the
critical value for this test
BTL-6
Creating
6(a)
Apply Mann-Whitney U test to determine if there is a significant
difference in the age distribution of the two groups
Day :26 18 25 27 19 30 34 21 33 31
Evening :32 24 23 30 40 41 42 39 45 35
BTL -3
Applying
6(b)
Apply the K-S test to check that the observed frequencies match with
the expected frequencies which are obtained from Normal
distribution. (Given at n=5).
Test Score 51-60 61-70 71-80 81-90 91-100
Observed Frequency
30 100 440 500 130
Expected Frequency 40 170 500 390 100
BTL -5 Evaluating
7
A research company has designed three different systems to clean up
oil spills. The following table contains the results, measures by how
much surface area (in square meters) is cleaned in one hour. The data
were found by testing each method in several trials. Are there
systems equally effective? Use the 5% level of significance.
Sample A 55 60 63 56 59 55
Sample B 57 53 64 49 62
Sample C 66 52 61 57
BTL -1 Remembering
8(a)
Suppose it is desired to check whether pinholes in electrolytic tin
plate are distributed uniformly across a plated coil on the basis of the
following distances (in inches) of 10 pinholes from one edge of a
BTL -1 Remembering
FirstRanker.com - FirstRanker's Choice
1
(An
Ka ttankulathur ?
DEPARTMENT OF MATHEMATICS
QUESTION BANK
I SEMESTER
1918108 ? STATISTICS FOR MANAGEMENT
Regulation ? 2019
Academic Year 2019 - 2020
Prepared by
Ms. B. Vasuki, Assistant Professor/Mathematics
Ms.B.Elakkiavani, Assistant Professor/Mathematics
2
(An
? .
DEPARTMENT OF MATHEMATICS
QUESTION BANK
SUBJECT : 1918108 ? STATISTICS FOR MANAGEMENT
SEM / YEAR : I Semester / I Year
UNIT I - INTRODUCTION
SYLLABUS: Basic definitions and rules for probability, conditional probability independence of events, Baye?s
theorem, and random variables, Probability distributions: Binomial, Poisson, Uniform and Normal distributions.
PART- A
S.NO QUESTIONS
BT Level
COMPETENCE
PART ? A
1. Define Statistics. BTL -6 Creating
2. What is the addition and multiplication theorem on probability. BTL -1 Remembering
3. Distinguish between a priori and posterior probability?. BTL -6 Creating
4.
The price of the selected stock over a five day period shown as 170, 110,
130, 170 and 160. Compute mean , median and mode.
BTL -6 Creating
5.
A car travels 25 miles at 25 mph, 25 miles at 50 mph and 25 miles at 75
mph. Find the harmonic of three velocities?
BTL -4 Analyse
6.
A ball is drawn at random from a box containg 6 red balls, 4 white balls
and 5 blue balls. Find the probability that the ball drawn is not red.
BTL -4 Analyse
7.
Find the median and mode for the weights (kgs) of 15 persons given as
68, 85, 70, 65, 71, 67, 65, 55, 80, 62, 65, 64, 70, 60, 56.
BTL -3 Applying
8. Name few measures of dispersion. BTL -1 Remembering
9. write the common measures of central tendency? BTL -1 Remembering
10. Define continuous and discrete variables examples. BTL -1 Remembering
11.
Let X be the lifetime in years of a mechanical part. Assume that X has
the cdf F(x) = 1- e
-x
, x ? 0. Find P[1< X ? 3].
BTL -1 Remembering
12. Define independent events. BTL -1 Remembering
13. State the theorem of total probability BTL -1 Remembering
14. What is the use of Baye?s theorem? BTL -6 Creating
15. Mention the properties of a discrete probability distribution. BTL -1 Remembering
16. Define a Poisson distribution and mention its mean and variance. BTL -1 Remembering
17. If the mean and variance of a binomial distribution are respectively 6 BTL -3 Applying
3
and 2.4, find P(x=2).
18.
If x is a Poisson distribution such that P(x=1)=4P(x=2). Find its
mean and variance.
BTL -3 Applying
19.
Suppose that X has a Poisson distribution with parameter ? = 2.
Compute P[X ? 1].
BTL -1 Remembering
20. Define mutually exclusive events. BTL -1 Remembering
PART-B
1(a).
Calculate the mean and standard deviation for the following table
giving the age distribution of 542 members.
Age
20-30 30-40 40-50 50-60 60-70 70-80 80-90
No 3 61 132 153 140 51 2
BTL-2 Understanding
1(b).
Find the geometric mean for the following data:
Group
2-4 4-6 6-8 8-10
Frequency 200 400 300 100
BTL-2
Understanding
2(a).
Find the mean, median and modal ages of married women at first
child birth
Age at the
birth of
first child
13
14
15
16
17
18
19
20
21
22
23
24
25
No of
married
women
37
162
343
390
256
433
161
355
65
85
49
46
40
BTL -6 Creating
2(b).
If A and B are independent event with P(A)=2/5, and P(B)=3/5,
find P(A ?B). Let S= {1,2,3,4,5,6} if A = {2,4,6} then find the
probability of A complement.
BTL -3 Applying
3(a).
Given: The probabilities of three events A, B and C occurring are
P(A) = 0.35, P(B) = 0.45 and P(C) = 0.2. Assuming that A, B, or
C has occurred, the probabilities of another event X occurring are
P(X/A) = 0.8, P(X/B) = 0.65 and P(X/C) = 0.3. Find P(A/X),
P(B/X) and P(C/X).
BTL -6 Creating
3(b).
4 cards are drawn from a well shuffled pack of cards. Find the
probability that
(i) All the four are queens
(ii) There is one card from each suit.
(iii) Two cards are diamonds and two are spades
All the four cards are hearts and one of them is jack
BTL -6 Creating
4(a).
Three machines all turn out non ferrous castings. Machine A
produces 1% defective and Machine B- 2% and machine C ? 5%.
Each machine produces 1/3 of the output. An inspector examines
a single casting, which he determines as non defective. Estimate
the probabilities of its having been produced by each machine.
BTL -6 Creating
4(b).
If the random variable X takes values 1, 2, 3, 4 such that
2P(X = 1) = 3P(X = 2) = P( X=3) = 5P(X = 4), find the
probability distribution and cumulative distribution of X.
BTL-2 Understanding
5(a).
Two dice are thrown together once. Find the probabilities for
BTL -3 Applying
4
getting the sum of the two numbers (i) equal to 5, (ii) multiple of
3, (iii) divisible by 4.
5(b).
Given ? = 4.2, for a poisson distribution. Find (a) P(X ? 2) (b)
P(X ? 5) (c) P(X = 8).
BTL -6 Creating
6(a).
An urn contains 5 balls. Two balls are drawn and found to be
white. What is the probability that all the balls are white?
BTL-1 Remembering
6(b).
The contents of urns I, II, III are as follows:
1 white, 2 black and 3 red balls;
2 white, 1 black and 1 red balls;
4 white, 5 black and 3 red balls;
One urn is chosen at random and two balls drawn. They happen to
be white and red. What is the probability that they come from
urns I, II, III?
BTL -3 Applying
7(a).
In 1989, there were three candidates for the position of principal
Mr. Chatterji, Mr. Ayangar and Dr. Singh. Whose chances of
getting the appointment are in the proportion 4:2:3 respectively.
The probability that Mr. Chatterji is selected, would introduce co-
education in the is 0.3. The probabilities of Mr. Ayangar
and Dr. Singh doing the same are respectively 0.5 and .08. What
is the probability that there was co-education in the in
1990?
BTL -3
Applying
7(b).
Find the probability that atmost 5 defective bolts will be found in
a box of 200 bolts, if it is known that 2% of such bolts are
expected to be defective. (e
-4
= 0.0183)
BTL -6 Creating
8(a).
A coin is tossed 6 times what is the probability of obtaining (a) 4
heads (b) 5 heads (c) 6 heads (d) getting 4 or more heads.
BTL -3 Applying
8(b).
In a bolt factory machines A, B, C manufacture respectively 25%,
35% and 40% of the total of their output 5, 4, 2 percent are
defective bolts. If A bolt is drawn at random from the product and
is found to be defective, what are the probabilities that is was
manufactured by machines A, B and C?
BTL -6 Creating
9(a).
In a test of 2000 electric blubs it was found that the life of a
particular make was normally distributed with an average life of
2040 hours and S. D. of 60 hours. Estimate the number of blubs
likely to burn for
(1) More than 2150 hours
(2) Less than 1950 hours
(3) More than 1920 hours but less than 2160 hours.
BTL -3 Applying
9(b).
The latest nationwide political poll indicates that for Americans
who are randomly selected, the probability that they are
conservative is 0.55, the probability that they are liberal is 0.30
and the probability that they are middle of the road is 0.15.
Assuming these probabilities are accurate, answer the following
BTL -4 Analyzing
5
questions from a randomly chosen group of 10 Americans
(a) What the probability that 4 are liberal?
(b) What the probability that none are conservative
(c) What the probability that two are middle of the road
(d) What the probability that a least 8 are liberal
10.
If X follows a normal distribution with mean 12 and variance 16
cm, find the probabilities for (i) X ? 20 (ii) X ? 20, and (iii) 0 ? X
? 12.
BTL -3 Applying
11.
A discerete random variable X has the probability function given
below:
Value of X=x: 0 1 2 3 4 5 6 7
P(X=x) : 0 k 2k 2k 3k k
2
2k
2
7k
2
+k
Find (1) The value of k
(2) P(1.5 < X < 4.5 / X > 2)
(3) P(X < 6), P(X ? 5), P( 0 < X < 4)
(4) The distribution of X.
BTL -3 Applying
12.
X is a normal variable with mean 30 and standard deviation of 5.
Find (i) P[26 ? X ? 40] (ii) P [X?45] (iii) P [ ?X - 30 ?> 5] use
normal distribution tables
BTL -4 Analyzing
13.
In an intelligence test administered on 1000 students, the average
was 42 and standard deviation 24, find (i) the number of students
exceeding a score 50. (ii) the number of students lying between
30 and 54(iii) the value of score exceeded by top 100 students.
BTL -4 Analyzing
14(a).
The probability that an entering student will graduate is 0.4
Determine the probability that out of 5 students atleast one will
graduate.
BTL-5
Evaluating
14(b).
Fit a Poisson Distribution to the following data which gives the
number of doddens in a sample of clover seeds
No 0 1 2 3 4 5 6 7 8
f 56 156 132 92 37 22 4 0 1
.
BTL -4 Analyzing
PART-C
1(a).
A disciplinary committee is formed from the staff of XYZ
Company which has three departments Marketing, Finance and
Production of the 10,5,20 members respectively. All departments
have two female staff each. A department is selected at random
and from which two matters are selected for the committee,
What is the probability that both the team members are female?
BTL-6 Creating
6
1(b).
In a bolt factory machines A, B, C manufacture respectively 25,
35 and 40 percent of the total. Of their output 5, 4 and 2 percent
are defective bolts respectively. A bolt is drawn at random from
the product and is found o be defective. What are the probabilities
that it was manufactured by machines A, B or C?
BTL-2
Understanding
2(a). State Bayes theorem and brief about its applications. BTL-2 Understanding
2(b).
Out of 800 families with 4 children each, how many families
would be expected to have (i) 2 boys and 2 girls (ii) at least 1 boy
(iii) at most 2 girls (iv) children of both sexes? Assume equal
probabilities for boys and girls.
BTL-1 Remembering
3. Describe the classifications of probability ? BTL-1 Remembering
4. What are the applications of Normal distribution in statistics? BTL-6 Creating
UNIT ?II- SAMPLING DISTRIBUTION & ESTIMATION.
SYLLABUS: Introduction to sampling distributions, sampling distribution of mean and proportion, application of central
limit theorem, sampling techniques. Estimation: Point and Interval estimates for population parameters of large sample and
small samples, determining the sample size.
PART - A
S.N
O
QUESTIONS
BT Level
COMPETENCE
1. Define Sampling distribution of proportion. BTL -1 Remembering
2. Define Probable standard error. BTL -1 Remembering
3. Define standard error and mention its importance BTL -1 Remembering
4. Define central limit theorem BTL -1 Remembering
5.
What is the role of central limit theorem in estimation and testing
problems
BTL -6 Creating
6. Define stratified sampling technique BTL -1 Remembering
7. Briefly describe the significance level. BTL -1 Remembering
8. Distinguish between parameter and statistic. BTL -2 Understanding
9. Define estimator, estimate and estimation. BTL -1 Remembering
10. Distinguish between point estimation and interval estimation BTL -2 Understanding
11. Mention the properties of a good estimator. BTL -1 Remembering
12. Define confidence coefficient. BTL -1 Remembering
13. What is the level of significance in testing of hypothesis BTL -6 Creating
14. Define confidence limits for a parameter BTL -1 Remembering
15.
State the conditions under which a binomial distribution becomes a
normal distribution
BTL -4 Analyzing
16.
If the random sample comes from a normal population, what can
be said about the sampling distribution of the mean.
BTL -5 Evaluating
17.
An automobile repair shop has taken a random sample of 40
services that the average service time on an automobile is 130
minutes with a standard deviation of 26 minutes. Compute the
standard error of the mean.
BTL -6 Creating
7
18. What is a random number? How it is useful in sampling? BTL -6 Creating
19.
A population has the numbers: 12, 8, 10, 30, 12, 16, 40, 5, 16, 24,
22, 31, 30, 16, 15. Draw a systematic sample of size 5. Find out its
mean.
BTL -3 Applying
20. How large sample is useful in estimation and testing BTL -4 Analyzing
PART -B
1(a).
A random sample of 700 units from a large consignment showed
that 200 were damaged. Find (i) 95% (ii) 99% confidence limits
for the proportion of damaged units in the consignment.
BTL -3 Applying
1(b).
A random sample of size 9 is obtained from a Normal population
with mean 25 and if the variance 100 find the probability that the
sample mean exceeds 31.2.
BTL -4 Analyzing
2(a).
In a normally distributed population, average income per
household is Rs.20,000 with a standard deviation of Rs. 1,600.
Find the probability that the sample mean will be between
Rs.19,600 and Rs.20,200 in a survey of a random sample of 100
households.
BTL -6 Creating
2(b).
A university wants to determine the percentage of students who
would accept proposed fees hike for improving facilities. The
university wants to be 90% confident that the percentage is
within2% of the true value. Find the sample size to achieve the
accuracy regardless of the true percentage assuming the percentage
of students accepting the increase in tuition fees to be 0.5.
BTL -6 Creating
3(a).
A bank has kept records of the checking balances of its customers
and determined that the average daily balances of its customers is
Rs.300 with a standard deviation of Rs. 48. A random sample of
144 checking accounts is selected.
(i) What is the probability that the sample mean will be more
than Rs. 306.60?
(ii) What is the probability that the sample mean will be less
than Rs. 308?
BTL -6 Creating
3(b).
From the question 3(a)
(i) What is probability that the sample mean will between Rs.
302 and Rs. 308?
(ii) What is probability that the sample mean will be atleast
Rs. 296?
BTL -6 Creating
4(a).
Explain Stratified sampling technique and discuss how it is better
than simple random sampling in a particular situation.
BTL -4
Analyzing
4(b). Discuss the standard error of proportion BTL-2 Understanding
5.
Explain the methods of drawing simple random sample from a
finite population.
BTL -4 Analyzing
8
6(a).
In a sample of 1000 citizens of India, 540 are wheat eaters and the
rest are rice eaters. Can we assume that both rice and wheat
equally popular in India at 1 % level of significance?
BTL-5
Evaluating
6(b).
A simple random sample of 144 items resulted in a sample mean
of 1257.85 and standard deviation of 480. Develop a 95%
confidence interval for the population mean
BTL -6
Creating
7(a).
A car dealer wants to estimate the proportion of customers who
still own the cars they purchased 5 years earlier. A random sample
of 500 customers selected from the dealer?s records indicate that
315 customers still own cars that they were purchased 5 years
earlier. Set up 95% confidence interval estimation of the
population proportion of all the customers who still own the cars 5
years after they were purchased.
BTL-2
Understanding
7(b).
A movie maker sampled 55 fans who viewed his master piece
movie and asked them whether they had planned to see it again.
Only 10 of them believed that the movie was worthy of a second
look. Find the standard error of the population of fans who will
view the film a second time. Construct a 90% confidence interval
for this population.
BTL -5 Evaluating
8(a).
From a population of size 600, a sample of 60 individuals revealed
mean and standard deviation as 6.2 and 1.45 respectively. (i) Find
the estimated standard error (ii) Construct 96% confidence
interval for the mean.
BTL -3 Applying
8(b).
The age of employees in a company follows normal distribution
with its mean and variance as 40 years and 121 years respectively.
If a random sample of 36 employees is taken from a finite normal
population of size 1000, what is the probability that the sample
mean is
(i) less than 45
(ii) greater than 42 and
(iii) between 40 and 42?
BTL -6
Creating
9(a).
A firm wishes to estimate with an error of not more than 0.03 and
a level of confidence of 98%, the proportion of consumers that
prefer its brand of household detergent. Sales report indicate the
about 0.20 of all consumers prefer the firm?s brand. What is the
requisite sample size?
BTL -5 Evaluating
9(b).
A random sample of 700 units from a large consignment should
that 200 were damaged.
Find (i) 95%
(ii) 99% confidence limits for the proportion of damaged
units in the consignment
BTL -3 Applying
10(a).
From a population of 500 items with a mean of 100 gms and
standard deviation of 12.5 gms, 65 items were chosen. (i) What is
the standard error? (ii) Find P(99.5 < X < 101.5).
BTL -6 Creating
10(b).
A non-normal distribution representing the number of trips
BTL -6 Creating
9
performed by lorries per week in a coal field has a mean of 100
trips and variance of 121 trips. A random sample of 36 lorries is
taken from the non-normal population. What is the probability that
the sample mean is
(i) greater than 105
(ii) less than 102
(iii) between 101 and 103 trips?
11.
Test the significance of the difference between the means of the
sample from the following data
Size of sample Mean SD
Sample A 100 61 4
Sample B 200 63 6
BTL -4 Analyzing
12(a).
A cigarete manufacturing firm claims that its brand. A outsells
brand B by 8%. If it is found that 42 out of a sample of 200
smokers prefer brand a and 18 out of another sample of 100
smokers prefer brand B, test whether the 8% difference is a valid
claim(use 5% level of significance).
BTL -4
Analyzing
12(b).
In an automotive safety test conducted by the North Carolina
Highway Safety Research center, the average tyre pressure in a
sample of 62 tyres was found to be 24 pounds per square inch, and
the standard deviation was 2.1 pounds per square inch.
(i) What is the estimated population standard deviation for this
population
(ii) Calculate the estimated standard error of the mean
(iii) Construct a 95% confidence interval for the population mean.
BTL -3 Applying
13(a).
The manager of a shop selling beverages wants to estimate the
actual amount of beverages in one litre bottles from a nationally
known manufacturer. As per manufacturer?s specifications, the
standard deviation of the volume of the beverage is 0.02 litre. The
average amount of beverage per 1 litre bottle is found to be 0.995
litre on checking 50 bottles. Setup 99% confidence interval
estimate of the true population average amount of beverage in a 1
liter bottle. Check whether the manufacturer is genuine in filling
the beverage.
BTL -6
Creating
13(b).
In a batch chemical process used for etching printed circuit boards,
two different catalysts are being compared to determine whether
they require different emersion times for removal of identical
quantities of photo resist material. Twelve batch were run with
catalyst 1, resulting in a sample mean emersion time of 24.6
minutes and sample standard deviation of 0.85 minutes. Fifteen
batches were run with catalyst 2, resulting in a mean emersion time
of 22.1 minutes and a standard deviation of 0.98 minutes. Find a
95% confidence interval on the difference in means, assuming that
2
2
2
1
? ? ? .
BTL -3 Applying
10
14.
In a random sample of 75 axle shafts. 12 have a surface finish that
is rougher than the specifications will allow. Suppose that a
modification is made in the surface finishing process and
subsequently a second random sample of 85 axle shafts is
obtained. The number of defective shafts in this second sample is
10. Obtain an approximate 95% confidence interval on the
difference in the proportions of defectives produced under the two
processes
BTL -5 Evaluating
PART-C
1.
In a sample of 25 observations from a Normal distribution with
mean 98.6 and standard deviation 17.2.
(i)What is P(92<102)
(ii)Find the corresponding probability given a sample of 36.
BTL -6 Creating
2.
Mary, an auditor for a large credit card company, knows that, on
average, the monthly balance of any customer is Rs.112, and the
standard deviation is Rs.56. If Mary audits 50 randomly selected
accounts, What is the probability that the sample average balance
is
(i) Below Rs. 100
(ii)Between Rs.100 and Rs.130
BTL -6 Creating
3(a).
Write the type of sampling methods and the uses of standard error?
BTL -1 Remembering
3(b).
From a population of 540, a sample of 60 individual is taken. From
this sample, the mean is found to 6.2 and the standard deviation
1.368
(i) Find the estimated standard error of the mean.
(ii) Construct a 96 % confidence interval for the mean.
BTL-2 Understanding
4(a).
Explain the properties of good point estimator.
BTL -4 Analyzing
4(b).
What do you mean by interval estimation? Give examples
BTL-6 Creating
UNIT III - TESTS OF HYPOTHESIS- PARAMETRIC TESTS
SYLLABUS: Hypothesis testing: one sample and two sample tests for means and proportions of large samples (z-test),
one sample and two sample tests for means of small samples (t-test), F-test for two sample standard deviations. ANOVA
one and two way.
PART-A
Q.
No.
Question
Bloom?s
Taxonomy
Level
Domain
1. Define Test of Significance. BTL-1 Remembering
2. What are the Type I and Type II errors? BTL-6 Creating
3. What do you mean by one tail test? BTL-6 Creating
4. State the applications of Z-test and t-test. BTL-4 Analyzing
5. Define critical region BTL-1 Remembering
6. Distinguish between one tail and two tail tests BTL-2 Understanding
7. What is the aim of design of experiments? BTL-6 Creating
8. Distinguish between one-way and two-way analysis of variance. BTL-2 Understanding
9. When does the Z-test apply? BTL-1 Remembering
10. Explain SSB , SSW and SSY
and relationship in ANOVA. BTL-4 Analyzing
11
11. Describe any two applications of t-distribution BTL-1 Remembering
12. Write the uses of F-test? BTL-6 Creating
13. Define the level of significance. BTL-1 Remembering
14. Write the properties of t-distribution? BTL-6 Creating
15. What is the role of standard error? BTL-6 Creating
16. Mention any four applications of t-distribution in tests of hypothesis. BTL-1 Remembering
17. Mention any four uses of Chi-square distribution in test of hypothesis. BTL-1 Remembering
18. Define null hypothesis ? Explain. BTL-6 Creating
19.
Estimate the standard error of difference between two proportion if
p
1
=0.10,p
2=
0.133 and n
1
=50,n
2
=75.
BTL-6 Creating
20.
Mention any two assumptions made in analysis of variance
techniques.
BTL-1 Remembering
PART-B
1(a).
A study compares the effect of four 1-month point-of-purchase
promotions on sales. The unit sales for five stores using all four
promotions in different months follow.
Free Sample
78 87 81 89 58
One-pack gift
94 91 87 90 88
Cents off
73 73 78 69 83
76Refund by mail
79 83 78 69 81
(i)Compute the mean unit sales for each promotion and then
determine the grand mean.
(ii)Estimate the population variance using the between column
variance.
BTL-5 Evaluating
1(b).
From the question 1(a)
(i)Estimate the population variance using the within-column variance
computed from the variance within the samples.
(ii)Calculate the F ratio. At the 0.01 level of significance, do the
promotions produce different effects on sales.
BTL-2 Understanding
2(a).
In a low cost Toy production system, the molding machine has been
set with standard of 1% defective. The 80 sample units produced from
this machine shows defective of one unit. Is it necessary to stop the
product for corrective mechanism? Test at 5% level of significance
BTL-5 Evaluating
2(b).
Block Enterprises, a manufacturer of chips for computers. Is in the
process of deciding whether to replace its current semi automated
assembly line with a fully automated assembly line. Block has
gathered some preliminary test data about hourly chip production,
which is summarized in the following table, and it would like to know
whether it should upgrade its assembly line. State (and test at a =0.02)
appropriate hypothesis to help Block decide.
BTL-5 Evaluating
3(a).
Three samples below have been obtained from normal population
with equal variance. Test the hypothesis that the means are equal.
Sample I : 10 12 18 15 16
Sample II : 7 15 10 12 8
Sample III : 12 8 15 16 15
BTL-5 Evaluating
3(b). The I.Q.s of 16 students from one class of an showed a BTL-2 Understanding
12
mean of 107 with a standard deviation of 10, while the I.Q.s of 14
students from another class showed a mean of 112 with a standard
deviation of 8. Check whether there is an appreciable difference
between the I.Q.s of the two groups at (i) 0.01and (ii) 0.05 level of
significance
4(a).
The following is the information obtained from a random sample of 5
observations. Assume the population has a normal distribution.
30 31 27 32 28
To test if the sample was drawn from a normal distribution with mean
less than 30, (i)State the null and alternative hypotheses
(ii)Compute the standard error.
BTL-2 Understanding
4(b).
From the question 4(a)
(i)Determine the test statistic.
(ii)Decide at 10% level whether or not the mean value could be
greater than 30
BTL-2 Understanding
5.
The following data relate to the number of units produced per week by
three methods.
Method 1 : 170 192 190 120
Method 2 : 160 165 170 172
Method 3 : 182 190 170 178 185
Prepare ANOVA table and write your comments
BTL-6 Creating
6(a).
Test if the following samples could have come from two populations
with the same means, assuming the population variances are equal.
Sample I Sample II
Sample size 12 10
Sample Mean 40.5 43.8
Sample variance 2.6 3.2
BTL-5 Evaluating
6(b).
The weights of 10 people of a locality are found to be
70,67,62,68,61,68,70,64,64,66 kilograms. Is it reasonable to believe
that the average weights of the people of locality is greater than 64
kg? Test at 5%level of significance.
BTL-5 Evaluating
7(a).
In Town A, there were 850 birds of which 52% was males, while in
Town A and Town B combined, the proportion of males in a total of
1200 birds was 0.49. Is there any significance difference in the
proportions of male birds in the two Towns?
BTL-2
Understanding
7(b).
IQ test result of randomly selected five employees in an organization
is given below. Test whether minimum requirement of average IQ
level 87 is maintained in that company or not.
Employee code 234 232 121 343 111
IQ test 85 95 90 93 87
BTL-4 Analyzing
8(a).
The weights of 8 persons are found to be 60, 65, 70, 68, 62, 63, 60,
and 66 kgs. The weights of another group of 12 persons are found to
be 70, 60, 58, 56, 50, 48, 52, 56, 52, 50, 54, and 50. Can we conclude
that both samples have come from populations with same variances?
BTL -4 Analyzing
13
8(b).
ATMs must be stocked with enough cash to meet the requirements of
customers over a week, but excess cash results in loss of income as
investment opportunities could not be utilized. In an ATM, the
average transaction per customer in a week is Rs.8000 with a standard
deviation of Rs.1500. If a random sample of 36 customer transactions
is examined and it is observed that the sample mean with drawl is
Rs.8600, check the belief that the true average withdrawal is no longer
Rs.8000. Assume 0.05 level of significance
BTL -3 Applying
9.
Apply ANOVA technique and write your comment regarding the
sales(in Rs. Lakhs)
Area
Representatives
1 2 3 4
A 12 16 20 18
B 15 10 12 16
C 10 08 16 15
BTL -3 Applying
10(a).
A farmer wishes to determine whether there is a difference in yields
between two different varieties of wheat I and II. The following data
shows the production of wheat per unit area using the two varieties.
Can the farmer conclude at significance levels of
(i) 0.05
(ii) 0.01 that a difference exists?
BTL -4 Analyzing
10(b).
Test if the samples could have come from equal population means.
Sample A Sample B
Size 200 400
Mean 154.8 164.3
Variance 15.2 18.2
BTL-5 Evaluating
11(a).
The number of accidents per week in a city are as follows:
12, 8, 20, 2, 14, 10, 15, 6, 9 and 4. Are these frequencies in agreement
with the belief that accident conditions were the same during this 10
weeks period?
BTL -4
Analyzing
11(b).
Two samples are drawn from two normal population. From the
following data, Test whether the two samples have the same variance
5% level of significance.
Sample 1 60 65 69 74 76 82 85 87
Sample 2 61 66 67 85 78 63 85 86 88 91
BTL -3 Applying
12(a).
Given a sample mean of 83, a sample standard deviation of 12.5 and a
sample size of 22, test the hypothesis that the value of the population
mean is 70 against alternative that it is more than 70. Use the 0.025
significance level.
BTL-2
Understanding
12(b).
The following table shows the lifetimes in hours of samples from
three different types of television tables manufactured by a company.
Determine whether there is a difference between the three types at
significance level of 0.01.
Table:
BTL-2
Understanding
14
Sample 1 407 411 409
Sample 2 404 406 408 405 402
Sample 3 410 408 406 408
13.
The following table shows the yields per acre of hour different plants
crops grown on lots treated with three different types of fertilizer.
Determine at the 5% significance level whether there is a difference in
yield per acre.
(i) due to the fertilizers and
(ii) due to the crops
Table:
Crop -I Crop -II Crop -III Crop -IV
Fertilizer A 4.5 6.4 7.2 6.7
Fertilizer B 8.8 7.8 9.6 7.0
Fertilizer C 5.9 6.8 5.7 5.2
BTL-2
Understanding
14.
Time of 6 machine operator (in minute) in making product is given
below. Use paired t-test for training effectiveness.
Machine operator 1 2 3 4 5 6
Before training 12 23 4 5 16 17
After training 2 3 10 8 12 6
BTL -3 Applying
PART C
1(a).
What are non-parametric tests? Point out their advantages and
disadvantages?
BTL -6 Creating
1(b).
The success of a sales engineer in adopting the proven sales technique
was found to be 12 out of 30 occasions. Hence he tried a novel
technique and achieved success at a rate of 23 out of 40 occasions.
Check whether the novel technique is effective at 5% level of
significance.
BTL-2 Understanding
2(a).
The following are the final examination marks of three groups of
students who were taught computer by three difference methods.
First method: 94 88 91 74 87 97
Second method: 85 82 79 84 61 72 80
Third method: 89 67 72 76 69
BTL -5 Evaluating
2(b).
A consumer product manufacturing company was selling one of its
leading products through a large number of retail shops. Before a
heavy advertisement campaign, the average sale per week per shop
was 140 dozens. After the campaign, a sample of 26 shops was taken
and the mean sales improved to 147 dozens with a standard deviation
of 16. Check the effectiveness of the advertisement campaign at 5%
level of significance
BTL-2
Understanding
3.
Discuss the test procedure to test hypothesized population proportion
using single sample proportion.
BTL-1 Understanding
15
4.
(i)Write the application testing of hypothesis in statistics. (ii)What is
t-test? When should we apply a t-test?
BTL -3 Applying
UNIT IV: NON-PARAMETRIC TESTS
SYLLABUS: Chi-square test for single sample standard deviation. Chi-square tests for independence ofattributes and
goodness of fit. Sign test for paired data. Rank sum test. Kolmogorov-Smirnov ? test for goodness of fit, comparing two
populations. Mann ? Whitney U test and Kruskal Wallis test. One sample run test.
PART-A
Q.
No.
Question
Bloom?s
Taxonomy
Level
Domain
1. Define Rank Correlation test. BTL-1 Remembering
2. Write the formula in chi square test and any two uses. BTL-1 Remembering
3. Define Rank-Sum test. BTL-1 Remembering
4. Mention the advantages of Nonparametric Tests. BTL-1 Remembering
5. What is the other name or non-parametric test? Why? BTL-6 Creating
6. When are non parametric tests used? BTL-1 Remembering
7. What is the null hypothesis framed in Mann-Whitney test? BTL-6 Creating
8.
Write down the working rule for Mann-Whitney U-test and Kruskal-
Wallis test.
BTL-1 Remembering
9. Explain sign test. BTL-4 Analyzing
10. Define one sample run test? BTL-1 Remembering
11. When is Krushkal-Wallis test used? BTL-1 Remembering
12. Distinguish between Mann-Whitney U-test and Krushkal-Wallis test. BTL-2 Understanding
13. Write the contingency 2*2 table for
test. BTL-5 Evaluating
14.
Write down the formula to calculate rank correlation coefficient
(including tie values).
BTL-1 Remembering
15.
Two HR managers (A and B) ranked five candidates for a new
position. Their rankings of the candidates are show below:
Candidate Rank by A Rank by B
Nancy 2 1
Mary 1 3
John 3 4
Lynda 5 5
Steve 4 2
Compute the Spearman rank correlation.
BTL-6 Creating
16. Define rank correlation co-efficient. BTL-1 Remembering
17.
The following are the ranks obtained by 10 students in Statistics and
Mathematics. Find out the rank correlation coefficient.
Statistics 1 2 3 4 5 6 7
Mathematics 2 5 1 6 7 4 3
BTL-4 Analyzing
18. Explain Kolmogorov-Smirnov Test for one sample problem. BTL-4 Analyzing
19. What adjustment is to be done for tie values to find rank correlation. BTL-6 Creating
20. Mention the properties of linear coefficient of correlation. BTL-1 Remembering
PART -B
1(a).
The scores of a written examination of 24 students, who were trained
by using three different methods, are given below.
Video cassette A 74 88 82 93 55 70 65
BTL-3 Applying
16
Audio cassette B 78 80 65 57 89 85 78 70
Class Room C 68 83 50 91 84 77 94 81 92
Use Krushkal-Wallis test at ? = 5% level of significance, whether the
three methods of training yield the same results.
1(b). Explain Rank sum tests and its applications
2(a).
The production volume of units assembled by three different
operators during 9 shifts is summarized below. Check whether there
is significant difference between the production volumes of units
assembled by the three operators using Krushkal-Wallis test at a
significant level of 0.05.
Operator I 29 34 34 20 32 45 42 24 35
Operator II 30 21 23 25 44 37 34 19 38
Operator III 26 36 41 48 27 39 28 46 15
BTL-3
Applying
2(b).
Two faculty members ranked 12 candidates for scholarships.
Calculate the spearman rank-correlation coefficient and test it for
significance. Use 0.02level of significance.
Candidate Rank by Professor A Rank by Professor B
1 6 5
2 10 11
3 2 6
4 1 3
5 5 4
6 11 12
7 4 2
8 3 1
9 7 7
10 12 10
11 9 8
12 8 9
BTL-3
Applying
3(a).
In a study of sedimentary rocks, the following data were obtained
from samples of 32 grains from two kinds of sand :
Apply Mann-Whitney U test with suitable null and alternative
hypotheses.
Sand I 63 17 35 49 18 43 12 20 47
? 136 51 45 84 32 40 44 25
Sand II 113 54 96 26 39 88 92 53 101
? 48 89 107 111 58 62
BTL -3 Applying
3(b).
The Molisa?s shop has 3 mall locations. She keeps a daily record for
each locations of the number of the customers who actually make a
purchase. A sample of these data follows. Using Kruskal- Wallis test
can you say that at 5% level of significance that her stores have the
same number of customers who buy.
Eastowin 99 64 101 85 79 88 97 95 90 100
Craborchard 83 102 125 61 91 96 94 89 93 75
Fair forest 89 98 56 105 87 90 87 101 76 89
BTL -3 Applying
4(a)
The following are the prices in Rs. per kg of a commodity from 2
random samples of shops from 2 cities A&B.
BTL -3 Applying
17
City A 2.7 3.8 4.3 3.2 4.7 3.6 3.8 4.1
2.7 2.8 3.2 3.4 3.8 4.4 4.9 3.9 4.7
City B 3.7 5.3 4.7 3.6 4.7 4.8 6.0 4.8 4.9
3.8 3.9 4.8 5.2 6.1 3.6 3.8
Apply the run test to examine whether the distribution of prices of
commodity in the two cities is the same.
4(b)
Distinguish Nonparametric methods over parametric methods.
BTL -2 Understanding
5(a)
From a poll of 800 television viewers, the following data have been
accumulated as to,their levels of education and their performance of
television stations. We are interested in determining if the selection
of Tv station is independent of the level of education.
Education Level
High school Bachelor graduate Total
Public Broadcasting 50 150 80 280
Commercial
stations
150 250 120 520
Total 200 400 200 800
(i) State the null and alternative hypothesis.
(ii) Show the contingency table of the expected
frequencies
BTL -3 Applying
5(b)
From the question 5(a)
(i)Compute the test static
(ii)The null hypothesis to be tested at 95% confidence Determine the
critical value for this test
BTL-6
Creating
6(a)
Apply Mann-Whitney U test to determine if there is a significant
difference in the age distribution of the two groups
Day :26 18 25 27 19 30 34 21 33 31
Evening :32 24 23 30 40 41 42 39 45 35
BTL -3
Applying
6(b)
Apply the K-S test to check that the observed frequencies match with
the expected frequencies which are obtained from Normal
distribution. (Given at n=5).
Test Score 51-60 61-70 71-80 81-90 91-100
Observed Frequency
30 100 440 500 130
Expected Frequency 40 170 500 390 100
BTL -5 Evaluating
7
A research company has designed three different systems to clean up
oil spills. The following table contains the results, measures by how
much surface area (in square meters) is cleaned in one hour. The data
were found by testing each method in several trials. Are there
systems equally effective? Use the 5% level of significance.
Sample A 55 60 63 56 59 55
Sample B 57 53 64 49 62
Sample C 66 52 61 57
BTL -1 Remembering
8(a)
Suppose it is desired to check whether pinholes in electrolytic tin
plate are distributed uniformly across a plated coil on the basis of the
following distances (in inches) of 10 pinholes from one edge of a
BTL -1 Remembering
18
long strip of tin plate 320 inches wide.
4.8 14.8 28.2 23.1 4.4 28.7 19.5 2.4 25.0 6.2
Use Kolmogorov Smirnov test to test the null hypothesis.
8(b) Explain Mann- WhitneyU test with an example BTL-4 Analyzing
9.
Ten competitors in a beauty contest are ranked by 3 judges in the
following order.
A : 1 6 5 3 10 2 4 9 7 8
B : 3 5 8 4 7 10 2 1 6 9
C : 6 4 9 8 1 2 3 10 5 7
Find out which pair of Judges has awarded the ranks to the nearest
common taste of beauty.
BTL -3 Applying
10(a).
Test the association of Age and preference of colour of Toy from the
following data
Age/Colour Below 5 6-10 Above 10 years
Pink 60 40 5
Purple 30 30 30
Red 80 10 10
BTL -4 Analyzing
10(b).
Melisa?s Boutique has three mall locations. Melisa keeps a dairy
record for each location of number of customers who actually make a
purchase. A sample of those data follows. Using the kruskal-wallis
test, can you say at the 0.05 level of significance that her stores have
the same number of customers who busy?
DSF Mall 99 64 101 85 79 88 97 95 90 100
Forest Mall 83 102 125 61 91 96 94 89 98 75
Big-Ben Mall 89 98 56 105 87 90 87 101 76 89
BTL -3 Applying
11(a).
A brand manager is concerned that her brand?s share may he
unevenly distributes through the country. In a survey in which the
country was divided into four geographic regions, a random
sampling of 100 consumers in each region was surveyed, with the
following results:
NE NW SE SW TOTAL
Purchase the brand 40 55 45 50 190
Do not purchase 60 45 55 50 210
Total 100 100 100 100 400
(i) Develop a table of observed and expected frequencies for
this problem.
(ii) Calculate the sample
value.
BTL -6 Creating
11(b).
From the question 11(a)
(i)State the null and alternative hypothesis.
(ii)At test whether brand share is the same across the four
regions
BTL -2 Understanding
12(a).
In 30 tosses of a coin, the following sequence of head and tails is
obtained HTTHTHHHTHHTTHTHTHHTHTTHTHHTHT
(i) Determine the number of runs
BTL -2 Understanding
12(b).
From the question 12(a ) Test at 0.10 level of significance, whether
the sequence is random
BTL -3 Applying
13. An experiment designed to compare three preventative methods BTL -3 Applying
FirstRanker.com - FirstRanker's Choice
1
(An
Ka ttankulathur ?
DEPARTMENT OF MATHEMATICS
QUESTION BANK
I SEMESTER
1918108 ? STATISTICS FOR MANAGEMENT
Regulation ? 2019
Academic Year 2019 - 2020
Prepared by
Ms. B. Vasuki, Assistant Professor/Mathematics
Ms.B.Elakkiavani, Assistant Professor/Mathematics
2
(An
? .
DEPARTMENT OF MATHEMATICS
QUESTION BANK
SUBJECT : 1918108 ? STATISTICS FOR MANAGEMENT
SEM / YEAR : I Semester / I Year
UNIT I - INTRODUCTION
SYLLABUS: Basic definitions and rules for probability, conditional probability independence of events, Baye?s
theorem, and random variables, Probability distributions: Binomial, Poisson, Uniform and Normal distributions.
PART- A
S.NO QUESTIONS
BT Level
COMPETENCE
PART ? A
1. Define Statistics. BTL -6 Creating
2. What is the addition and multiplication theorem on probability. BTL -1 Remembering
3. Distinguish between a priori and posterior probability?. BTL -6 Creating
4.
The price of the selected stock over a five day period shown as 170, 110,
130, 170 and 160. Compute mean , median and mode.
BTL -6 Creating
5.
A car travels 25 miles at 25 mph, 25 miles at 50 mph and 25 miles at 75
mph. Find the harmonic of three velocities?
BTL -4 Analyse
6.
A ball is drawn at random from a box containg 6 red balls, 4 white balls
and 5 blue balls. Find the probability that the ball drawn is not red.
BTL -4 Analyse
7.
Find the median and mode for the weights (kgs) of 15 persons given as
68, 85, 70, 65, 71, 67, 65, 55, 80, 62, 65, 64, 70, 60, 56.
BTL -3 Applying
8. Name few measures of dispersion. BTL -1 Remembering
9. write the common measures of central tendency? BTL -1 Remembering
10. Define continuous and discrete variables examples. BTL -1 Remembering
11.
Let X be the lifetime in years of a mechanical part. Assume that X has
the cdf F(x) = 1- e
-x
, x ? 0. Find P[1< X ? 3].
BTL -1 Remembering
12. Define independent events. BTL -1 Remembering
13. State the theorem of total probability BTL -1 Remembering
14. What is the use of Baye?s theorem? BTL -6 Creating
15. Mention the properties of a discrete probability distribution. BTL -1 Remembering
16. Define a Poisson distribution and mention its mean and variance. BTL -1 Remembering
17. If the mean and variance of a binomial distribution are respectively 6 BTL -3 Applying
3
and 2.4, find P(x=2).
18.
If x is a Poisson distribution such that P(x=1)=4P(x=2). Find its
mean and variance.
BTL -3 Applying
19.
Suppose that X has a Poisson distribution with parameter ? = 2.
Compute P[X ? 1].
BTL -1 Remembering
20. Define mutually exclusive events. BTL -1 Remembering
PART-B
1(a).
Calculate the mean and standard deviation for the following table
giving the age distribution of 542 members.
Age
20-30 30-40 40-50 50-60 60-70 70-80 80-90
No 3 61 132 153 140 51 2
BTL-2 Understanding
1(b).
Find the geometric mean for the following data:
Group
2-4 4-6 6-8 8-10
Frequency 200 400 300 100
BTL-2
Understanding
2(a).
Find the mean, median and modal ages of married women at first
child birth
Age at the
birth of
first child
13
14
15
16
17
18
19
20
21
22
23
24
25
No of
married
women
37
162
343
390
256
433
161
355
65
85
49
46
40
BTL -6 Creating
2(b).
If A and B are independent event with P(A)=2/5, and P(B)=3/5,
find P(A ?B). Let S= {1,2,3,4,5,6} if A = {2,4,6} then find the
probability of A complement.
BTL -3 Applying
3(a).
Given: The probabilities of three events A, B and C occurring are
P(A) = 0.35, P(B) = 0.45 and P(C) = 0.2. Assuming that A, B, or
C has occurred, the probabilities of another event X occurring are
P(X/A) = 0.8, P(X/B) = 0.65 and P(X/C) = 0.3. Find P(A/X),
P(B/X) and P(C/X).
BTL -6 Creating
3(b).
4 cards are drawn from a well shuffled pack of cards. Find the
probability that
(i) All the four are queens
(ii) There is one card from each suit.
(iii) Two cards are diamonds and two are spades
All the four cards are hearts and one of them is jack
BTL -6 Creating
4(a).
Three machines all turn out non ferrous castings. Machine A
produces 1% defective and Machine B- 2% and machine C ? 5%.
Each machine produces 1/3 of the output. An inspector examines
a single casting, which he determines as non defective. Estimate
the probabilities of its having been produced by each machine.
BTL -6 Creating
4(b).
If the random variable X takes values 1, 2, 3, 4 such that
2P(X = 1) = 3P(X = 2) = P( X=3) = 5P(X = 4), find the
probability distribution and cumulative distribution of X.
BTL-2 Understanding
5(a).
Two dice are thrown together once. Find the probabilities for
BTL -3 Applying
4
getting the sum of the two numbers (i) equal to 5, (ii) multiple of
3, (iii) divisible by 4.
5(b).
Given ? = 4.2, for a poisson distribution. Find (a) P(X ? 2) (b)
P(X ? 5) (c) P(X = 8).
BTL -6 Creating
6(a).
An urn contains 5 balls. Two balls are drawn and found to be
white. What is the probability that all the balls are white?
BTL-1 Remembering
6(b).
The contents of urns I, II, III are as follows:
1 white, 2 black and 3 red balls;
2 white, 1 black and 1 red balls;
4 white, 5 black and 3 red balls;
One urn is chosen at random and two balls drawn. They happen to
be white and red. What is the probability that they come from
urns I, II, III?
BTL -3 Applying
7(a).
In 1989, there were three candidates for the position of principal
Mr. Chatterji, Mr. Ayangar and Dr. Singh. Whose chances of
getting the appointment are in the proportion 4:2:3 respectively.
The probability that Mr. Chatterji is selected, would introduce co-
education in the is 0.3. The probabilities of Mr. Ayangar
and Dr. Singh doing the same are respectively 0.5 and .08. What
is the probability that there was co-education in the in
1990?
BTL -3
Applying
7(b).
Find the probability that atmost 5 defective bolts will be found in
a box of 200 bolts, if it is known that 2% of such bolts are
expected to be defective. (e
-4
= 0.0183)
BTL -6 Creating
8(a).
A coin is tossed 6 times what is the probability of obtaining (a) 4
heads (b) 5 heads (c) 6 heads (d) getting 4 or more heads.
BTL -3 Applying
8(b).
In a bolt factory machines A, B, C manufacture respectively 25%,
35% and 40% of the total of their output 5, 4, 2 percent are
defective bolts. If A bolt is drawn at random from the product and
is found to be defective, what are the probabilities that is was
manufactured by machines A, B and C?
BTL -6 Creating
9(a).
In a test of 2000 electric blubs it was found that the life of a
particular make was normally distributed with an average life of
2040 hours and S. D. of 60 hours. Estimate the number of blubs
likely to burn for
(1) More than 2150 hours
(2) Less than 1950 hours
(3) More than 1920 hours but less than 2160 hours.
BTL -3 Applying
9(b).
The latest nationwide political poll indicates that for Americans
who are randomly selected, the probability that they are
conservative is 0.55, the probability that they are liberal is 0.30
and the probability that they are middle of the road is 0.15.
Assuming these probabilities are accurate, answer the following
BTL -4 Analyzing
5
questions from a randomly chosen group of 10 Americans
(a) What the probability that 4 are liberal?
(b) What the probability that none are conservative
(c) What the probability that two are middle of the road
(d) What the probability that a least 8 are liberal
10.
If X follows a normal distribution with mean 12 and variance 16
cm, find the probabilities for (i) X ? 20 (ii) X ? 20, and (iii) 0 ? X
? 12.
BTL -3 Applying
11.
A discerete random variable X has the probability function given
below:
Value of X=x: 0 1 2 3 4 5 6 7
P(X=x) : 0 k 2k 2k 3k k
2
2k
2
7k
2
+k
Find (1) The value of k
(2) P(1.5 < X < 4.5 / X > 2)
(3) P(X < 6), P(X ? 5), P( 0 < X < 4)
(4) The distribution of X.
BTL -3 Applying
12.
X is a normal variable with mean 30 and standard deviation of 5.
Find (i) P[26 ? X ? 40] (ii) P [X?45] (iii) P [ ?X - 30 ?> 5] use
normal distribution tables
BTL -4 Analyzing
13.
In an intelligence test administered on 1000 students, the average
was 42 and standard deviation 24, find (i) the number of students
exceeding a score 50. (ii) the number of students lying between
30 and 54(iii) the value of score exceeded by top 100 students.
BTL -4 Analyzing
14(a).
The probability that an entering student will graduate is 0.4
Determine the probability that out of 5 students atleast one will
graduate.
BTL-5
Evaluating
14(b).
Fit a Poisson Distribution to the following data which gives the
number of doddens in a sample of clover seeds
No 0 1 2 3 4 5 6 7 8
f 56 156 132 92 37 22 4 0 1
.
BTL -4 Analyzing
PART-C
1(a).
A disciplinary committee is formed from the staff of XYZ
Company which has three departments Marketing, Finance and
Production of the 10,5,20 members respectively. All departments
have two female staff each. A department is selected at random
and from which two matters are selected for the committee,
What is the probability that both the team members are female?
BTL-6 Creating
6
1(b).
In a bolt factory machines A, B, C manufacture respectively 25,
35 and 40 percent of the total. Of their output 5, 4 and 2 percent
are defective bolts respectively. A bolt is drawn at random from
the product and is found o be defective. What are the probabilities
that it was manufactured by machines A, B or C?
BTL-2
Understanding
2(a). State Bayes theorem and brief about its applications. BTL-2 Understanding
2(b).
Out of 800 families with 4 children each, how many families
would be expected to have (i) 2 boys and 2 girls (ii) at least 1 boy
(iii) at most 2 girls (iv) children of both sexes? Assume equal
probabilities for boys and girls.
BTL-1 Remembering
3. Describe the classifications of probability ? BTL-1 Remembering
4. What are the applications of Normal distribution in statistics? BTL-6 Creating
UNIT ?II- SAMPLING DISTRIBUTION & ESTIMATION.
SYLLABUS: Introduction to sampling distributions, sampling distribution of mean and proportion, application of central
limit theorem, sampling techniques. Estimation: Point and Interval estimates for population parameters of large sample and
small samples, determining the sample size.
PART - A
S.N
O
QUESTIONS
BT Level
COMPETENCE
1. Define Sampling distribution of proportion. BTL -1 Remembering
2. Define Probable standard error. BTL -1 Remembering
3. Define standard error and mention its importance BTL -1 Remembering
4. Define central limit theorem BTL -1 Remembering
5.
What is the role of central limit theorem in estimation and testing
problems
BTL -6 Creating
6. Define stratified sampling technique BTL -1 Remembering
7. Briefly describe the significance level. BTL -1 Remembering
8. Distinguish between parameter and statistic. BTL -2 Understanding
9. Define estimator, estimate and estimation. BTL -1 Remembering
10. Distinguish between point estimation and interval estimation BTL -2 Understanding
11. Mention the properties of a good estimator. BTL -1 Remembering
12. Define confidence coefficient. BTL -1 Remembering
13. What is the level of significance in testing of hypothesis BTL -6 Creating
14. Define confidence limits for a parameter BTL -1 Remembering
15.
State the conditions under which a binomial distribution becomes a
normal distribution
BTL -4 Analyzing
16.
If the random sample comes from a normal population, what can
be said about the sampling distribution of the mean.
BTL -5 Evaluating
17.
An automobile repair shop has taken a random sample of 40
services that the average service time on an automobile is 130
minutes with a standard deviation of 26 minutes. Compute the
standard error of the mean.
BTL -6 Creating
7
18. What is a random number? How it is useful in sampling? BTL -6 Creating
19.
A population has the numbers: 12, 8, 10, 30, 12, 16, 40, 5, 16, 24,
22, 31, 30, 16, 15. Draw a systematic sample of size 5. Find out its
mean.
BTL -3 Applying
20. How large sample is useful in estimation and testing BTL -4 Analyzing
PART -B
1(a).
A random sample of 700 units from a large consignment showed
that 200 were damaged. Find (i) 95% (ii) 99% confidence limits
for the proportion of damaged units in the consignment.
BTL -3 Applying
1(b).
A random sample of size 9 is obtained from a Normal population
with mean 25 and if the variance 100 find the probability that the
sample mean exceeds 31.2.
BTL -4 Analyzing
2(a).
In a normally distributed population, average income per
household is Rs.20,000 with a standard deviation of Rs. 1,600.
Find the probability that the sample mean will be between
Rs.19,600 and Rs.20,200 in a survey of a random sample of 100
households.
BTL -6 Creating
2(b).
A university wants to determine the percentage of students who
would accept proposed fees hike for improving facilities. The
university wants to be 90% confident that the percentage is
within2% of the true value. Find the sample size to achieve the
accuracy regardless of the true percentage assuming the percentage
of students accepting the increase in tuition fees to be 0.5.
BTL -6 Creating
3(a).
A bank has kept records of the checking balances of its customers
and determined that the average daily balances of its customers is
Rs.300 with a standard deviation of Rs. 48. A random sample of
144 checking accounts is selected.
(i) What is the probability that the sample mean will be more
than Rs. 306.60?
(ii) What is the probability that the sample mean will be less
than Rs. 308?
BTL -6 Creating
3(b).
From the question 3(a)
(i) What is probability that the sample mean will between Rs.
302 and Rs. 308?
(ii) What is probability that the sample mean will be atleast
Rs. 296?
BTL -6 Creating
4(a).
Explain Stratified sampling technique and discuss how it is better
than simple random sampling in a particular situation.
BTL -4
Analyzing
4(b). Discuss the standard error of proportion BTL-2 Understanding
5.
Explain the methods of drawing simple random sample from a
finite population.
BTL -4 Analyzing
8
6(a).
In a sample of 1000 citizens of India, 540 are wheat eaters and the
rest are rice eaters. Can we assume that both rice and wheat
equally popular in India at 1 % level of significance?
BTL-5
Evaluating
6(b).
A simple random sample of 144 items resulted in a sample mean
of 1257.85 and standard deviation of 480. Develop a 95%
confidence interval for the population mean
BTL -6
Creating
7(a).
A car dealer wants to estimate the proportion of customers who
still own the cars they purchased 5 years earlier. A random sample
of 500 customers selected from the dealer?s records indicate that
315 customers still own cars that they were purchased 5 years
earlier. Set up 95% confidence interval estimation of the
population proportion of all the customers who still own the cars 5
years after they were purchased.
BTL-2
Understanding
7(b).
A movie maker sampled 55 fans who viewed his master piece
movie and asked them whether they had planned to see it again.
Only 10 of them believed that the movie was worthy of a second
look. Find the standard error of the population of fans who will
view the film a second time. Construct a 90% confidence interval
for this population.
BTL -5 Evaluating
8(a).
From a population of size 600, a sample of 60 individuals revealed
mean and standard deviation as 6.2 and 1.45 respectively. (i) Find
the estimated standard error (ii) Construct 96% confidence
interval for the mean.
BTL -3 Applying
8(b).
The age of employees in a company follows normal distribution
with its mean and variance as 40 years and 121 years respectively.
If a random sample of 36 employees is taken from a finite normal
population of size 1000, what is the probability that the sample
mean is
(i) less than 45
(ii) greater than 42 and
(iii) between 40 and 42?
BTL -6
Creating
9(a).
A firm wishes to estimate with an error of not more than 0.03 and
a level of confidence of 98%, the proportion of consumers that
prefer its brand of household detergent. Sales report indicate the
about 0.20 of all consumers prefer the firm?s brand. What is the
requisite sample size?
BTL -5 Evaluating
9(b).
A random sample of 700 units from a large consignment should
that 200 were damaged.
Find (i) 95%
(ii) 99% confidence limits for the proportion of damaged
units in the consignment
BTL -3 Applying
10(a).
From a population of 500 items with a mean of 100 gms and
standard deviation of 12.5 gms, 65 items were chosen. (i) What is
the standard error? (ii) Find P(99.5 < X < 101.5).
BTL -6 Creating
10(b).
A non-normal distribution representing the number of trips
BTL -6 Creating
9
performed by lorries per week in a coal field has a mean of 100
trips and variance of 121 trips. A random sample of 36 lorries is
taken from the non-normal population. What is the probability that
the sample mean is
(i) greater than 105
(ii) less than 102
(iii) between 101 and 103 trips?
11.
Test the significance of the difference between the means of the
sample from the following data
Size of sample Mean SD
Sample A 100 61 4
Sample B 200 63 6
BTL -4 Analyzing
12(a).
A cigarete manufacturing firm claims that its brand. A outsells
brand B by 8%. If it is found that 42 out of a sample of 200
smokers prefer brand a and 18 out of another sample of 100
smokers prefer brand B, test whether the 8% difference is a valid
claim(use 5% level of significance).
BTL -4
Analyzing
12(b).
In an automotive safety test conducted by the North Carolina
Highway Safety Research center, the average tyre pressure in a
sample of 62 tyres was found to be 24 pounds per square inch, and
the standard deviation was 2.1 pounds per square inch.
(i) What is the estimated population standard deviation for this
population
(ii) Calculate the estimated standard error of the mean
(iii) Construct a 95% confidence interval for the population mean.
BTL -3 Applying
13(a).
The manager of a shop selling beverages wants to estimate the
actual amount of beverages in one litre bottles from a nationally
known manufacturer. As per manufacturer?s specifications, the
standard deviation of the volume of the beverage is 0.02 litre. The
average amount of beverage per 1 litre bottle is found to be 0.995
litre on checking 50 bottles. Setup 99% confidence interval
estimate of the true population average amount of beverage in a 1
liter bottle. Check whether the manufacturer is genuine in filling
the beverage.
BTL -6
Creating
13(b).
In a batch chemical process used for etching printed circuit boards,
two different catalysts are being compared to determine whether
they require different emersion times for removal of identical
quantities of photo resist material. Twelve batch were run with
catalyst 1, resulting in a sample mean emersion time of 24.6
minutes and sample standard deviation of 0.85 minutes. Fifteen
batches were run with catalyst 2, resulting in a mean emersion time
of 22.1 minutes and a standard deviation of 0.98 minutes. Find a
95% confidence interval on the difference in means, assuming that
2
2
2
1
? ? ? .
BTL -3 Applying
10
14.
In a random sample of 75 axle shafts. 12 have a surface finish that
is rougher than the specifications will allow. Suppose that a
modification is made in the surface finishing process and
subsequently a second random sample of 85 axle shafts is
obtained. The number of defective shafts in this second sample is
10. Obtain an approximate 95% confidence interval on the
difference in the proportions of defectives produced under the two
processes
BTL -5 Evaluating
PART-C
1.
In a sample of 25 observations from a Normal distribution with
mean 98.6 and standard deviation 17.2.
(i)What is P(92<102)
(ii)Find the corresponding probability given a sample of 36.
BTL -6 Creating
2.
Mary, an auditor for a large credit card company, knows that, on
average, the monthly balance of any customer is Rs.112, and the
standard deviation is Rs.56. If Mary audits 50 randomly selected
accounts, What is the probability that the sample average balance
is
(i) Below Rs. 100
(ii)Between Rs.100 and Rs.130
BTL -6 Creating
3(a).
Write the type of sampling methods and the uses of standard error?
BTL -1 Remembering
3(b).
From a population of 540, a sample of 60 individual is taken. From
this sample, the mean is found to 6.2 and the standard deviation
1.368
(i) Find the estimated standard error of the mean.
(ii) Construct a 96 % confidence interval for the mean.
BTL-2 Understanding
4(a).
Explain the properties of good point estimator.
BTL -4 Analyzing
4(b).
What do you mean by interval estimation? Give examples
BTL-6 Creating
UNIT III - TESTS OF HYPOTHESIS- PARAMETRIC TESTS
SYLLABUS: Hypothesis testing: one sample and two sample tests for means and proportions of large samples (z-test),
one sample and two sample tests for means of small samples (t-test), F-test for two sample standard deviations. ANOVA
one and two way.
PART-A
Q.
No.
Question
Bloom?s
Taxonomy
Level
Domain
1. Define Test of Significance. BTL-1 Remembering
2. What are the Type I and Type II errors? BTL-6 Creating
3. What do you mean by one tail test? BTL-6 Creating
4. State the applications of Z-test and t-test. BTL-4 Analyzing
5. Define critical region BTL-1 Remembering
6. Distinguish between one tail and two tail tests BTL-2 Understanding
7. What is the aim of design of experiments? BTL-6 Creating
8. Distinguish between one-way and two-way analysis of variance. BTL-2 Understanding
9. When does the Z-test apply? BTL-1 Remembering
10. Explain SSB , SSW and SSY
and relationship in ANOVA. BTL-4 Analyzing
11
11. Describe any two applications of t-distribution BTL-1 Remembering
12. Write the uses of F-test? BTL-6 Creating
13. Define the level of significance. BTL-1 Remembering
14. Write the properties of t-distribution? BTL-6 Creating
15. What is the role of standard error? BTL-6 Creating
16. Mention any four applications of t-distribution in tests of hypothesis. BTL-1 Remembering
17. Mention any four uses of Chi-square distribution in test of hypothesis. BTL-1 Remembering
18. Define null hypothesis ? Explain. BTL-6 Creating
19.
Estimate the standard error of difference between two proportion if
p
1
=0.10,p
2=
0.133 and n
1
=50,n
2
=75.
BTL-6 Creating
20.
Mention any two assumptions made in analysis of variance
techniques.
BTL-1 Remembering
PART-B
1(a).
A study compares the effect of four 1-month point-of-purchase
promotions on sales. The unit sales for five stores using all four
promotions in different months follow.
Free Sample
78 87 81 89 58
One-pack gift
94 91 87 90 88
Cents off
73 73 78 69 83
76Refund by mail
79 83 78 69 81
(i)Compute the mean unit sales for each promotion and then
determine the grand mean.
(ii)Estimate the population variance using the between column
variance.
BTL-5 Evaluating
1(b).
From the question 1(a)
(i)Estimate the population variance using the within-column variance
computed from the variance within the samples.
(ii)Calculate the F ratio. At the 0.01 level of significance, do the
promotions produce different effects on sales.
BTL-2 Understanding
2(a).
In a low cost Toy production system, the molding machine has been
set with standard of 1% defective. The 80 sample units produced from
this machine shows defective of one unit. Is it necessary to stop the
product for corrective mechanism? Test at 5% level of significance
BTL-5 Evaluating
2(b).
Block Enterprises, a manufacturer of chips for computers. Is in the
process of deciding whether to replace its current semi automated
assembly line with a fully automated assembly line. Block has
gathered some preliminary test data about hourly chip production,
which is summarized in the following table, and it would like to know
whether it should upgrade its assembly line. State (and test at a =0.02)
appropriate hypothesis to help Block decide.
BTL-5 Evaluating
3(a).
Three samples below have been obtained from normal population
with equal variance. Test the hypothesis that the means are equal.
Sample I : 10 12 18 15 16
Sample II : 7 15 10 12 8
Sample III : 12 8 15 16 15
BTL-5 Evaluating
3(b). The I.Q.s of 16 students from one class of an showed a BTL-2 Understanding
12
mean of 107 with a standard deviation of 10, while the I.Q.s of 14
students from another class showed a mean of 112 with a standard
deviation of 8. Check whether there is an appreciable difference
between the I.Q.s of the two groups at (i) 0.01and (ii) 0.05 level of
significance
4(a).
The following is the information obtained from a random sample of 5
observations. Assume the population has a normal distribution.
30 31 27 32 28
To test if the sample was drawn from a normal distribution with mean
less than 30, (i)State the null and alternative hypotheses
(ii)Compute the standard error.
BTL-2 Understanding
4(b).
From the question 4(a)
(i)Determine the test statistic.
(ii)Decide at 10% level whether or not the mean value could be
greater than 30
BTL-2 Understanding
5.
The following data relate to the number of units produced per week by
three methods.
Method 1 : 170 192 190 120
Method 2 : 160 165 170 172
Method 3 : 182 190 170 178 185
Prepare ANOVA table and write your comments
BTL-6 Creating
6(a).
Test if the following samples could have come from two populations
with the same means, assuming the population variances are equal.
Sample I Sample II
Sample size 12 10
Sample Mean 40.5 43.8
Sample variance 2.6 3.2
BTL-5 Evaluating
6(b).
The weights of 10 people of a locality are found to be
70,67,62,68,61,68,70,64,64,66 kilograms. Is it reasonable to believe
that the average weights of the people of locality is greater than 64
kg? Test at 5%level of significance.
BTL-5 Evaluating
7(a).
In Town A, there were 850 birds of which 52% was males, while in
Town A and Town B combined, the proportion of males in a total of
1200 birds was 0.49. Is there any significance difference in the
proportions of male birds in the two Towns?
BTL-2
Understanding
7(b).
IQ test result of randomly selected five employees in an organization
is given below. Test whether minimum requirement of average IQ
level 87 is maintained in that company or not.
Employee code 234 232 121 343 111
IQ test 85 95 90 93 87
BTL-4 Analyzing
8(a).
The weights of 8 persons are found to be 60, 65, 70, 68, 62, 63, 60,
and 66 kgs. The weights of another group of 12 persons are found to
be 70, 60, 58, 56, 50, 48, 52, 56, 52, 50, 54, and 50. Can we conclude
that both samples have come from populations with same variances?
BTL -4 Analyzing
13
8(b).
ATMs must be stocked with enough cash to meet the requirements of
customers over a week, but excess cash results in loss of income as
investment opportunities could not be utilized. In an ATM, the
average transaction per customer in a week is Rs.8000 with a standard
deviation of Rs.1500. If a random sample of 36 customer transactions
is examined and it is observed that the sample mean with drawl is
Rs.8600, check the belief that the true average withdrawal is no longer
Rs.8000. Assume 0.05 level of significance
BTL -3 Applying
9.
Apply ANOVA technique and write your comment regarding the
sales(in Rs. Lakhs)
Area
Representatives
1 2 3 4
A 12 16 20 18
B 15 10 12 16
C 10 08 16 15
BTL -3 Applying
10(a).
A farmer wishes to determine whether there is a difference in yields
between two different varieties of wheat I and II. The following data
shows the production of wheat per unit area using the two varieties.
Can the farmer conclude at significance levels of
(i) 0.05
(ii) 0.01 that a difference exists?
BTL -4 Analyzing
10(b).
Test if the samples could have come from equal population means.
Sample A Sample B
Size 200 400
Mean 154.8 164.3
Variance 15.2 18.2
BTL-5 Evaluating
11(a).
The number of accidents per week in a city are as follows:
12, 8, 20, 2, 14, 10, 15, 6, 9 and 4. Are these frequencies in agreement
with the belief that accident conditions were the same during this 10
weeks period?
BTL -4
Analyzing
11(b).
Two samples are drawn from two normal population. From the
following data, Test whether the two samples have the same variance
5% level of significance.
Sample 1 60 65 69 74 76 82 85 87
Sample 2 61 66 67 85 78 63 85 86 88 91
BTL -3 Applying
12(a).
Given a sample mean of 83, a sample standard deviation of 12.5 and a
sample size of 22, test the hypothesis that the value of the population
mean is 70 against alternative that it is more than 70. Use the 0.025
significance level.
BTL-2
Understanding
12(b).
The following table shows the lifetimes in hours of samples from
three different types of television tables manufactured by a company.
Determine whether there is a difference between the three types at
significance level of 0.01.
Table:
BTL-2
Understanding
14
Sample 1 407 411 409
Sample 2 404 406 408 405 402
Sample 3 410 408 406 408
13.
The following table shows the yields per acre of hour different plants
crops grown on lots treated with three different types of fertilizer.
Determine at the 5% significance level whether there is a difference in
yield per acre.
(i) due to the fertilizers and
(ii) due to the crops
Table:
Crop -I Crop -II Crop -III Crop -IV
Fertilizer A 4.5 6.4 7.2 6.7
Fertilizer B 8.8 7.8 9.6 7.0
Fertilizer C 5.9 6.8 5.7 5.2
BTL-2
Understanding
14.
Time of 6 machine operator (in minute) in making product is given
below. Use paired t-test for training effectiveness.
Machine operator 1 2 3 4 5 6
Before training 12 23 4 5 16 17
After training 2 3 10 8 12 6
BTL -3 Applying
PART C
1(a).
What are non-parametric tests? Point out their advantages and
disadvantages?
BTL -6 Creating
1(b).
The success of a sales engineer in adopting the proven sales technique
was found to be 12 out of 30 occasions. Hence he tried a novel
technique and achieved success at a rate of 23 out of 40 occasions.
Check whether the novel technique is effective at 5% level of
significance.
BTL-2 Understanding
2(a).
The following are the final examination marks of three groups of
students who were taught computer by three difference methods.
First method: 94 88 91 74 87 97
Second method: 85 82 79 84 61 72 80
Third method: 89 67 72 76 69
BTL -5 Evaluating
2(b).
A consumer product manufacturing company was selling one of its
leading products through a large number of retail shops. Before a
heavy advertisement campaign, the average sale per week per shop
was 140 dozens. After the campaign, a sample of 26 shops was taken
and the mean sales improved to 147 dozens with a standard deviation
of 16. Check the effectiveness of the advertisement campaign at 5%
level of significance
BTL-2
Understanding
3.
Discuss the test procedure to test hypothesized population proportion
using single sample proportion.
BTL-1 Understanding
15
4.
(i)Write the application testing of hypothesis in statistics. (ii)What is
t-test? When should we apply a t-test?
BTL -3 Applying
UNIT IV: NON-PARAMETRIC TESTS
SYLLABUS: Chi-square test for single sample standard deviation. Chi-square tests for independence ofattributes and
goodness of fit. Sign test for paired data. Rank sum test. Kolmogorov-Smirnov ? test for goodness of fit, comparing two
populations. Mann ? Whitney U test and Kruskal Wallis test. One sample run test.
PART-A
Q.
No.
Question
Bloom?s
Taxonomy
Level
Domain
1. Define Rank Correlation test. BTL-1 Remembering
2. Write the formula in chi square test and any two uses. BTL-1 Remembering
3. Define Rank-Sum test. BTL-1 Remembering
4. Mention the advantages of Nonparametric Tests. BTL-1 Remembering
5. What is the other name or non-parametric test? Why? BTL-6 Creating
6. When are non parametric tests used? BTL-1 Remembering
7. What is the null hypothesis framed in Mann-Whitney test? BTL-6 Creating
8.
Write down the working rule for Mann-Whitney U-test and Kruskal-
Wallis test.
BTL-1 Remembering
9. Explain sign test. BTL-4 Analyzing
10. Define one sample run test? BTL-1 Remembering
11. When is Krushkal-Wallis test used? BTL-1 Remembering
12. Distinguish between Mann-Whitney U-test and Krushkal-Wallis test. BTL-2 Understanding
13. Write the contingency 2*2 table for
test. BTL-5 Evaluating
14.
Write down the formula to calculate rank correlation coefficient
(including tie values).
BTL-1 Remembering
15.
Two HR managers (A and B) ranked five candidates for a new
position. Their rankings of the candidates are show below:
Candidate Rank by A Rank by B
Nancy 2 1
Mary 1 3
John 3 4
Lynda 5 5
Steve 4 2
Compute the Spearman rank correlation.
BTL-6 Creating
16. Define rank correlation co-efficient. BTL-1 Remembering
17.
The following are the ranks obtained by 10 students in Statistics and
Mathematics. Find out the rank correlation coefficient.
Statistics 1 2 3 4 5 6 7
Mathematics 2 5 1 6 7 4 3
BTL-4 Analyzing
18. Explain Kolmogorov-Smirnov Test for one sample problem. BTL-4 Analyzing
19. What adjustment is to be done for tie values to find rank correlation. BTL-6 Creating
20. Mention the properties of linear coefficient of correlation. BTL-1 Remembering
PART -B
1(a).
The scores of a written examination of 24 students, who were trained
by using three different methods, are given below.
Video cassette A 74 88 82 93 55 70 65
BTL-3 Applying
16
Audio cassette B 78 80 65 57 89 85 78 70
Class Room C 68 83 50 91 84 77 94 81 92
Use Krushkal-Wallis test at ? = 5% level of significance, whether the
three methods of training yield the same results.
1(b). Explain Rank sum tests and its applications
2(a).
The production volume of units assembled by three different
operators during 9 shifts is summarized below. Check whether there
is significant difference between the production volumes of units
assembled by the three operators using Krushkal-Wallis test at a
significant level of 0.05.
Operator I 29 34 34 20 32 45 42 24 35
Operator II 30 21 23 25 44 37 34 19 38
Operator III 26 36 41 48 27 39 28 46 15
BTL-3
Applying
2(b).
Two faculty members ranked 12 candidates for scholarships.
Calculate the spearman rank-correlation coefficient and test it for
significance. Use 0.02level of significance.
Candidate Rank by Professor A Rank by Professor B
1 6 5
2 10 11
3 2 6
4 1 3
5 5 4
6 11 12
7 4 2
8 3 1
9 7 7
10 12 10
11 9 8
12 8 9
BTL-3
Applying
3(a).
In a study of sedimentary rocks, the following data were obtained
from samples of 32 grains from two kinds of sand :
Apply Mann-Whitney U test with suitable null and alternative
hypotheses.
Sand I 63 17 35 49 18 43 12 20 47
? 136 51 45 84 32 40 44 25
Sand II 113 54 96 26 39 88 92 53 101
? 48 89 107 111 58 62
BTL -3 Applying
3(b).
The Molisa?s shop has 3 mall locations. She keeps a daily record for
each locations of the number of the customers who actually make a
purchase. A sample of these data follows. Using Kruskal- Wallis test
can you say that at 5% level of significance that her stores have the
same number of customers who buy.
Eastowin 99 64 101 85 79 88 97 95 90 100
Craborchard 83 102 125 61 91 96 94 89 93 75
Fair forest 89 98 56 105 87 90 87 101 76 89
BTL -3 Applying
4(a)
The following are the prices in Rs. per kg of a commodity from 2
random samples of shops from 2 cities A&B.
BTL -3 Applying
17
City A 2.7 3.8 4.3 3.2 4.7 3.6 3.8 4.1
2.7 2.8 3.2 3.4 3.8 4.4 4.9 3.9 4.7
City B 3.7 5.3 4.7 3.6 4.7 4.8 6.0 4.8 4.9
3.8 3.9 4.8 5.2 6.1 3.6 3.8
Apply the run test to examine whether the distribution of prices of
commodity in the two cities is the same.
4(b)
Distinguish Nonparametric methods over parametric methods.
BTL -2 Understanding
5(a)
From a poll of 800 television viewers, the following data have been
accumulated as to,their levels of education and their performance of
television stations. We are interested in determining if the selection
of Tv station is independent of the level of education.
Education Level
High school Bachelor graduate Total
Public Broadcasting 50 150 80 280
Commercial
stations
150 250 120 520
Total 200 400 200 800
(i) State the null and alternative hypothesis.
(ii) Show the contingency table of the expected
frequencies
BTL -3 Applying
5(b)
From the question 5(a)
(i)Compute the test static
(ii)The null hypothesis to be tested at 95% confidence Determine the
critical value for this test
BTL-6
Creating
6(a)
Apply Mann-Whitney U test to determine if there is a significant
difference in the age distribution of the two groups
Day :26 18 25 27 19 30 34 21 33 31
Evening :32 24 23 30 40 41 42 39 45 35
BTL -3
Applying
6(b)
Apply the K-S test to check that the observed frequencies match with
the expected frequencies which are obtained from Normal
distribution. (Given at n=5).
Test Score 51-60 61-70 71-80 81-90 91-100
Observed Frequency
30 100 440 500 130
Expected Frequency 40 170 500 390 100
BTL -5 Evaluating
7
A research company has designed three different systems to clean up
oil spills. The following table contains the results, measures by how
much surface area (in square meters) is cleaned in one hour. The data
were found by testing each method in several trials. Are there
systems equally effective? Use the 5% level of significance.
Sample A 55 60 63 56 59 55
Sample B 57 53 64 49 62
Sample C 66 52 61 57
BTL -1 Remembering
8(a)
Suppose it is desired to check whether pinholes in electrolytic tin
plate are distributed uniformly across a plated coil on the basis of the
following distances (in inches) of 10 pinholes from one edge of a
BTL -1 Remembering
18
long strip of tin plate 320 inches wide.
4.8 14.8 28.2 23.1 4.4 28.7 19.5 2.4 25.0 6.2
Use Kolmogorov Smirnov test to test the null hypothesis.
8(b) Explain Mann- WhitneyU test with an example BTL-4 Analyzing
9.
Ten competitors in a beauty contest are ranked by 3 judges in the
following order.
A : 1 6 5 3 10 2 4 9 7 8
B : 3 5 8 4 7 10 2 1 6 9
C : 6 4 9 8 1 2 3 10 5 7
Find out which pair of Judges has awarded the ranks to the nearest
common taste of beauty.
BTL -3 Applying
10(a).
Test the association of Age and preference of colour of Toy from the
following data
Age/Colour Below 5 6-10 Above 10 years
Pink 60 40 5
Purple 30 30 30
Red 80 10 10
BTL -4 Analyzing
10(b).
Melisa?s Boutique has three mall locations. Melisa keeps a dairy
record for each location of number of customers who actually make a
purchase. A sample of those data follows. Using the kruskal-wallis
test, can you say at the 0.05 level of significance that her stores have
the same number of customers who busy?
DSF Mall 99 64 101 85 79 88 97 95 90 100
Forest Mall 83 102 125 61 91 96 94 89 98 75
Big-Ben Mall 89 98 56 105 87 90 87 101 76 89
BTL -3 Applying
11(a).
A brand manager is concerned that her brand?s share may he
unevenly distributes through the country. In a survey in which the
country was divided into four geographic regions, a random
sampling of 100 consumers in each region was surveyed, with the
following results:
NE NW SE SW TOTAL
Purchase the brand 40 55 45 50 190
Do not purchase 60 45 55 50 210
Total 100 100 100 100 400
(i) Develop a table of observed and expected frequencies for
this problem.
(ii) Calculate the sample
value.
BTL -6 Creating
11(b).
From the question 11(a)
(i)State the null and alternative hypothesis.
(ii)At test whether brand share is the same across the four
regions
BTL -2 Understanding
12(a).
In 30 tosses of a coin, the following sequence of head and tails is
obtained HTTHTHHHTHHTTHTHTHHTHTTHTHHTHT
(i) Determine the number of runs
BTL -2 Understanding
12(b).
From the question 12(a ) Test at 0.10 level of significance, whether
the sequence is random
BTL -3 Applying
13. An experiment designed to compare three preventative methods BTL -3 Applying
19
against corrosion yielded the following maximum depths of pits ( in
thousandths of an inch) in pieces of wire subjected to the respective
treatments:
Method A: 77 54 67 74 71 66
Method B: 60 41 59 65 62 64 52
Method C: 49 52 69 47 56
Use the Kruskal-Wallis test at the 5% level of significance to test the
null hypothesis that the three samples come from identical
populations.
14.
The number of defects in printed circuit boards in hypothesized to
follow a poisson distribution. A random sample of 60 printed boards
have been collected and the number of defects observed. The
following table gives the results.
Table:
No. of defects Observed Frequency
0 32
1 15
2 9
3 4
Does the assumption of a poisson distribution seem appropriate as a
probability model for this process?
BTL -4
Analyzing
PART C
1. Explain the Mann-Whitney test procedure with appropriate examples BTL-1 Remembering
2.
Write the application of Non parametric test and Sign test in
statictics.
BTL-1 Remembering
3(a).
The sales records of two branches of a department store over the last
12 months are shown below.(sales figures are in thousands of
dollars). We want to use the Mann-Whitney-Wilcoxon test to
determine if there is a significant difference in the sales of the two
branches.
Month Branch A Branch B
1 257 210
2 280 230
3 200 250
4 250 260
5 284 275
6 295 300
7 297 320
8 265 290
9 330 310
10 350 325
11 340 329
12 372 335
(i) Compute the sum of the ranks for branch A
(ii) Compute the mean ?T
BTL-4 Analyzing
3(b).
From the question 3(a)
(i)Compute ?T
BTL -6 Creating
FirstRanker.com - FirstRanker's Choice
1
(An
Ka ttankulathur ?
DEPARTMENT OF MATHEMATICS
QUESTION BANK
I SEMESTER
1918108 ? STATISTICS FOR MANAGEMENT
Regulation ? 2019
Academic Year 2019 - 2020
Prepared by
Ms. B. Vasuki, Assistant Professor/Mathematics
Ms.B.Elakkiavani, Assistant Professor/Mathematics
2
(An
? .
DEPARTMENT OF MATHEMATICS
QUESTION BANK
SUBJECT : 1918108 ? STATISTICS FOR MANAGEMENT
SEM / YEAR : I Semester / I Year
UNIT I - INTRODUCTION
SYLLABUS: Basic definitions and rules for probability, conditional probability independence of events, Baye?s
theorem, and random variables, Probability distributions: Binomial, Poisson, Uniform and Normal distributions.
PART- A
S.NO QUESTIONS
BT Level
COMPETENCE
PART ? A
1. Define Statistics. BTL -6 Creating
2. What is the addition and multiplication theorem on probability. BTL -1 Remembering
3. Distinguish between a priori and posterior probability?. BTL -6 Creating
4.
The price of the selected stock over a five day period shown as 170, 110,
130, 170 and 160. Compute mean , median and mode.
BTL -6 Creating
5.
A car travels 25 miles at 25 mph, 25 miles at 50 mph and 25 miles at 75
mph. Find the harmonic of three velocities?
BTL -4 Analyse
6.
A ball is drawn at random from a box containg 6 red balls, 4 white balls
and 5 blue balls. Find the probability that the ball drawn is not red.
BTL -4 Analyse
7.
Find the median and mode for the weights (kgs) of 15 persons given as
68, 85, 70, 65, 71, 67, 65, 55, 80, 62, 65, 64, 70, 60, 56.
BTL -3 Applying
8. Name few measures of dispersion. BTL -1 Remembering
9. write the common measures of central tendency? BTL -1 Remembering
10. Define continuous and discrete variables examples. BTL -1 Remembering
11.
Let X be the lifetime in years of a mechanical part. Assume that X has
the cdf F(x) = 1- e
-x
, x ? 0. Find P[1< X ? 3].
BTL -1 Remembering
12. Define independent events. BTL -1 Remembering
13. State the theorem of total probability BTL -1 Remembering
14. What is the use of Baye?s theorem? BTL -6 Creating
15. Mention the properties of a discrete probability distribution. BTL -1 Remembering
16. Define a Poisson distribution and mention its mean and variance. BTL -1 Remembering
17. If the mean and variance of a binomial distribution are respectively 6 BTL -3 Applying
3
and 2.4, find P(x=2).
18.
If x is a Poisson distribution such that P(x=1)=4P(x=2). Find its
mean and variance.
BTL -3 Applying
19.
Suppose that X has a Poisson distribution with parameter ? = 2.
Compute P[X ? 1].
BTL -1 Remembering
20. Define mutually exclusive events. BTL -1 Remembering
PART-B
1(a).
Calculate the mean and standard deviation for the following table
giving the age distribution of 542 members.
Age
20-30 30-40 40-50 50-60 60-70 70-80 80-90
No 3 61 132 153 140 51 2
BTL-2 Understanding
1(b).
Find the geometric mean for the following data:
Group
2-4 4-6 6-8 8-10
Frequency 200 400 300 100
BTL-2
Understanding
2(a).
Find the mean, median and modal ages of married women at first
child birth
Age at the
birth of
first child
13
14
15
16
17
18
19
20
21
22
23
24
25
No of
married
women
37
162
343
390
256
433
161
355
65
85
49
46
40
BTL -6 Creating
2(b).
If A and B are independent event with P(A)=2/5, and P(B)=3/5,
find P(A ?B). Let S= {1,2,3,4,5,6} if A = {2,4,6} then find the
probability of A complement.
BTL -3 Applying
3(a).
Given: The probabilities of three events A, B and C occurring are
P(A) = 0.35, P(B) = 0.45 and P(C) = 0.2. Assuming that A, B, or
C has occurred, the probabilities of another event X occurring are
P(X/A) = 0.8, P(X/B) = 0.65 and P(X/C) = 0.3. Find P(A/X),
P(B/X) and P(C/X).
BTL -6 Creating
3(b).
4 cards are drawn from a well shuffled pack of cards. Find the
probability that
(i) All the four are queens
(ii) There is one card from each suit.
(iii) Two cards are diamonds and two are spades
All the four cards are hearts and one of them is jack
BTL -6 Creating
4(a).
Three machines all turn out non ferrous castings. Machine A
produces 1% defective and Machine B- 2% and machine C ? 5%.
Each machine produces 1/3 of the output. An inspector examines
a single casting, which he determines as non defective. Estimate
the probabilities of its having been produced by each machine.
BTL -6 Creating
4(b).
If the random variable X takes values 1, 2, 3, 4 such that
2P(X = 1) = 3P(X = 2) = P( X=3) = 5P(X = 4), find the
probability distribution and cumulative distribution of X.
BTL-2 Understanding
5(a).
Two dice are thrown together once. Find the probabilities for
BTL -3 Applying
4
getting the sum of the two numbers (i) equal to 5, (ii) multiple of
3, (iii) divisible by 4.
5(b).
Given ? = 4.2, for a poisson distribution. Find (a) P(X ? 2) (b)
P(X ? 5) (c) P(X = 8).
BTL -6 Creating
6(a).
An urn contains 5 balls. Two balls are drawn and found to be
white. What is the probability that all the balls are white?
BTL-1 Remembering
6(b).
The contents of urns I, II, III are as follows:
1 white, 2 black and 3 red balls;
2 white, 1 black and 1 red balls;
4 white, 5 black and 3 red balls;
One urn is chosen at random and two balls drawn. They happen to
be white and red. What is the probability that they come from
urns I, II, III?
BTL -3 Applying
7(a).
In 1989, there were three candidates for the position of principal
Mr. Chatterji, Mr. Ayangar and Dr. Singh. Whose chances of
getting the appointment are in the proportion 4:2:3 respectively.
The probability that Mr. Chatterji is selected, would introduce co-
education in the is 0.3. The probabilities of Mr. Ayangar
and Dr. Singh doing the same are respectively 0.5 and .08. What
is the probability that there was co-education in the in
1990?
BTL -3
Applying
7(b).
Find the probability that atmost 5 defective bolts will be found in
a box of 200 bolts, if it is known that 2% of such bolts are
expected to be defective. (e
-4
= 0.0183)
BTL -6 Creating
8(a).
A coin is tossed 6 times what is the probability of obtaining (a) 4
heads (b) 5 heads (c) 6 heads (d) getting 4 or more heads.
BTL -3 Applying
8(b).
In a bolt factory machines A, B, C manufacture respectively 25%,
35% and 40% of the total of their output 5, 4, 2 percent are
defective bolts. If A bolt is drawn at random from the product and
is found to be defective, what are the probabilities that is was
manufactured by machines A, B and C?
BTL -6 Creating
9(a).
In a test of 2000 electric blubs it was found that the life of a
particular make was normally distributed with an average life of
2040 hours and S. D. of 60 hours. Estimate the number of blubs
likely to burn for
(1) More than 2150 hours
(2) Less than 1950 hours
(3) More than 1920 hours but less than 2160 hours.
BTL -3 Applying
9(b).
The latest nationwide political poll indicates that for Americans
who are randomly selected, the probability that they are
conservative is 0.55, the probability that they are liberal is 0.30
and the probability that they are middle of the road is 0.15.
Assuming these probabilities are accurate, answer the following
BTL -4 Analyzing
5
questions from a randomly chosen group of 10 Americans
(a) What the probability that 4 are liberal?
(b) What the probability that none are conservative
(c) What the probability that two are middle of the road
(d) What the probability that a least 8 are liberal
10.
If X follows a normal distribution with mean 12 and variance 16
cm, find the probabilities for (i) X ? 20 (ii) X ? 20, and (iii) 0 ? X
? 12.
BTL -3 Applying
11.
A discerete random variable X has the probability function given
below:
Value of X=x: 0 1 2 3 4 5 6 7
P(X=x) : 0 k 2k 2k 3k k
2
2k
2
7k
2
+k
Find (1) The value of k
(2) P(1.5 < X < 4.5 / X > 2)
(3) P(X < 6), P(X ? 5), P( 0 < X < 4)
(4) The distribution of X.
BTL -3 Applying
12.
X is a normal variable with mean 30 and standard deviation of 5.
Find (i) P[26 ? X ? 40] (ii) P [X?45] (iii) P [ ?X - 30 ?> 5] use
normal distribution tables
BTL -4 Analyzing
13.
In an intelligence test administered on 1000 students, the average
was 42 and standard deviation 24, find (i) the number of students
exceeding a score 50. (ii) the number of students lying between
30 and 54(iii) the value of score exceeded by top 100 students.
BTL -4 Analyzing
14(a).
The probability that an entering student will graduate is 0.4
Determine the probability that out of 5 students atleast one will
graduate.
BTL-5
Evaluating
14(b).
Fit a Poisson Distribution to the following data which gives the
number of doddens in a sample of clover seeds
No 0 1 2 3 4 5 6 7 8
f 56 156 132 92 37 22 4 0 1
.
BTL -4 Analyzing
PART-C
1(a).
A disciplinary committee is formed from the staff of XYZ
Company which has three departments Marketing, Finance and
Production of the 10,5,20 members respectively. All departments
have two female staff each. A department is selected at random
and from which two matters are selected for the committee,
What is the probability that both the team members are female?
BTL-6 Creating
6
1(b).
In a bolt factory machines A, B, C manufacture respectively 25,
35 and 40 percent of the total. Of their output 5, 4 and 2 percent
are defective bolts respectively. A bolt is drawn at random from
the product and is found o be defective. What are the probabilities
that it was manufactured by machines A, B or C?
BTL-2
Understanding
2(a). State Bayes theorem and brief about its applications. BTL-2 Understanding
2(b).
Out of 800 families with 4 children each, how many families
would be expected to have (i) 2 boys and 2 girls (ii) at least 1 boy
(iii) at most 2 girls (iv) children of both sexes? Assume equal
probabilities for boys and girls.
BTL-1 Remembering
3. Describe the classifications of probability ? BTL-1 Remembering
4. What are the applications of Normal distribution in statistics? BTL-6 Creating
UNIT ?II- SAMPLING DISTRIBUTION & ESTIMATION.
SYLLABUS: Introduction to sampling distributions, sampling distribution of mean and proportion, application of central
limit theorem, sampling techniques. Estimation: Point and Interval estimates for population parameters of large sample and
small samples, determining the sample size.
PART - A
S.N
O
QUESTIONS
BT Level
COMPETENCE
1. Define Sampling distribution of proportion. BTL -1 Remembering
2. Define Probable standard error. BTL -1 Remembering
3. Define standard error and mention its importance BTL -1 Remembering
4. Define central limit theorem BTL -1 Remembering
5.
What is the role of central limit theorem in estimation and testing
problems
BTL -6 Creating
6. Define stratified sampling technique BTL -1 Remembering
7. Briefly describe the significance level. BTL -1 Remembering
8. Distinguish between parameter and statistic. BTL -2 Understanding
9. Define estimator, estimate and estimation. BTL -1 Remembering
10. Distinguish between point estimation and interval estimation BTL -2 Understanding
11. Mention the properties of a good estimator. BTL -1 Remembering
12. Define confidence coefficient. BTL -1 Remembering
13. What is the level of significance in testing of hypothesis BTL -6 Creating
14. Define confidence limits for a parameter BTL -1 Remembering
15.
State the conditions under which a binomial distribution becomes a
normal distribution
BTL -4 Analyzing
16.
If the random sample comes from a normal population, what can
be said about the sampling distribution of the mean.
BTL -5 Evaluating
17.
An automobile repair shop has taken a random sample of 40
services that the average service time on an automobile is 130
minutes with a standard deviation of 26 minutes. Compute the
standard error of the mean.
BTL -6 Creating
7
18. What is a random number? How it is useful in sampling? BTL -6 Creating
19.
A population has the numbers: 12, 8, 10, 30, 12, 16, 40, 5, 16, 24,
22, 31, 30, 16, 15. Draw a systematic sample of size 5. Find out its
mean.
BTL -3 Applying
20. How large sample is useful in estimation and testing BTL -4 Analyzing
PART -B
1(a).
A random sample of 700 units from a large consignment showed
that 200 were damaged. Find (i) 95% (ii) 99% confidence limits
for the proportion of damaged units in the consignment.
BTL -3 Applying
1(b).
A random sample of size 9 is obtained from a Normal population
with mean 25 and if the variance 100 find the probability that the
sample mean exceeds 31.2.
BTL -4 Analyzing
2(a).
In a normally distributed population, average income per
household is Rs.20,000 with a standard deviation of Rs. 1,600.
Find the probability that the sample mean will be between
Rs.19,600 and Rs.20,200 in a survey of a random sample of 100
households.
BTL -6 Creating
2(b).
A university wants to determine the percentage of students who
would accept proposed fees hike for improving facilities. The
university wants to be 90% confident that the percentage is
within2% of the true value. Find the sample size to achieve the
accuracy regardless of the true percentage assuming the percentage
of students accepting the increase in tuition fees to be 0.5.
BTL -6 Creating
3(a).
A bank has kept records of the checking balances of its customers
and determined that the average daily balances of its customers is
Rs.300 with a standard deviation of Rs. 48. A random sample of
144 checking accounts is selected.
(i) What is the probability that the sample mean will be more
than Rs. 306.60?
(ii) What is the probability that the sample mean will be less
than Rs. 308?
BTL -6 Creating
3(b).
From the question 3(a)
(i) What is probability that the sample mean will between Rs.
302 and Rs. 308?
(ii) What is probability that the sample mean will be atleast
Rs. 296?
BTL -6 Creating
4(a).
Explain Stratified sampling technique and discuss how it is better
than simple random sampling in a particular situation.
BTL -4
Analyzing
4(b). Discuss the standard error of proportion BTL-2 Understanding
5.
Explain the methods of drawing simple random sample from a
finite population.
BTL -4 Analyzing
8
6(a).
In a sample of 1000 citizens of India, 540 are wheat eaters and the
rest are rice eaters. Can we assume that both rice and wheat
equally popular in India at 1 % level of significance?
BTL-5
Evaluating
6(b).
A simple random sample of 144 items resulted in a sample mean
of 1257.85 and standard deviation of 480. Develop a 95%
confidence interval for the population mean
BTL -6
Creating
7(a).
A car dealer wants to estimate the proportion of customers who
still own the cars they purchased 5 years earlier. A random sample
of 500 customers selected from the dealer?s records indicate that
315 customers still own cars that they were purchased 5 years
earlier. Set up 95% confidence interval estimation of the
population proportion of all the customers who still own the cars 5
years after they were purchased.
BTL-2
Understanding
7(b).
A movie maker sampled 55 fans who viewed his master piece
movie and asked them whether they had planned to see it again.
Only 10 of them believed that the movie was worthy of a second
look. Find the standard error of the population of fans who will
view the film a second time. Construct a 90% confidence interval
for this population.
BTL -5 Evaluating
8(a).
From a population of size 600, a sample of 60 individuals revealed
mean and standard deviation as 6.2 and 1.45 respectively. (i) Find
the estimated standard error (ii) Construct 96% confidence
interval for the mean.
BTL -3 Applying
8(b).
The age of employees in a company follows normal distribution
with its mean and variance as 40 years and 121 years respectively.
If a random sample of 36 employees is taken from a finite normal
population of size 1000, what is the probability that the sample
mean is
(i) less than 45
(ii) greater than 42 and
(iii) between 40 and 42?
BTL -6
Creating
9(a).
A firm wishes to estimate with an error of not more than 0.03 and
a level of confidence of 98%, the proportion of consumers that
prefer its brand of household detergent. Sales report indicate the
about 0.20 of all consumers prefer the firm?s brand. What is the
requisite sample size?
BTL -5 Evaluating
9(b).
A random sample of 700 units from a large consignment should
that 200 were damaged.
Find (i) 95%
(ii) 99% confidence limits for the proportion of damaged
units in the consignment
BTL -3 Applying
10(a).
From a population of 500 items with a mean of 100 gms and
standard deviation of 12.5 gms, 65 items were chosen. (i) What is
the standard error? (ii) Find P(99.5 < X < 101.5).
BTL -6 Creating
10(b).
A non-normal distribution representing the number of trips
BTL -6 Creating
9
performed by lorries per week in a coal field has a mean of 100
trips and variance of 121 trips. A random sample of 36 lorries is
taken from the non-normal population. What is the probability that
the sample mean is
(i) greater than 105
(ii) less than 102
(iii) between 101 and 103 trips?
11.
Test the significance of the difference between the means of the
sample from the following data
Size of sample Mean SD
Sample A 100 61 4
Sample B 200 63 6
BTL -4 Analyzing
12(a).
A cigarete manufacturing firm claims that its brand. A outsells
brand B by 8%. If it is found that 42 out of a sample of 200
smokers prefer brand a and 18 out of another sample of 100
smokers prefer brand B, test whether the 8% difference is a valid
claim(use 5% level of significance).
BTL -4
Analyzing
12(b).
In an automotive safety test conducted by the North Carolina
Highway Safety Research center, the average tyre pressure in a
sample of 62 tyres was found to be 24 pounds per square inch, and
the standard deviation was 2.1 pounds per square inch.
(i) What is the estimated population standard deviation for this
population
(ii) Calculate the estimated standard error of the mean
(iii) Construct a 95% confidence interval for the population mean.
BTL -3 Applying
13(a).
The manager of a shop selling beverages wants to estimate the
actual amount of beverages in one litre bottles from a nationally
known manufacturer. As per manufacturer?s specifications, the
standard deviation of the volume of the beverage is 0.02 litre. The
average amount of beverage per 1 litre bottle is found to be 0.995
litre on checking 50 bottles. Setup 99% confidence interval
estimate of the true population average amount of beverage in a 1
liter bottle. Check whether the manufacturer is genuine in filling
the beverage.
BTL -6
Creating
13(b).
In a batch chemical process used for etching printed circuit boards,
two different catalysts are being compared to determine whether
they require different emersion times for removal of identical
quantities of photo resist material. Twelve batch were run with
catalyst 1, resulting in a sample mean emersion time of 24.6
minutes and sample standard deviation of 0.85 minutes. Fifteen
batches were run with catalyst 2, resulting in a mean emersion time
of 22.1 minutes and a standard deviation of 0.98 minutes. Find a
95% confidence interval on the difference in means, assuming that
2
2
2
1
? ? ? .
BTL -3 Applying
10
14.
In a random sample of 75 axle shafts. 12 have a surface finish that
is rougher than the specifications will allow. Suppose that a
modification is made in the surface finishing process and
subsequently a second random sample of 85 axle shafts is
obtained. The number of defective shafts in this second sample is
10. Obtain an approximate 95% confidence interval on the
difference in the proportions of defectives produced under the two
processes
BTL -5 Evaluating
PART-C
1.
In a sample of 25 observations from a Normal distribution with
mean 98.6 and standard deviation 17.2.
(i)What is P(92<102)
(ii)Find the corresponding probability given a sample of 36.
BTL -6 Creating
2.
Mary, an auditor for a large credit card company, knows that, on
average, the monthly balance of any customer is Rs.112, and the
standard deviation is Rs.56. If Mary audits 50 randomly selected
accounts, What is the probability that the sample average balance
is
(i) Below Rs. 100
(ii)Between Rs.100 and Rs.130
BTL -6 Creating
3(a).
Write the type of sampling methods and the uses of standard error?
BTL -1 Remembering
3(b).
From a population of 540, a sample of 60 individual is taken. From
this sample, the mean is found to 6.2 and the standard deviation
1.368
(i) Find the estimated standard error of the mean.
(ii) Construct a 96 % confidence interval for the mean.
BTL-2 Understanding
4(a).
Explain the properties of good point estimator.
BTL -4 Analyzing
4(b).
What do you mean by interval estimation? Give examples
BTL-6 Creating
UNIT III - TESTS OF HYPOTHESIS- PARAMETRIC TESTS
SYLLABUS: Hypothesis testing: one sample and two sample tests for means and proportions of large samples (z-test),
one sample and two sample tests for means of small samples (t-test), F-test for two sample standard deviations. ANOVA
one and two way.
PART-A
Q.
No.
Question
Bloom?s
Taxonomy
Level
Domain
1. Define Test of Significance. BTL-1 Remembering
2. What are the Type I and Type II errors? BTL-6 Creating
3. What do you mean by one tail test? BTL-6 Creating
4. State the applications of Z-test and t-test. BTL-4 Analyzing
5. Define critical region BTL-1 Remembering
6. Distinguish between one tail and two tail tests BTL-2 Understanding
7. What is the aim of design of experiments? BTL-6 Creating
8. Distinguish between one-way and two-way analysis of variance. BTL-2 Understanding
9. When does the Z-test apply? BTL-1 Remembering
10. Explain SSB , SSW and SSY
and relationship in ANOVA. BTL-4 Analyzing
11
11. Describe any two applications of t-distribution BTL-1 Remembering
12. Write the uses of F-test? BTL-6 Creating
13. Define the level of significance. BTL-1 Remembering
14. Write the properties of t-distribution? BTL-6 Creating
15. What is the role of standard error? BTL-6 Creating
16. Mention any four applications of t-distribution in tests of hypothesis. BTL-1 Remembering
17. Mention any four uses of Chi-square distribution in test of hypothesis. BTL-1 Remembering
18. Define null hypothesis ? Explain. BTL-6 Creating
19.
Estimate the standard error of difference between two proportion if
p
1
=0.10,p
2=
0.133 and n
1
=50,n
2
=75.
BTL-6 Creating
20.
Mention any two assumptions made in analysis of variance
techniques.
BTL-1 Remembering
PART-B
1(a).
A study compares the effect of four 1-month point-of-purchase
promotions on sales. The unit sales for five stores using all four
promotions in different months follow.
Free Sample
78 87 81 89 58
One-pack gift
94 91 87 90 88
Cents off
73 73 78 69 83
76Refund by mail
79 83 78 69 81
(i)Compute the mean unit sales for each promotion and then
determine the grand mean.
(ii)Estimate the population variance using the between column
variance.
BTL-5 Evaluating
1(b).
From the question 1(a)
(i)Estimate the population variance using the within-column variance
computed from the variance within the samples.
(ii)Calculate the F ratio. At the 0.01 level of significance, do the
promotions produce different effects on sales.
BTL-2 Understanding
2(a).
In a low cost Toy production system, the molding machine has been
set with standard of 1% defective. The 80 sample units produced from
this machine shows defective of one unit. Is it necessary to stop the
product for corrective mechanism? Test at 5% level of significance
BTL-5 Evaluating
2(b).
Block Enterprises, a manufacturer of chips for computers. Is in the
process of deciding whether to replace its current semi automated
assembly line with a fully automated assembly line. Block has
gathered some preliminary test data about hourly chip production,
which is summarized in the following table, and it would like to know
whether it should upgrade its assembly line. State (and test at a =0.02)
appropriate hypothesis to help Block decide.
BTL-5 Evaluating
3(a).
Three samples below have been obtained from normal population
with equal variance. Test the hypothesis that the means are equal.
Sample I : 10 12 18 15 16
Sample II : 7 15 10 12 8
Sample III : 12 8 15 16 15
BTL-5 Evaluating
3(b). The I.Q.s of 16 students from one class of an showed a BTL-2 Understanding
12
mean of 107 with a standard deviation of 10, while the I.Q.s of 14
students from another class showed a mean of 112 with a standard
deviation of 8. Check whether there is an appreciable difference
between the I.Q.s of the two groups at (i) 0.01and (ii) 0.05 level of
significance
4(a).
The following is the information obtained from a random sample of 5
observations. Assume the population has a normal distribution.
30 31 27 32 28
To test if the sample was drawn from a normal distribution with mean
less than 30, (i)State the null and alternative hypotheses
(ii)Compute the standard error.
BTL-2 Understanding
4(b).
From the question 4(a)
(i)Determine the test statistic.
(ii)Decide at 10% level whether or not the mean value could be
greater than 30
BTL-2 Understanding
5.
The following data relate to the number of units produced per week by
three methods.
Method 1 : 170 192 190 120
Method 2 : 160 165 170 172
Method 3 : 182 190 170 178 185
Prepare ANOVA table and write your comments
BTL-6 Creating
6(a).
Test if the following samples could have come from two populations
with the same means, assuming the population variances are equal.
Sample I Sample II
Sample size 12 10
Sample Mean 40.5 43.8
Sample variance 2.6 3.2
BTL-5 Evaluating
6(b).
The weights of 10 people of a locality are found to be
70,67,62,68,61,68,70,64,64,66 kilograms. Is it reasonable to believe
that the average weights of the people of locality is greater than 64
kg? Test at 5%level of significance.
BTL-5 Evaluating
7(a).
In Town A, there were 850 birds of which 52% was males, while in
Town A and Town B combined, the proportion of males in a total of
1200 birds was 0.49. Is there any significance difference in the
proportions of male birds in the two Towns?
BTL-2
Understanding
7(b).
IQ test result of randomly selected five employees in an organization
is given below. Test whether minimum requirement of average IQ
level 87 is maintained in that company or not.
Employee code 234 232 121 343 111
IQ test 85 95 90 93 87
BTL-4 Analyzing
8(a).
The weights of 8 persons are found to be 60, 65, 70, 68, 62, 63, 60,
and 66 kgs. The weights of another group of 12 persons are found to
be 70, 60, 58, 56, 50, 48, 52, 56, 52, 50, 54, and 50. Can we conclude
that both samples have come from populations with same variances?
BTL -4 Analyzing
13
8(b).
ATMs must be stocked with enough cash to meet the requirements of
customers over a week, but excess cash results in loss of income as
investment opportunities could not be utilized. In an ATM, the
average transaction per customer in a week is Rs.8000 with a standard
deviation of Rs.1500. If a random sample of 36 customer transactions
is examined and it is observed that the sample mean with drawl is
Rs.8600, check the belief that the true average withdrawal is no longer
Rs.8000. Assume 0.05 level of significance
BTL -3 Applying
9.
Apply ANOVA technique and write your comment regarding the
sales(in Rs. Lakhs)
Area
Representatives
1 2 3 4
A 12 16 20 18
B 15 10 12 16
C 10 08 16 15
BTL -3 Applying
10(a).
A farmer wishes to determine whether there is a difference in yields
between two different varieties of wheat I and II. The following data
shows the production of wheat per unit area using the two varieties.
Can the farmer conclude at significance levels of
(i) 0.05
(ii) 0.01 that a difference exists?
BTL -4 Analyzing
10(b).
Test if the samples could have come from equal population means.
Sample A Sample B
Size 200 400
Mean 154.8 164.3
Variance 15.2 18.2
BTL-5 Evaluating
11(a).
The number of accidents per week in a city are as follows:
12, 8, 20, 2, 14, 10, 15, 6, 9 and 4. Are these frequencies in agreement
with the belief that accident conditions were the same during this 10
weeks period?
BTL -4
Analyzing
11(b).
Two samples are drawn from two normal population. From the
following data, Test whether the two samples have the same variance
5% level of significance.
Sample 1 60 65 69 74 76 82 85 87
Sample 2 61 66 67 85 78 63 85 86 88 91
BTL -3 Applying
12(a).
Given a sample mean of 83, a sample standard deviation of 12.5 and a
sample size of 22, test the hypothesis that the value of the population
mean is 70 against alternative that it is more than 70. Use the 0.025
significance level.
BTL-2
Understanding
12(b).
The following table shows the lifetimes in hours of samples from
three different types of television tables manufactured by a company.
Determine whether there is a difference between the three types at
significance level of 0.01.
Table:
BTL-2
Understanding
14
Sample 1 407 411 409
Sample 2 404 406 408 405 402
Sample 3 410 408 406 408
13.
The following table shows the yields per acre of hour different plants
crops grown on lots treated with three different types of fertilizer.
Determine at the 5% significance level whether there is a difference in
yield per acre.
(i) due to the fertilizers and
(ii) due to the crops
Table:
Crop -I Crop -II Crop -III Crop -IV
Fertilizer A 4.5 6.4 7.2 6.7
Fertilizer B 8.8 7.8 9.6 7.0
Fertilizer C 5.9 6.8 5.7 5.2
BTL-2
Understanding
14.
Time of 6 machine operator (in minute) in making product is given
below. Use paired t-test for training effectiveness.
Machine operator 1 2 3 4 5 6
Before training 12 23 4 5 16 17
After training 2 3 10 8 12 6
BTL -3 Applying
PART C
1(a).
What are non-parametric tests? Point out their advantages and
disadvantages?
BTL -6 Creating
1(b).
The success of a sales engineer in adopting the proven sales technique
was found to be 12 out of 30 occasions. Hence he tried a novel
technique and achieved success at a rate of 23 out of 40 occasions.
Check whether the novel technique is effective at 5% level of
significance.
BTL-2 Understanding
2(a).
The following are the final examination marks of three groups of
students who were taught computer by three difference methods.
First method: 94 88 91 74 87 97
Second method: 85 82 79 84 61 72 80
Third method: 89 67 72 76 69
BTL -5 Evaluating
2(b).
A consumer product manufacturing company was selling one of its
leading products through a large number of retail shops. Before a
heavy advertisement campaign, the average sale per week per shop
was 140 dozens. After the campaign, a sample of 26 shops was taken
and the mean sales improved to 147 dozens with a standard deviation
of 16. Check the effectiveness of the advertisement campaign at 5%
level of significance
BTL-2
Understanding
3.
Discuss the test procedure to test hypothesized population proportion
using single sample proportion.
BTL-1 Understanding
15
4.
(i)Write the application testing of hypothesis in statistics. (ii)What is
t-test? When should we apply a t-test?
BTL -3 Applying
UNIT IV: NON-PARAMETRIC TESTS
SYLLABUS: Chi-square test for single sample standard deviation. Chi-square tests for independence ofattributes and
goodness of fit. Sign test for paired data. Rank sum test. Kolmogorov-Smirnov ? test for goodness of fit, comparing two
populations. Mann ? Whitney U test and Kruskal Wallis test. One sample run test.
PART-A
Q.
No.
Question
Bloom?s
Taxonomy
Level
Domain
1. Define Rank Correlation test. BTL-1 Remembering
2. Write the formula in chi square test and any two uses. BTL-1 Remembering
3. Define Rank-Sum test. BTL-1 Remembering
4. Mention the advantages of Nonparametric Tests. BTL-1 Remembering
5. What is the other name or non-parametric test? Why? BTL-6 Creating
6. When are non parametric tests used? BTL-1 Remembering
7. What is the null hypothesis framed in Mann-Whitney test? BTL-6 Creating
8.
Write down the working rule for Mann-Whitney U-test and Kruskal-
Wallis test.
BTL-1 Remembering
9. Explain sign test. BTL-4 Analyzing
10. Define one sample run test? BTL-1 Remembering
11. When is Krushkal-Wallis test used? BTL-1 Remembering
12. Distinguish between Mann-Whitney U-test and Krushkal-Wallis test. BTL-2 Understanding
13. Write the contingency 2*2 table for
test. BTL-5 Evaluating
14.
Write down the formula to calculate rank correlation coefficient
(including tie values).
BTL-1 Remembering
15.
Two HR managers (A and B) ranked five candidates for a new
position. Their rankings of the candidates are show below:
Candidate Rank by A Rank by B
Nancy 2 1
Mary 1 3
John 3 4
Lynda 5 5
Steve 4 2
Compute the Spearman rank correlation.
BTL-6 Creating
16. Define rank correlation co-efficient. BTL-1 Remembering
17.
The following are the ranks obtained by 10 students in Statistics and
Mathematics. Find out the rank correlation coefficient.
Statistics 1 2 3 4 5 6 7
Mathematics 2 5 1 6 7 4 3
BTL-4 Analyzing
18. Explain Kolmogorov-Smirnov Test for one sample problem. BTL-4 Analyzing
19. What adjustment is to be done for tie values to find rank correlation. BTL-6 Creating
20. Mention the properties of linear coefficient of correlation. BTL-1 Remembering
PART -B
1(a).
The scores of a written examination of 24 students, who were trained
by using three different methods, are given below.
Video cassette A 74 88 82 93 55 70 65
BTL-3 Applying
16
Audio cassette B 78 80 65 57 89 85 78 70
Class Room C 68 83 50 91 84 77 94 81 92
Use Krushkal-Wallis test at ? = 5% level of significance, whether the
three methods of training yield the same results.
1(b). Explain Rank sum tests and its applications
2(a).
The production volume of units assembled by three different
operators during 9 shifts is summarized below. Check whether there
is significant difference between the production volumes of units
assembled by the three operators using Krushkal-Wallis test at a
significant level of 0.05.
Operator I 29 34 34 20 32 45 42 24 35
Operator II 30 21 23 25 44 37 34 19 38
Operator III 26 36 41 48 27 39 28 46 15
BTL-3
Applying
2(b).
Two faculty members ranked 12 candidates for scholarships.
Calculate the spearman rank-correlation coefficient and test it for
significance. Use 0.02level of significance.
Candidate Rank by Professor A Rank by Professor B
1 6 5
2 10 11
3 2 6
4 1 3
5 5 4
6 11 12
7 4 2
8 3 1
9 7 7
10 12 10
11 9 8
12 8 9
BTL-3
Applying
3(a).
In a study of sedimentary rocks, the following data were obtained
from samples of 32 grains from two kinds of sand :
Apply Mann-Whitney U test with suitable null and alternative
hypotheses.
Sand I 63 17 35 49 18 43 12 20 47
? 136 51 45 84 32 40 44 25
Sand II 113 54 96 26 39 88 92 53 101
? 48 89 107 111 58 62
BTL -3 Applying
3(b).
The Molisa?s shop has 3 mall locations. She keeps a daily record for
each locations of the number of the customers who actually make a
purchase. A sample of these data follows. Using Kruskal- Wallis test
can you say that at 5% level of significance that her stores have the
same number of customers who buy.
Eastowin 99 64 101 85 79 88 97 95 90 100
Craborchard 83 102 125 61 91 96 94 89 93 75
Fair forest 89 98 56 105 87 90 87 101 76 89
BTL -3 Applying
4(a)
The following are the prices in Rs. per kg of a commodity from 2
random samples of shops from 2 cities A&B.
BTL -3 Applying
17
City A 2.7 3.8 4.3 3.2 4.7 3.6 3.8 4.1
2.7 2.8 3.2 3.4 3.8 4.4 4.9 3.9 4.7
City B 3.7 5.3 4.7 3.6 4.7 4.8 6.0 4.8 4.9
3.8 3.9 4.8 5.2 6.1 3.6 3.8
Apply the run test to examine whether the distribution of prices of
commodity in the two cities is the same.
4(b)
Distinguish Nonparametric methods over parametric methods.
BTL -2 Understanding
5(a)
From a poll of 800 television viewers, the following data have been
accumulated as to,their levels of education and their performance of
television stations. We are interested in determining if the selection
of Tv station is independent of the level of education.
Education Level
High school Bachelor graduate Total
Public Broadcasting 50 150 80 280
Commercial
stations
150 250 120 520
Total 200 400 200 800
(i) State the null and alternative hypothesis.
(ii) Show the contingency table of the expected
frequencies
BTL -3 Applying
5(b)
From the question 5(a)
(i)Compute the test static
(ii)The null hypothesis to be tested at 95% confidence Determine the
critical value for this test
BTL-6
Creating
6(a)
Apply Mann-Whitney U test to determine if there is a significant
difference in the age distribution of the two groups
Day :26 18 25 27 19 30 34 21 33 31
Evening :32 24 23 30 40 41 42 39 45 35
BTL -3
Applying
6(b)
Apply the K-S test to check that the observed frequencies match with
the expected frequencies which are obtained from Normal
distribution. (Given at n=5).
Test Score 51-60 61-70 71-80 81-90 91-100
Observed Frequency
30 100 440 500 130
Expected Frequency 40 170 500 390 100
BTL -5 Evaluating
7
A research company has designed three different systems to clean up
oil spills. The following table contains the results, measures by how
much surface area (in square meters) is cleaned in one hour. The data
were found by testing each method in several trials. Are there
systems equally effective? Use the 5% level of significance.
Sample A 55 60 63 56 59 55
Sample B 57 53 64 49 62
Sample C 66 52 61 57
BTL -1 Remembering
8(a)
Suppose it is desired to check whether pinholes in electrolytic tin
plate are distributed uniformly across a plated coil on the basis of the
following distances (in inches) of 10 pinholes from one edge of a
BTL -1 Remembering
18
long strip of tin plate 320 inches wide.
4.8 14.8 28.2 23.1 4.4 28.7 19.5 2.4 25.0 6.2
Use Kolmogorov Smirnov test to test the null hypothesis.
8(b) Explain Mann- WhitneyU test with an example BTL-4 Analyzing
9.
Ten competitors in a beauty contest are ranked by 3 judges in the
following order.
A : 1 6 5 3 10 2 4 9 7 8
B : 3 5 8 4 7 10 2 1 6 9
C : 6 4 9 8 1 2 3 10 5 7
Find out which pair of Judges has awarded the ranks to the nearest
common taste of beauty.
BTL -3 Applying
10(a).
Test the association of Age and preference of colour of Toy from the
following data
Age/Colour Below 5 6-10 Above 10 years
Pink 60 40 5
Purple 30 30 30
Red 80 10 10
BTL -4 Analyzing
10(b).
Melisa?s Boutique has three mall locations. Melisa keeps a dairy
record for each location of number of customers who actually make a
purchase. A sample of those data follows. Using the kruskal-wallis
test, can you say at the 0.05 level of significance that her stores have
the same number of customers who busy?
DSF Mall 99 64 101 85 79 88 97 95 90 100
Forest Mall 83 102 125 61 91 96 94 89 98 75
Big-Ben Mall 89 98 56 105 87 90 87 101 76 89
BTL -3 Applying
11(a).
A brand manager is concerned that her brand?s share may he
unevenly distributes through the country. In a survey in which the
country was divided into four geographic regions, a random
sampling of 100 consumers in each region was surveyed, with the
following results:
NE NW SE SW TOTAL
Purchase the brand 40 55 45 50 190
Do not purchase 60 45 55 50 210
Total 100 100 100 100 400
(i) Develop a table of observed and expected frequencies for
this problem.
(ii) Calculate the sample
value.
BTL -6 Creating
11(b).
From the question 11(a)
(i)State the null and alternative hypothesis.
(ii)At test whether brand share is the same across the four
regions
BTL -2 Understanding
12(a).
In 30 tosses of a coin, the following sequence of head and tails is
obtained HTTHTHHHTHHTTHTHTHHTHTTHTHHTHT
(i) Determine the number of runs
BTL -2 Understanding
12(b).
From the question 12(a ) Test at 0.10 level of significance, whether
the sequence is random
BTL -3 Applying
13. An experiment designed to compare three preventative methods BTL -3 Applying
19
against corrosion yielded the following maximum depths of pits ( in
thousandths of an inch) in pieces of wire subjected to the respective
treatments:
Method A: 77 54 67 74 71 66
Method B: 60 41 59 65 62 64 52
Method C: 49 52 69 47 56
Use the Kruskal-Wallis test at the 5% level of significance to test the
null hypothesis that the three samples come from identical
populations.
14.
The number of defects in printed circuit boards in hypothesized to
follow a poisson distribution. A random sample of 60 printed boards
have been collected and the number of defects observed. The
following table gives the results.
Table:
No. of defects Observed Frequency
0 32
1 15
2 9
3 4
Does the assumption of a poisson distribution seem appropriate as a
probability model for this process?
BTL -4
Analyzing
PART C
1. Explain the Mann-Whitney test procedure with appropriate examples BTL-1 Remembering
2.
Write the application of Non parametric test and Sign test in
statictics.
BTL-1 Remembering
3(a).
The sales records of two branches of a department store over the last
12 months are shown below.(sales figures are in thousands of
dollars). We want to use the Mann-Whitney-Wilcoxon test to
determine if there is a significant difference in the sales of the two
branches.
Month Branch A Branch B
1 257 210
2 280 230
3 200 250
4 250 260
5 284 275
6 295 300
7 297 320
8 265 290
9 330 310
10 350 325
11 340 329
12 372 335
(i) Compute the sum of the ranks for branch A
(ii) Compute the mean ?T
BTL-4 Analyzing
3(b).
From the question 3(a)
(i)Compute ?T
BTL -6 Creating
20
(ii)Use and test to determine if there is a significant
difference in the population of the sales of the two branches
4(a).
Independent random samples of ten day students and ten evening
students at a university showed the following age distributions. We
want to use the Mann-Whitney-Wilcoxon test to determine if there is
a significant different in the age distribution of the two groups.
Day Evening
26 32
18 24
25 23
27 30
19 40
30 41
34 42
21 39
33 45
31 35
(i) Compute the sum of the ranks for the day students.
(ii) Compute the mean ?
BTL-2 Understanding
4(b).
From the question 4(a)
(i)Compute ?
(ii)Use and test for any significant difference in the age
distribution of the two populations
BTL -4
Analyzing
UNIT ? V CORRELATION AND REGRESSION
SYLLABUS: Correlation ? Coefficient of Determination ? Rank Correlation ? Regression ? Estimation of Regression line
? Method of Least Squares ? Standard Error of estimate.
PART ? A
Q.No. Question
Bloom?s
Taxonomy
Level
Domain
1. Define regression coefficient?. BTL -1 Remembering
2. Define Linear Relationship of Correlation. BTL -6 Creating
3. Write the Properties of Correlation Coefficient? BTL -1 Remembering
4. What is the angle between the regression lines? BTL -1 Remembering
5. When is linear regression used? BTL -1 Remembering
6. Distinguish between correlation and regression BTL -2 Understanding
7. What is regression analysis? BTL -6 Creating
8. What do you interpret if the r = 0 , r = + 1 and r = -1? BTL -1 Remembering
9. Specify the range of correlation. BTL -6 Creating
10. Briefly explain how a scatter diagram benefits the researcher? BTL -4 Analyzing
11. Define correlation coefficient between two variables. BTL -1 Remembering
12. What is a scatter diagram and write its benefits? BTL -6 Creating
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Ka ttankulathur ?
DEPARTMENT OF MATHEMATICS
QUESTION BANK
I SEMESTER
1918108 ? STATISTICS FOR MANAGEMENT
Regulation ? 2019
Academic Year 2019 - 2020
Prepared by
Ms. B. Vasuki, Assistant Professor/Mathematics
Ms.B.Elakkiavani, Assistant Professor/Mathematics
2
(An
? .
DEPARTMENT OF MATHEMATICS
QUESTION BANK
SUBJECT : 1918108 ? STATISTICS FOR MANAGEMENT
SEM / YEAR : I Semester / I Year
UNIT I - INTRODUCTION
SYLLABUS: Basic definitions and rules for probability, conditional probability independence of events, Baye?s
theorem, and random variables, Probability distributions: Binomial, Poisson, Uniform and Normal distributions.
PART- A
S.NO QUESTIONS
BT Level
COMPETENCE
PART ? A
1. Define Statistics. BTL -6 Creating
2. What is the addition and multiplication theorem on probability. BTL -1 Remembering
3. Distinguish between a priori and posterior probability?. BTL -6 Creating
4.
The price of the selected stock over a five day period shown as 170, 110,
130, 170 and 160. Compute mean , median and mode.
BTL -6 Creating
5.
A car travels 25 miles at 25 mph, 25 miles at 50 mph and 25 miles at 75
mph. Find the harmonic of three velocities?
BTL -4 Analyse
6.
A ball is drawn at random from a box containg 6 red balls, 4 white balls
and 5 blue balls. Find the probability that the ball drawn is not red.
BTL -4 Analyse
7.
Find the median and mode for the weights (kgs) of 15 persons given as
68, 85, 70, 65, 71, 67, 65, 55, 80, 62, 65, 64, 70, 60, 56.
BTL -3 Applying
8. Name few measures of dispersion. BTL -1 Remembering
9. write the common measures of central tendency? BTL -1 Remembering
10. Define continuous and discrete variables examples. BTL -1 Remembering
11.
Let X be the lifetime in years of a mechanical part. Assume that X has
the cdf F(x) = 1- e
-x
, x ? 0. Find P[1< X ? 3].
BTL -1 Remembering
12. Define independent events. BTL -1 Remembering
13. State the theorem of total probability BTL -1 Remembering
14. What is the use of Baye?s theorem? BTL -6 Creating
15. Mention the properties of a discrete probability distribution. BTL -1 Remembering
16. Define a Poisson distribution and mention its mean and variance. BTL -1 Remembering
17. If the mean and variance of a binomial distribution are respectively 6 BTL -3 Applying
3
and 2.4, find P(x=2).
18.
If x is a Poisson distribution such that P(x=1)=4P(x=2). Find its
mean and variance.
BTL -3 Applying
19.
Suppose that X has a Poisson distribution with parameter ? = 2.
Compute P[X ? 1].
BTL -1 Remembering
20. Define mutually exclusive events. BTL -1 Remembering
PART-B
1(a).
Calculate the mean and standard deviation for the following table
giving the age distribution of 542 members.
Age
20-30 30-40 40-50 50-60 60-70 70-80 80-90
No 3 61 132 153 140 51 2
BTL-2 Understanding
1(b).
Find the geometric mean for the following data:
Group
2-4 4-6 6-8 8-10
Frequency 200 400 300 100
BTL-2
Understanding
2(a).
Find the mean, median and modal ages of married women at first
child birth
Age at the
birth of
first child
13
14
15
16
17
18
19
20
21
22
23
24
25
No of
married
women
37
162
343
390
256
433
161
355
65
85
49
46
40
BTL -6 Creating
2(b).
If A and B are independent event with P(A)=2/5, and P(B)=3/5,
find P(A ?B). Let S= {1,2,3,4,5,6} if A = {2,4,6} then find the
probability of A complement.
BTL -3 Applying
3(a).
Given: The probabilities of three events A, B and C occurring are
P(A) = 0.35, P(B) = 0.45 and P(C) = 0.2. Assuming that A, B, or
C has occurred, the probabilities of another event X occurring are
P(X/A) = 0.8, P(X/B) = 0.65 and P(X/C) = 0.3. Find P(A/X),
P(B/X) and P(C/X).
BTL -6 Creating
3(b).
4 cards are drawn from a well shuffled pack of cards. Find the
probability that
(i) All the four are queens
(ii) There is one card from each suit.
(iii) Two cards are diamonds and two are spades
All the four cards are hearts and one of them is jack
BTL -6 Creating
4(a).
Three machines all turn out non ferrous castings. Machine A
produces 1% defective and Machine B- 2% and machine C ? 5%.
Each machine produces 1/3 of the output. An inspector examines
a single casting, which he determines as non defective. Estimate
the probabilities of its having been produced by each machine.
BTL -6 Creating
4(b).
If the random variable X takes values 1, 2, 3, 4 such that
2P(X = 1) = 3P(X = 2) = P( X=3) = 5P(X = 4), find the
probability distribution and cumulative distribution of X.
BTL-2 Understanding
5(a).
Two dice are thrown together once. Find the probabilities for
BTL -3 Applying
4
getting the sum of the two numbers (i) equal to 5, (ii) multiple of
3, (iii) divisible by 4.
5(b).
Given ? = 4.2, for a poisson distribution. Find (a) P(X ? 2) (b)
P(X ? 5) (c) P(X = 8).
BTL -6 Creating
6(a).
An urn contains 5 balls. Two balls are drawn and found to be
white. What is the probability that all the balls are white?
BTL-1 Remembering
6(b).
The contents of urns I, II, III are as follows:
1 white, 2 black and 3 red balls;
2 white, 1 black and 1 red balls;
4 white, 5 black and 3 red balls;
One urn is chosen at random and two balls drawn. They happen to
be white and red. What is the probability that they come from
urns I, II, III?
BTL -3 Applying
7(a).
In 1989, there were three candidates for the position of principal
Mr. Chatterji, Mr. Ayangar and Dr. Singh. Whose chances of
getting the appointment are in the proportion 4:2:3 respectively.
The probability that Mr. Chatterji is selected, would introduce co-
education in the is 0.3. The probabilities of Mr. Ayangar
and Dr. Singh doing the same are respectively 0.5 and .08. What
is the probability that there was co-education in the in
1990?
BTL -3
Applying
7(b).
Find the probability that atmost 5 defective bolts will be found in
a box of 200 bolts, if it is known that 2% of such bolts are
expected to be defective. (e
-4
= 0.0183)
BTL -6 Creating
8(a).
A coin is tossed 6 times what is the probability of obtaining (a) 4
heads (b) 5 heads (c) 6 heads (d) getting 4 or more heads.
BTL -3 Applying
8(b).
In a bolt factory machines A, B, C manufacture respectively 25%,
35% and 40% of the total of their output 5, 4, 2 percent are
defective bolts. If A bolt is drawn at random from the product and
is found to be defective, what are the probabilities that is was
manufactured by machines A, B and C?
BTL -6 Creating
9(a).
In a test of 2000 electric blubs it was found that the life of a
particular make was normally distributed with an average life of
2040 hours and S. D. of 60 hours. Estimate the number of blubs
likely to burn for
(1) More than 2150 hours
(2) Less than 1950 hours
(3) More than 1920 hours but less than 2160 hours.
BTL -3 Applying
9(b).
The latest nationwide political poll indicates that for Americans
who are randomly selected, the probability that they are
conservative is 0.55, the probability that they are liberal is 0.30
and the probability that they are middle of the road is 0.15.
Assuming these probabilities are accurate, answer the following
BTL -4 Analyzing
5
questions from a randomly chosen group of 10 Americans
(a) What the probability that 4 are liberal?
(b) What the probability that none are conservative
(c) What the probability that two are middle of the road
(d) What the probability that a least 8 are liberal
10.
If X follows a normal distribution with mean 12 and variance 16
cm, find the probabilities for (i) X ? 20 (ii) X ? 20, and (iii) 0 ? X
? 12.
BTL -3 Applying
11.
A discerete random variable X has the probability function given
below:
Value of X=x: 0 1 2 3 4 5 6 7
P(X=x) : 0 k 2k 2k 3k k
2
2k
2
7k
2
+k
Find (1) The value of k
(2) P(1.5 < X < 4.5 / X > 2)
(3) P(X < 6), P(X ? 5), P( 0 < X < 4)
(4) The distribution of X.
BTL -3 Applying
12.
X is a normal variable with mean 30 and standard deviation of 5.
Find (i) P[26 ? X ? 40] (ii) P [X?45] (iii) P [ ?X - 30 ?> 5] use
normal distribution tables
BTL -4 Analyzing
13.
In an intelligence test administered on 1000 students, the average
was 42 and standard deviation 24, find (i) the number of students
exceeding a score 50. (ii) the number of students lying between
30 and 54(iii) the value of score exceeded by top 100 students.
BTL -4 Analyzing
14(a).
The probability that an entering student will graduate is 0.4
Determine the probability that out of 5 students atleast one will
graduate.
BTL-5
Evaluating
14(b).
Fit a Poisson Distribution to the following data which gives the
number of doddens in a sample of clover seeds
No 0 1 2 3 4 5 6 7 8
f 56 156 132 92 37 22 4 0 1
.
BTL -4 Analyzing
PART-C
1(a).
A disciplinary committee is formed from the staff of XYZ
Company which has three departments Marketing, Finance and
Production of the 10,5,20 members respectively. All departments
have two female staff each. A department is selected at random
and from which two matters are selected for the committee,
What is the probability that both the team members are female?
BTL-6 Creating
6
1(b).
In a bolt factory machines A, B, C manufacture respectively 25,
35 and 40 percent of the total. Of their output 5, 4 and 2 percent
are defective bolts respectively. A bolt is drawn at random from
the product and is found o be defective. What are the probabilities
that it was manufactured by machines A, B or C?
BTL-2
Understanding
2(a). State Bayes theorem and brief about its applications. BTL-2 Understanding
2(b).
Out of 800 families with 4 children each, how many families
would be expected to have (i) 2 boys and 2 girls (ii) at least 1 boy
(iii) at most 2 girls (iv) children of both sexes? Assume equal
probabilities for boys and girls.
BTL-1 Remembering
3. Describe the classifications of probability ? BTL-1 Remembering
4. What are the applications of Normal distribution in statistics? BTL-6 Creating
UNIT ?II- SAMPLING DISTRIBUTION & ESTIMATION.
SYLLABUS: Introduction to sampling distributions, sampling distribution of mean and proportion, application of central
limit theorem, sampling techniques. Estimation: Point and Interval estimates for population parameters of large sample and
small samples, determining the sample size.
PART - A
S.N
O
QUESTIONS
BT Level
COMPETENCE
1. Define Sampling distribution of proportion. BTL -1 Remembering
2. Define Probable standard error. BTL -1 Remembering
3. Define standard error and mention its importance BTL -1 Remembering
4. Define central limit theorem BTL -1 Remembering
5.
What is the role of central limit theorem in estimation and testing
problems
BTL -6 Creating
6. Define stratified sampling technique BTL -1 Remembering
7. Briefly describe the significance level. BTL -1 Remembering
8. Distinguish between parameter and statistic. BTL -2 Understanding
9. Define estimator, estimate and estimation. BTL -1 Remembering
10. Distinguish between point estimation and interval estimation BTL -2 Understanding
11. Mention the properties of a good estimator. BTL -1 Remembering
12. Define confidence coefficient. BTL -1 Remembering
13. What is the level of significance in testing of hypothesis BTL -6 Creating
14. Define confidence limits for a parameter BTL -1 Remembering
15.
State the conditions under which a binomial distribution becomes a
normal distribution
BTL -4 Analyzing
16.
If the random sample comes from a normal population, what can
be said about the sampling distribution of the mean.
BTL -5 Evaluating
17.
An automobile repair shop has taken a random sample of 40
services that the average service time on an automobile is 130
minutes with a standard deviation of 26 minutes. Compute the
standard error of the mean.
BTL -6 Creating
7
18. What is a random number? How it is useful in sampling? BTL -6 Creating
19.
A population has the numbers: 12, 8, 10, 30, 12, 16, 40, 5, 16, 24,
22, 31, 30, 16, 15. Draw a systematic sample of size 5. Find out its
mean.
BTL -3 Applying
20. How large sample is useful in estimation and testing BTL -4 Analyzing
PART -B
1(a).
A random sample of 700 units from a large consignment showed
that 200 were damaged. Find (i) 95% (ii) 99% confidence limits
for the proportion of damaged units in the consignment.
BTL -3 Applying
1(b).
A random sample of size 9 is obtained from a Normal population
with mean 25 and if the variance 100 find the probability that the
sample mean exceeds 31.2.
BTL -4 Analyzing
2(a).
In a normally distributed population, average income per
household is Rs.20,000 with a standard deviation of Rs. 1,600.
Find the probability that the sample mean will be between
Rs.19,600 and Rs.20,200 in a survey of a random sample of 100
households.
BTL -6 Creating
2(b).
A university wants to determine the percentage of students who
would accept proposed fees hike for improving facilities. The
university wants to be 90% confident that the percentage is
within2% of the true value. Find the sample size to achieve the
accuracy regardless of the true percentage assuming the percentage
of students accepting the increase in tuition fees to be 0.5.
BTL -6 Creating
3(a).
A bank has kept records of the checking balances of its customers
and determined that the average daily balances of its customers is
Rs.300 with a standard deviation of Rs. 48. A random sample of
144 checking accounts is selected.
(i) What is the probability that the sample mean will be more
than Rs. 306.60?
(ii) What is the probability that the sample mean will be less
than Rs. 308?
BTL -6 Creating
3(b).
From the question 3(a)
(i) What is probability that the sample mean will between Rs.
302 and Rs. 308?
(ii) What is probability that the sample mean will be atleast
Rs. 296?
BTL -6 Creating
4(a).
Explain Stratified sampling technique and discuss how it is better
than simple random sampling in a particular situation.
BTL -4
Analyzing
4(b). Discuss the standard error of proportion BTL-2 Understanding
5.
Explain the methods of drawing simple random sample from a
finite population.
BTL -4 Analyzing
8
6(a).
In a sample of 1000 citizens of India, 540 are wheat eaters and the
rest are rice eaters. Can we assume that both rice and wheat
equally popular in India at 1 % level of significance?
BTL-5
Evaluating
6(b).
A simple random sample of 144 items resulted in a sample mean
of 1257.85 and standard deviation of 480. Develop a 95%
confidence interval for the population mean
BTL -6
Creating
7(a).
A car dealer wants to estimate the proportion of customers who
still own the cars they purchased 5 years earlier. A random sample
of 500 customers selected from the dealer?s records indicate that
315 customers still own cars that they were purchased 5 years
earlier. Set up 95% confidence interval estimation of the
population proportion of all the customers who still own the cars 5
years after they were purchased.
BTL-2
Understanding
7(b).
A movie maker sampled 55 fans who viewed his master piece
movie and asked them whether they had planned to see it again.
Only 10 of them believed that the movie was worthy of a second
look. Find the standard error of the population of fans who will
view the film a second time. Construct a 90% confidence interval
for this population.
BTL -5 Evaluating
8(a).
From a population of size 600, a sample of 60 individuals revealed
mean and standard deviation as 6.2 and 1.45 respectively. (i) Find
the estimated standard error (ii) Construct 96% confidence
interval for the mean.
BTL -3 Applying
8(b).
The age of employees in a company follows normal distribution
with its mean and variance as 40 years and 121 years respectively.
If a random sample of 36 employees is taken from a finite normal
population of size 1000, what is the probability that the sample
mean is
(i) less than 45
(ii) greater than 42 and
(iii) between 40 and 42?
BTL -6
Creating
9(a).
A firm wishes to estimate with an error of not more than 0.03 and
a level of confidence of 98%, the proportion of consumers that
prefer its brand of household detergent. Sales report indicate the
about 0.20 of all consumers prefer the firm?s brand. What is the
requisite sample size?
BTL -5 Evaluating
9(b).
A random sample of 700 units from a large consignment should
that 200 were damaged.
Find (i) 95%
(ii) 99% confidence limits for the proportion of damaged
units in the consignment
BTL -3 Applying
10(a).
From a population of 500 items with a mean of 100 gms and
standard deviation of 12.5 gms, 65 items were chosen. (i) What is
the standard error? (ii) Find P(99.5 < X < 101.5).
BTL -6 Creating
10(b).
A non-normal distribution representing the number of trips
BTL -6 Creating
9
performed by lorries per week in a coal field has a mean of 100
trips and variance of 121 trips. A random sample of 36 lorries is
taken from the non-normal population. What is the probability that
the sample mean is
(i) greater than 105
(ii) less than 102
(iii) between 101 and 103 trips?
11.
Test the significance of the difference between the means of the
sample from the following data
Size of sample Mean SD
Sample A 100 61 4
Sample B 200 63 6
BTL -4 Analyzing
12(a).
A cigarete manufacturing firm claims that its brand. A outsells
brand B by 8%. If it is found that 42 out of a sample of 200
smokers prefer brand a and 18 out of another sample of 100
smokers prefer brand B, test whether the 8% difference is a valid
claim(use 5% level of significance).
BTL -4
Analyzing
12(b).
In an automotive safety test conducted by the North Carolina
Highway Safety Research center, the average tyre pressure in a
sample of 62 tyres was found to be 24 pounds per square inch, and
the standard deviation was 2.1 pounds per square inch.
(i) What is the estimated population standard deviation for this
population
(ii) Calculate the estimated standard error of the mean
(iii) Construct a 95% confidence interval for the population mean.
BTL -3 Applying
13(a).
The manager of a shop selling beverages wants to estimate the
actual amount of beverages in one litre bottles from a nationally
known manufacturer. As per manufacturer?s specifications, the
standard deviation of the volume of the beverage is 0.02 litre. The
average amount of beverage per 1 litre bottle is found to be 0.995
litre on checking 50 bottles. Setup 99% confidence interval
estimate of the true population average amount of beverage in a 1
liter bottle. Check whether the manufacturer is genuine in filling
the beverage.
BTL -6
Creating
13(b).
In a batch chemical process used for etching printed circuit boards,
two different catalysts are being compared to determine whether
they require different emersion times for removal of identical
quantities of photo resist material. Twelve batch were run with
catalyst 1, resulting in a sample mean emersion time of 24.6
minutes and sample standard deviation of 0.85 minutes. Fifteen
batches were run with catalyst 2, resulting in a mean emersion time
of 22.1 minutes and a standard deviation of 0.98 minutes. Find a
95% confidence interval on the difference in means, assuming that
2
2
2
1
? ? ? .
BTL -3 Applying
10
14.
In a random sample of 75 axle shafts. 12 have a surface finish that
is rougher than the specifications will allow. Suppose that a
modification is made in the surface finishing process and
subsequently a second random sample of 85 axle shafts is
obtained. The number of defective shafts in this second sample is
10. Obtain an approximate 95% confidence interval on the
difference in the proportions of defectives produced under the two
processes
BTL -5 Evaluating
PART-C
1.
In a sample of 25 observations from a Normal distribution with
mean 98.6 and standard deviation 17.2.
(i)What is P(92<102)
(ii)Find the corresponding probability given a sample of 36.
BTL -6 Creating
2.
Mary, an auditor for a large credit card company, knows that, on
average, the monthly balance of any customer is Rs.112, and the
standard deviation is Rs.56. If Mary audits 50 randomly selected
accounts, What is the probability that the sample average balance
is
(i) Below Rs. 100
(ii)Between Rs.100 and Rs.130
BTL -6 Creating
3(a).
Write the type of sampling methods and the uses of standard error?
BTL -1 Remembering
3(b).
From a population of 540, a sample of 60 individual is taken. From
this sample, the mean is found to 6.2 and the standard deviation
1.368
(i) Find the estimated standard error of the mean.
(ii) Construct a 96 % confidence interval for the mean.
BTL-2 Understanding
4(a).
Explain the properties of good point estimator.
BTL -4 Analyzing
4(b).
What do you mean by interval estimation? Give examples
BTL-6 Creating
UNIT III - TESTS OF HYPOTHESIS- PARAMETRIC TESTS
SYLLABUS: Hypothesis testing: one sample and two sample tests for means and proportions of large samples (z-test),
one sample and two sample tests for means of small samples (t-test), F-test for two sample standard deviations. ANOVA
one and two way.
PART-A
Q.
No.
Question
Bloom?s
Taxonomy
Level
Domain
1. Define Test of Significance. BTL-1 Remembering
2. What are the Type I and Type II errors? BTL-6 Creating
3. What do you mean by one tail test? BTL-6 Creating
4. State the applications of Z-test and t-test. BTL-4 Analyzing
5. Define critical region BTL-1 Remembering
6. Distinguish between one tail and two tail tests BTL-2 Understanding
7. What is the aim of design of experiments? BTL-6 Creating
8. Distinguish between one-way and two-way analysis of variance. BTL-2 Understanding
9. When does the Z-test apply? BTL-1 Remembering
10. Explain SSB , SSW and SSY
and relationship in ANOVA. BTL-4 Analyzing
11
11. Describe any two applications of t-distribution BTL-1 Remembering
12. Write the uses of F-test? BTL-6 Creating
13. Define the level of significance. BTL-1 Remembering
14. Write the properties of t-distribution? BTL-6 Creating
15. What is the role of standard error? BTL-6 Creating
16. Mention any four applications of t-distribution in tests of hypothesis. BTL-1 Remembering
17. Mention any four uses of Chi-square distribution in test of hypothesis. BTL-1 Remembering
18. Define null hypothesis ? Explain. BTL-6 Creating
19.
Estimate the standard error of difference between two proportion if
p
1
=0.10,p
2=
0.133 and n
1
=50,n
2
=75.
BTL-6 Creating
20.
Mention any two assumptions made in analysis of variance
techniques.
BTL-1 Remembering
PART-B
1(a).
A study compares the effect of four 1-month point-of-purchase
promotions on sales. The unit sales for five stores using all four
promotions in different months follow.
Free Sample
78 87 81 89 58
One-pack gift
94 91 87 90 88
Cents off
73 73 78 69 83
76Refund by mail
79 83 78 69 81
(i)Compute the mean unit sales for each promotion and then
determine the grand mean.
(ii)Estimate the population variance using the between column
variance.
BTL-5 Evaluating
1(b).
From the question 1(a)
(i)Estimate the population variance using the within-column variance
computed from the variance within the samples.
(ii)Calculate the F ratio. At the 0.01 level of significance, do the
promotions produce different effects on sales.
BTL-2 Understanding
2(a).
In a low cost Toy production system, the molding machine has been
set with standard of 1% defective. The 80 sample units produced from
this machine shows defective of one unit. Is it necessary to stop the
product for corrective mechanism? Test at 5% level of significance
BTL-5 Evaluating
2(b).
Block Enterprises, a manufacturer of chips for computers. Is in the
process of deciding whether to replace its current semi automated
assembly line with a fully automated assembly line. Block has
gathered some preliminary test data about hourly chip production,
which is summarized in the following table, and it would like to know
whether it should upgrade its assembly line. State (and test at a =0.02)
appropriate hypothesis to help Block decide.
BTL-5 Evaluating
3(a).
Three samples below have been obtained from normal population
with equal variance. Test the hypothesis that the means are equal.
Sample I : 10 12 18 15 16
Sample II : 7 15 10 12 8
Sample III : 12 8 15 16 15
BTL-5 Evaluating
3(b). The I.Q.s of 16 students from one class of an showed a BTL-2 Understanding
12
mean of 107 with a standard deviation of 10, while the I.Q.s of 14
students from another class showed a mean of 112 with a standard
deviation of 8. Check whether there is an appreciable difference
between the I.Q.s of the two groups at (i) 0.01and (ii) 0.05 level of
significance
4(a).
The following is the information obtained from a random sample of 5
observations. Assume the population has a normal distribution.
30 31 27 32 28
To test if the sample was drawn from a normal distribution with mean
less than 30, (i)State the null and alternative hypotheses
(ii)Compute the standard error.
BTL-2 Understanding
4(b).
From the question 4(a)
(i)Determine the test statistic.
(ii)Decide at 10% level whether or not the mean value could be
greater than 30
BTL-2 Understanding
5.
The following data relate to the number of units produced per week by
three methods.
Method 1 : 170 192 190 120
Method 2 : 160 165 170 172
Method 3 : 182 190 170 178 185
Prepare ANOVA table and write your comments
BTL-6 Creating
6(a).
Test if the following samples could have come from two populations
with the same means, assuming the population variances are equal.
Sample I Sample II
Sample size 12 10
Sample Mean 40.5 43.8
Sample variance 2.6 3.2
BTL-5 Evaluating
6(b).
The weights of 10 people of a locality are found to be
70,67,62,68,61,68,70,64,64,66 kilograms. Is it reasonable to believe
that the average weights of the people of locality is greater than 64
kg? Test at 5%level of significance.
BTL-5 Evaluating
7(a).
In Town A, there were 850 birds of which 52% was males, while in
Town A and Town B combined, the proportion of males in a total of
1200 birds was 0.49. Is there any significance difference in the
proportions of male birds in the two Towns?
BTL-2
Understanding
7(b).
IQ test result of randomly selected five employees in an organization
is given below. Test whether minimum requirement of average IQ
level 87 is maintained in that company or not.
Employee code 234 232 121 343 111
IQ test 85 95 90 93 87
BTL-4 Analyzing
8(a).
The weights of 8 persons are found to be 60, 65, 70, 68, 62, 63, 60,
and 66 kgs. The weights of another group of 12 persons are found to
be 70, 60, 58, 56, 50, 48, 52, 56, 52, 50, 54, and 50. Can we conclude
that both samples have come from populations with same variances?
BTL -4 Analyzing
13
8(b).
ATMs must be stocked with enough cash to meet the requirements of
customers over a week, but excess cash results in loss of income as
investment opportunities could not be utilized. In an ATM, the
average transaction per customer in a week is Rs.8000 with a standard
deviation of Rs.1500. If a random sample of 36 customer transactions
is examined and it is observed that the sample mean with drawl is
Rs.8600, check the belief that the true average withdrawal is no longer
Rs.8000. Assume 0.05 level of significance
BTL -3 Applying
9.
Apply ANOVA technique and write your comment regarding the
sales(in Rs. Lakhs)
Area
Representatives
1 2 3 4
A 12 16 20 18
B 15 10 12 16
C 10 08 16 15
BTL -3 Applying
10(a).
A farmer wishes to determine whether there is a difference in yields
between two different varieties of wheat I and II. The following data
shows the production of wheat per unit area using the two varieties.
Can the farmer conclude at significance levels of
(i) 0.05
(ii) 0.01 that a difference exists?
BTL -4 Analyzing
10(b).
Test if the samples could have come from equal population means.
Sample A Sample B
Size 200 400
Mean 154.8 164.3
Variance 15.2 18.2
BTL-5 Evaluating
11(a).
The number of accidents per week in a city are as follows:
12, 8, 20, 2, 14, 10, 15, 6, 9 and 4. Are these frequencies in agreement
with the belief that accident conditions were the same during this 10
weeks period?
BTL -4
Analyzing
11(b).
Two samples are drawn from two normal population. From the
following data, Test whether the two samples have the same variance
5% level of significance.
Sample 1 60 65 69 74 76 82 85 87
Sample 2 61 66 67 85 78 63 85 86 88 91
BTL -3 Applying
12(a).
Given a sample mean of 83, a sample standard deviation of 12.5 and a
sample size of 22, test the hypothesis that the value of the population
mean is 70 against alternative that it is more than 70. Use the 0.025
significance level.
BTL-2
Understanding
12(b).
The following table shows the lifetimes in hours of samples from
three different types of television tables manufactured by a company.
Determine whether there is a difference between the three types at
significance level of 0.01.
Table:
BTL-2
Understanding
14
Sample 1 407 411 409
Sample 2 404 406 408 405 402
Sample 3 410 408 406 408
13.
The following table shows the yields per acre of hour different plants
crops grown on lots treated with three different types of fertilizer.
Determine at the 5% significance level whether there is a difference in
yield per acre.
(i) due to the fertilizers and
(ii) due to the crops
Table:
Crop -I Crop -II Crop -III Crop -IV
Fertilizer A 4.5 6.4 7.2 6.7
Fertilizer B 8.8 7.8 9.6 7.0
Fertilizer C 5.9 6.8 5.7 5.2
BTL-2
Understanding
14.
Time of 6 machine operator (in minute) in making product is given
below. Use paired t-test for training effectiveness.
Machine operator 1 2 3 4 5 6
Before training 12 23 4 5 16 17
After training 2 3 10 8 12 6
BTL -3 Applying
PART C
1(a).
What are non-parametric tests? Point out their advantages and
disadvantages?
BTL -6 Creating
1(b).
The success of a sales engineer in adopting the proven sales technique
was found to be 12 out of 30 occasions. Hence he tried a novel
technique and achieved success at a rate of 23 out of 40 occasions.
Check whether the novel technique is effective at 5% level of
significance.
BTL-2 Understanding
2(a).
The following are the final examination marks of three groups of
students who were taught computer by three difference methods.
First method: 94 88 91 74 87 97
Second method: 85 82 79 84 61 72 80
Third method: 89 67 72 76 69
BTL -5 Evaluating
2(b).
A consumer product manufacturing company was selling one of its
leading products through a large number of retail shops. Before a
heavy advertisement campaign, the average sale per week per shop
was 140 dozens. After the campaign, a sample of 26 shops was taken
and the mean sales improved to 147 dozens with a standard deviation
of 16. Check the effectiveness of the advertisement campaign at 5%
level of significance
BTL-2
Understanding
3.
Discuss the test procedure to test hypothesized population proportion
using single sample proportion.
BTL-1 Understanding
15
4.
(i)Write the application testing of hypothesis in statistics. (ii)What is
t-test? When should we apply a t-test?
BTL -3 Applying
UNIT IV: NON-PARAMETRIC TESTS
SYLLABUS: Chi-square test for single sample standard deviation. Chi-square tests for independence ofattributes and
goodness of fit. Sign test for paired data. Rank sum test. Kolmogorov-Smirnov ? test for goodness of fit, comparing two
populations. Mann ? Whitney U test and Kruskal Wallis test. One sample run test.
PART-A
Q.
No.
Question
Bloom?s
Taxonomy
Level
Domain
1. Define Rank Correlation test. BTL-1 Remembering
2. Write the formula in chi square test and any two uses. BTL-1 Remembering
3. Define Rank-Sum test. BTL-1 Remembering
4. Mention the advantages of Nonparametric Tests. BTL-1 Remembering
5. What is the other name or non-parametric test? Why? BTL-6 Creating
6. When are non parametric tests used? BTL-1 Remembering
7. What is the null hypothesis framed in Mann-Whitney test? BTL-6 Creating
8.
Write down the working rule for Mann-Whitney U-test and Kruskal-
Wallis test.
BTL-1 Remembering
9. Explain sign test. BTL-4 Analyzing
10. Define one sample run test? BTL-1 Remembering
11. When is Krushkal-Wallis test used? BTL-1 Remembering
12. Distinguish between Mann-Whitney U-test and Krushkal-Wallis test. BTL-2 Understanding
13. Write the contingency 2*2 table for
test. BTL-5 Evaluating
14.
Write down the formula to calculate rank correlation coefficient
(including tie values).
BTL-1 Remembering
15.
Two HR managers (A and B) ranked five candidates for a new
position. Their rankings of the candidates are show below:
Candidate Rank by A Rank by B
Nancy 2 1
Mary 1 3
John 3 4
Lynda 5 5
Steve 4 2
Compute the Spearman rank correlation.
BTL-6 Creating
16. Define rank correlation co-efficient. BTL-1 Remembering
17.
The following are the ranks obtained by 10 students in Statistics and
Mathematics. Find out the rank correlation coefficient.
Statistics 1 2 3 4 5 6 7
Mathematics 2 5 1 6 7 4 3
BTL-4 Analyzing
18. Explain Kolmogorov-Smirnov Test for one sample problem. BTL-4 Analyzing
19. What adjustment is to be done for tie values to find rank correlation. BTL-6 Creating
20. Mention the properties of linear coefficient of correlation. BTL-1 Remembering
PART -B
1(a).
The scores of a written examination of 24 students, who were trained
by using three different methods, are given below.
Video cassette A 74 88 82 93 55 70 65
BTL-3 Applying
16
Audio cassette B 78 80 65 57 89 85 78 70
Class Room C 68 83 50 91 84 77 94 81 92
Use Krushkal-Wallis test at ? = 5% level of significance, whether the
three methods of training yield the same results.
1(b). Explain Rank sum tests and its applications
2(a).
The production volume of units assembled by three different
operators during 9 shifts is summarized below. Check whether there
is significant difference between the production volumes of units
assembled by the three operators using Krushkal-Wallis test at a
significant level of 0.05.
Operator I 29 34 34 20 32 45 42 24 35
Operator II 30 21 23 25 44 37 34 19 38
Operator III 26 36 41 48 27 39 28 46 15
BTL-3
Applying
2(b).
Two faculty members ranked 12 candidates for scholarships.
Calculate the spearman rank-correlation coefficient and test it for
significance. Use 0.02level of significance.
Candidate Rank by Professor A Rank by Professor B
1 6 5
2 10 11
3 2 6
4 1 3
5 5 4
6 11 12
7 4 2
8 3 1
9 7 7
10 12 10
11 9 8
12 8 9
BTL-3
Applying
3(a).
In a study of sedimentary rocks, the following data were obtained
from samples of 32 grains from two kinds of sand :
Apply Mann-Whitney U test with suitable null and alternative
hypotheses.
Sand I 63 17 35 49 18 43 12 20 47
? 136 51 45 84 32 40 44 25
Sand II 113 54 96 26 39 88 92 53 101
? 48 89 107 111 58 62
BTL -3 Applying
3(b).
The Molisa?s shop has 3 mall locations. She keeps a daily record for
each locations of the number of the customers who actually make a
purchase. A sample of these data follows. Using Kruskal- Wallis test
can you say that at 5% level of significance that her stores have the
same number of customers who buy.
Eastowin 99 64 101 85 79 88 97 95 90 100
Craborchard 83 102 125 61 91 96 94 89 93 75
Fair forest 89 98 56 105 87 90 87 101 76 89
BTL -3 Applying
4(a)
The following are the prices in Rs. per kg of a commodity from 2
random samples of shops from 2 cities A&B.
BTL -3 Applying
17
City A 2.7 3.8 4.3 3.2 4.7 3.6 3.8 4.1
2.7 2.8 3.2 3.4 3.8 4.4 4.9 3.9 4.7
City B 3.7 5.3 4.7 3.6 4.7 4.8 6.0 4.8 4.9
3.8 3.9 4.8 5.2 6.1 3.6 3.8
Apply the run test to examine whether the distribution of prices of
commodity in the two cities is the same.
4(b)
Distinguish Nonparametric methods over parametric methods.
BTL -2 Understanding
5(a)
From a poll of 800 television viewers, the following data have been
accumulated as to,their levels of education and their performance of
television stations. We are interested in determining if the selection
of Tv station is independent of the level of education.
Education Level
High school Bachelor graduate Total
Public Broadcasting 50 150 80 280
Commercial
stations
150 250 120 520
Total 200 400 200 800
(i) State the null and alternative hypothesis.
(ii) Show the contingency table of the expected
frequencies
BTL -3 Applying
5(b)
From the question 5(a)
(i)Compute the test static
(ii)The null hypothesis to be tested at 95% confidence Determine the
critical value for this test
BTL-6
Creating
6(a)
Apply Mann-Whitney U test to determine if there is a significant
difference in the age distribution of the two groups
Day :26 18 25 27 19 30 34 21 33 31
Evening :32 24 23 30 40 41 42 39 45 35
BTL -3
Applying
6(b)
Apply the K-S test to check that the observed frequencies match with
the expected frequencies which are obtained from Normal
distribution. (Given at n=5).
Test Score 51-60 61-70 71-80 81-90 91-100
Observed Frequency
30 100 440 500 130
Expected Frequency 40 170 500 390 100
BTL -5 Evaluating
7
A research company has designed three different systems to clean up
oil spills. The following table contains the results, measures by how
much surface area (in square meters) is cleaned in one hour. The data
were found by testing each method in several trials. Are there
systems equally effective? Use the 5% level of significance.
Sample A 55 60 63 56 59 55
Sample B 57 53 64 49 62
Sample C 66 52 61 57
BTL -1 Remembering
8(a)
Suppose it is desired to check whether pinholes in electrolytic tin
plate are distributed uniformly across a plated coil on the basis of the
following distances (in inches) of 10 pinholes from one edge of a
BTL -1 Remembering
18
long strip of tin plate 320 inches wide.
4.8 14.8 28.2 23.1 4.4 28.7 19.5 2.4 25.0 6.2
Use Kolmogorov Smirnov test to test the null hypothesis.
8(b) Explain Mann- WhitneyU test with an example BTL-4 Analyzing
9.
Ten competitors in a beauty contest are ranked by 3 judges in the
following order.
A : 1 6 5 3 10 2 4 9 7 8
B : 3 5 8 4 7 10 2 1 6 9
C : 6 4 9 8 1 2 3 10 5 7
Find out which pair of Judges has awarded the ranks to the nearest
common taste of beauty.
BTL -3 Applying
10(a).
Test the association of Age and preference of colour of Toy from the
following data
Age/Colour Below 5 6-10 Above 10 years
Pink 60 40 5
Purple 30 30 30
Red 80 10 10
BTL -4 Analyzing
10(b).
Melisa?s Boutique has three mall locations. Melisa keeps a dairy
record for each location of number of customers who actually make a
purchase. A sample of those data follows. Using the kruskal-wallis
test, can you say at the 0.05 level of significance that her stores have
the same number of customers who busy?
DSF Mall 99 64 101 85 79 88 97 95 90 100
Forest Mall 83 102 125 61 91 96 94 89 98 75
Big-Ben Mall 89 98 56 105 87 90 87 101 76 89
BTL -3 Applying
11(a).
A brand manager is concerned that her brand?s share may he
unevenly distributes through the country. In a survey in which the
country was divided into four geographic regions, a random
sampling of 100 consumers in each region was surveyed, with the
following results:
NE NW SE SW TOTAL
Purchase the brand 40 55 45 50 190
Do not purchase 60 45 55 50 210
Total 100 100 100 100 400
(i) Develop a table of observed and expected frequencies for
this problem.
(ii) Calculate the sample
value.
BTL -6 Creating
11(b).
From the question 11(a)
(i)State the null and alternative hypothesis.
(ii)At test whether brand share is the same across the four
regions
BTL -2 Understanding
12(a).
In 30 tosses of a coin, the following sequence of head and tails is
obtained HTTHTHHHTHHTTHTHTHHTHTTHTHHTHT
(i) Determine the number of runs
BTL -2 Understanding
12(b).
From the question 12(a ) Test at 0.10 level of significance, whether
the sequence is random
BTL -3 Applying
13. An experiment designed to compare three preventative methods BTL -3 Applying
19
against corrosion yielded the following maximum depths of pits ( in
thousandths of an inch) in pieces of wire subjected to the respective
treatments:
Method A: 77 54 67 74 71 66
Method B: 60 41 59 65 62 64 52
Method C: 49 52 69 47 56
Use the Kruskal-Wallis test at the 5% level of significance to test the
null hypothesis that the three samples come from identical
populations.
14.
The number of defects in printed circuit boards in hypothesized to
follow a poisson distribution. A random sample of 60 printed boards
have been collected and the number of defects observed. The
following table gives the results.
Table:
No. of defects Observed Frequency
0 32
1 15
2 9
3 4
Does the assumption of a poisson distribution seem appropriate as a
probability model for this process?
BTL -4
Analyzing
PART C
1. Explain the Mann-Whitney test procedure with appropriate examples BTL-1 Remembering
2.
Write the application of Non parametric test and Sign test in
statictics.
BTL-1 Remembering
3(a).
The sales records of two branches of a department store over the last
12 months are shown below.(sales figures are in thousands of
dollars). We want to use the Mann-Whitney-Wilcoxon test to
determine if there is a significant difference in the sales of the two
branches.
Month Branch A Branch B
1 257 210
2 280 230
3 200 250
4 250 260
5 284 275
6 295 300
7 297 320
8 265 290
9 330 310
10 350 325
11 340 329
12 372 335
(i) Compute the sum of the ranks for branch A
(ii) Compute the mean ?T
BTL-4 Analyzing
3(b).
From the question 3(a)
(i)Compute ?T
BTL -6 Creating
20
(ii)Use and test to determine if there is a significant
difference in the population of the sales of the two branches
4(a).
Independent random samples of ten day students and ten evening
students at a university showed the following age distributions. We
want to use the Mann-Whitney-Wilcoxon test to determine if there is
a significant different in the age distribution of the two groups.
Day Evening
26 32
18 24
25 23
27 30
19 40
30 41
34 42
21 39
33 45
31 35
(i) Compute the sum of the ranks for the day students.
(ii) Compute the mean ?
BTL-2 Understanding
4(b).
From the question 4(a)
(i)Compute ?
(ii)Use and test for any significant difference in the age
distribution of the two populations
BTL -4
Analyzing
UNIT ? V CORRELATION AND REGRESSION
SYLLABUS: Correlation ? Coefficient of Determination ? Rank Correlation ? Regression ? Estimation of Regression line
? Method of Least Squares ? Standard Error of estimate.
PART ? A
Q.No. Question
Bloom?s
Taxonomy
Level
Domain
1. Define regression coefficient?. BTL -1 Remembering
2. Define Linear Relationship of Correlation. BTL -6 Creating
3. Write the Properties of Correlation Coefficient? BTL -1 Remembering
4. What is the angle between the regression lines? BTL -1 Remembering
5. When is linear regression used? BTL -1 Remembering
6. Distinguish between correlation and regression BTL -2 Understanding
7. What is regression analysis? BTL -6 Creating
8. What do you interpret if the r = 0 , r = + 1 and r = -1? BTL -1 Remembering
9. Specify the range of correlation. BTL -6 Creating
10. Briefly explain how a scatter diagram benefits the researcher? BTL -4 Analyzing
11. Define correlation coefficient between two variables. BTL -1 Remembering
12. What is a scatter diagram and write its benefits? BTL -6 Creating
21
13.
If the equations of the regression lines are x+2y=5 and 2x+3y=8, find
the correlation coefficient between x and y.
BTL -3 Applying
14. Find the mean values of regression lines are 2y-x =50 and 3y-2x =10. BTL -1 Remembering
15. Write the correlation coefficient in terms of regression coefficients. BTL -6 Creating
16. Write the Equations of Regression lines. BTL -1 Remembering
17.
Explain the difference between the coefficient of determination and
the coefficient of correlation.
BTL -1 Remembering
18. What are the various methods in correlation? BTL -1 Remembering
19.
If the equations of the regression lines are x+2y=5 and 2x+3y=8, find
the correlation coefficient between x and y? Use the equations to find
the mean of X and Y. If the variance of X is 12, calculate the variance
of Y?
BTL -1 Remembering
20. What is positive and negative correlation? BTL -1 Remembering
PART-B
1(a).
The following data pertains of X = Revenue (in ?000 of rupees) generated at
a Corporate Hospital and Y = Number of Patients (in ?00) arrived for the last
ten years.
X 86 95 75 85 90 98 112 74 100 110
Y 21 24 18 24 22 30 27 18 25 28
Find the Karl Pearson?s coefficient of correlation and give your comment.
BTL -4
Analyzing
1(b).
Obtain the two regression lines:
X 45 48 50 55 65 70 75 72 80 85
y 25 30 35 30 40 50 45 55 60 65
BTL-5 Evaluating
2(a).
The revenue generated at a unit and is given below. Fit the trend
line using least squares method and estimate the revenue for the year 2013.
Year 2005 2006 2007 2008 2009 2010 2011 2012
Revenue
(Rs. 00)
268 209 390 290 280 450 350 455
BTL -2 Understanding
2(b).
The following table presents the results of a survey of 8 randomly selected
families:
Annual income (in 000 Rs.):
8 12 9 24 13 37 10 16
Percent allocation for investment
36 25 33 15 28 19 20 22
Find the Karl Pearson?s correlation and spearman?s rank correlation methods
for the above data.
BTL -4
Analyzing
3(a).
Given below are the figures of production (in thousand quintals) of a sugar
factory.
Year 1992 1993 1994 1995 1996 1997 1998
Production 75 80 95 85 95 100 105
Fit a straight line trend by the least squares method and tabulate the trend
values.
BTL -3 Applying
3(b).
Promotional expenses and sales data for an equipment manufacturer are as
follows. Calculate the correlation coefficient and comment.
BTL -3 Applying
FirstRanker.com - FirstRanker's Choice
1
(An
Ka ttankulathur ?
DEPARTMENT OF MATHEMATICS
QUESTION BANK
I SEMESTER
1918108 ? STATISTICS FOR MANAGEMENT
Regulation ? 2019
Academic Year 2019 - 2020
Prepared by
Ms. B. Vasuki, Assistant Professor/Mathematics
Ms.B.Elakkiavani, Assistant Professor/Mathematics
2
(An
? .
DEPARTMENT OF MATHEMATICS
QUESTION BANK
SUBJECT : 1918108 ? STATISTICS FOR MANAGEMENT
SEM / YEAR : I Semester / I Year
UNIT I - INTRODUCTION
SYLLABUS: Basic definitions and rules for probability, conditional probability independence of events, Baye?s
theorem, and random variables, Probability distributions: Binomial, Poisson, Uniform and Normal distributions.
PART- A
S.NO QUESTIONS
BT Level
COMPETENCE
PART ? A
1. Define Statistics. BTL -6 Creating
2. What is the addition and multiplication theorem on probability. BTL -1 Remembering
3. Distinguish between a priori and posterior probability?. BTL -6 Creating
4.
The price of the selected stock over a five day period shown as 170, 110,
130, 170 and 160. Compute mean , median and mode.
BTL -6 Creating
5.
A car travels 25 miles at 25 mph, 25 miles at 50 mph and 25 miles at 75
mph. Find the harmonic of three velocities?
BTL -4 Analyse
6.
A ball is drawn at random from a box containg 6 red balls, 4 white balls
and 5 blue balls. Find the probability that the ball drawn is not red.
BTL -4 Analyse
7.
Find the median and mode for the weights (kgs) of 15 persons given as
68, 85, 70, 65, 71, 67, 65, 55, 80, 62, 65, 64, 70, 60, 56.
BTL -3 Applying
8. Name few measures of dispersion. BTL -1 Remembering
9. write the common measures of central tendency? BTL -1 Remembering
10. Define continuous and discrete variables examples. BTL -1 Remembering
11.
Let X be the lifetime in years of a mechanical part. Assume that X has
the cdf F(x) = 1- e
-x
, x ? 0. Find P[1< X ? 3].
BTL -1 Remembering
12. Define independent events. BTL -1 Remembering
13. State the theorem of total probability BTL -1 Remembering
14. What is the use of Baye?s theorem? BTL -6 Creating
15. Mention the properties of a discrete probability distribution. BTL -1 Remembering
16. Define a Poisson distribution and mention its mean and variance. BTL -1 Remembering
17. If the mean and variance of a binomial distribution are respectively 6 BTL -3 Applying
3
and 2.4, find P(x=2).
18.
If x is a Poisson distribution such that P(x=1)=4P(x=2). Find its
mean and variance.
BTL -3 Applying
19.
Suppose that X has a Poisson distribution with parameter ? = 2.
Compute P[X ? 1].
BTL -1 Remembering
20. Define mutually exclusive events. BTL -1 Remembering
PART-B
1(a).
Calculate the mean and standard deviation for the following table
giving the age distribution of 542 members.
Age
20-30 30-40 40-50 50-60 60-70 70-80 80-90
No 3 61 132 153 140 51 2
BTL-2 Understanding
1(b).
Find the geometric mean for the following data:
Group
2-4 4-6 6-8 8-10
Frequency 200 400 300 100
BTL-2
Understanding
2(a).
Find the mean, median and modal ages of married women at first
child birth
Age at the
birth of
first child
13
14
15
16
17
18
19
20
21
22
23
24
25
No of
married
women
37
162
343
390
256
433
161
355
65
85
49
46
40
BTL -6 Creating
2(b).
If A and B are independent event with P(A)=2/5, and P(B)=3/5,
find P(A ?B). Let S= {1,2,3,4,5,6} if A = {2,4,6} then find the
probability of A complement.
BTL -3 Applying
3(a).
Given: The probabilities of three events A, B and C occurring are
P(A) = 0.35, P(B) = 0.45 and P(C) = 0.2. Assuming that A, B, or
C has occurred, the probabilities of another event X occurring are
P(X/A) = 0.8, P(X/B) = 0.65 and P(X/C) = 0.3. Find P(A/X),
P(B/X) and P(C/X).
BTL -6 Creating
3(b).
4 cards are drawn from a well shuffled pack of cards. Find the
probability that
(i) All the four are queens
(ii) There is one card from each suit.
(iii) Two cards are diamonds and two are spades
All the four cards are hearts and one of them is jack
BTL -6 Creating
4(a).
Three machines all turn out non ferrous castings. Machine A
produces 1% defective and Machine B- 2% and machine C ? 5%.
Each machine produces 1/3 of the output. An inspector examines
a single casting, which he determines as non defective. Estimate
the probabilities of its having been produced by each machine.
BTL -6 Creating
4(b).
If the random variable X takes values 1, 2, 3, 4 such that
2P(X = 1) = 3P(X = 2) = P( X=3) = 5P(X = 4), find the
probability distribution and cumulative distribution of X.
BTL-2 Understanding
5(a).
Two dice are thrown together once. Find the probabilities for
BTL -3 Applying
4
getting the sum of the two numbers (i) equal to 5, (ii) multiple of
3, (iii) divisible by 4.
5(b).
Given ? = 4.2, for a poisson distribution. Find (a) P(X ? 2) (b)
P(X ? 5) (c) P(X = 8).
BTL -6 Creating
6(a).
An urn contains 5 balls. Two balls are drawn and found to be
white. What is the probability that all the balls are white?
BTL-1 Remembering
6(b).
The contents of urns I, II, III are as follows:
1 white, 2 black and 3 red balls;
2 white, 1 black and 1 red balls;
4 white, 5 black and 3 red balls;
One urn is chosen at random and two balls drawn. They happen to
be white and red. What is the probability that they come from
urns I, II, III?
BTL -3 Applying
7(a).
In 1989, there were three candidates for the position of principal
Mr. Chatterji, Mr. Ayangar and Dr. Singh. Whose chances of
getting the appointment are in the proportion 4:2:3 respectively.
The probability that Mr. Chatterji is selected, would introduce co-
education in the is 0.3. The probabilities of Mr. Ayangar
and Dr. Singh doing the same are respectively 0.5 and .08. What
is the probability that there was co-education in the in
1990?
BTL -3
Applying
7(b).
Find the probability that atmost 5 defective bolts will be found in
a box of 200 bolts, if it is known that 2% of such bolts are
expected to be defective. (e
-4
= 0.0183)
BTL -6 Creating
8(a).
A coin is tossed 6 times what is the probability of obtaining (a) 4
heads (b) 5 heads (c) 6 heads (d) getting 4 or more heads.
BTL -3 Applying
8(b).
In a bolt factory machines A, B, C manufacture respectively 25%,
35% and 40% of the total of their output 5, 4, 2 percent are
defective bolts. If A bolt is drawn at random from the product and
is found to be defective, what are the probabilities that is was
manufactured by machines A, B and C?
BTL -6 Creating
9(a).
In a test of 2000 electric blubs it was found that the life of a
particular make was normally distributed with an average life of
2040 hours and S. D. of 60 hours. Estimate the number of blubs
likely to burn for
(1) More than 2150 hours
(2) Less than 1950 hours
(3) More than 1920 hours but less than 2160 hours.
BTL -3 Applying
9(b).
The latest nationwide political poll indicates that for Americans
who are randomly selected, the probability that they are
conservative is 0.55, the probability that they are liberal is 0.30
and the probability that they are middle of the road is 0.15.
Assuming these probabilities are accurate, answer the following
BTL -4 Analyzing
5
questions from a randomly chosen group of 10 Americans
(a) What the probability that 4 are liberal?
(b) What the probability that none are conservative
(c) What the probability that two are middle of the road
(d) What the probability that a least 8 are liberal
10.
If X follows a normal distribution with mean 12 and variance 16
cm, find the probabilities for (i) X ? 20 (ii) X ? 20, and (iii) 0 ? X
? 12.
BTL -3 Applying
11.
A discerete random variable X has the probability function given
below:
Value of X=x: 0 1 2 3 4 5 6 7
P(X=x) : 0 k 2k 2k 3k k
2
2k
2
7k
2
+k
Find (1) The value of k
(2) P(1.5 < X < 4.5 / X > 2)
(3) P(X < 6), P(X ? 5), P( 0 < X < 4)
(4) The distribution of X.
BTL -3 Applying
12.
X is a normal variable with mean 30 and standard deviation of 5.
Find (i) P[26 ? X ? 40] (ii) P [X?45] (iii) P [ ?X - 30 ?> 5] use
normal distribution tables
BTL -4 Analyzing
13.
In an intelligence test administered on 1000 students, the average
was 42 and standard deviation 24, find (i) the number of students
exceeding a score 50. (ii) the number of students lying between
30 and 54(iii) the value of score exceeded by top 100 students.
BTL -4 Analyzing
14(a).
The probability that an entering student will graduate is 0.4
Determine the probability that out of 5 students atleast one will
graduate.
BTL-5
Evaluating
14(b).
Fit a Poisson Distribution to the following data which gives the
number of doddens in a sample of clover seeds
No 0 1 2 3 4 5 6 7 8
f 56 156 132 92 37 22 4 0 1
.
BTL -4 Analyzing
PART-C
1(a).
A disciplinary committee is formed from the staff of XYZ
Company which has three departments Marketing, Finance and
Production of the 10,5,20 members respectively. All departments
have two female staff each. A department is selected at random
and from which two matters are selected for the committee,
What is the probability that both the team members are female?
BTL-6 Creating
6
1(b).
In a bolt factory machines A, B, C manufacture respectively 25,
35 and 40 percent of the total. Of their output 5, 4 and 2 percent
are defective bolts respectively. A bolt is drawn at random from
the product and is found o be defective. What are the probabilities
that it was manufactured by machines A, B or C?
BTL-2
Understanding
2(a). State Bayes theorem and brief about its applications. BTL-2 Understanding
2(b).
Out of 800 families with 4 children each, how many families
would be expected to have (i) 2 boys and 2 girls (ii) at least 1 boy
(iii) at most 2 girls (iv) children of both sexes? Assume equal
probabilities for boys and girls.
BTL-1 Remembering
3. Describe the classifications of probability ? BTL-1 Remembering
4. What are the applications of Normal distribution in statistics? BTL-6 Creating
UNIT ?II- SAMPLING DISTRIBUTION & ESTIMATION.
SYLLABUS: Introduction to sampling distributions, sampling distribution of mean and proportion, application of central
limit theorem, sampling techniques. Estimation: Point and Interval estimates for population parameters of large sample and
small samples, determining the sample size.
PART - A
S.N
O
QUESTIONS
BT Level
COMPETENCE
1. Define Sampling distribution of proportion. BTL -1 Remembering
2. Define Probable standard error. BTL -1 Remembering
3. Define standard error and mention its importance BTL -1 Remembering
4. Define central limit theorem BTL -1 Remembering
5.
What is the role of central limit theorem in estimation and testing
problems
BTL -6 Creating
6. Define stratified sampling technique BTL -1 Remembering
7. Briefly describe the significance level. BTL -1 Remembering
8. Distinguish between parameter and statistic. BTL -2 Understanding
9. Define estimator, estimate and estimation. BTL -1 Remembering
10. Distinguish between point estimation and interval estimation BTL -2 Understanding
11. Mention the properties of a good estimator. BTL -1 Remembering
12. Define confidence coefficient. BTL -1 Remembering
13. What is the level of significance in testing of hypothesis BTL -6 Creating
14. Define confidence limits for a parameter BTL -1 Remembering
15.
State the conditions under which a binomial distribution becomes a
normal distribution
BTL -4 Analyzing
16.
If the random sample comes from a normal population, what can
be said about the sampling distribution of the mean.
BTL -5 Evaluating
17.
An automobile repair shop has taken a random sample of 40
services that the average service time on an automobile is 130
minutes with a standard deviation of 26 minutes. Compute the
standard error of the mean.
BTL -6 Creating
7
18. What is a random number? How it is useful in sampling? BTL -6 Creating
19.
A population has the numbers: 12, 8, 10, 30, 12, 16, 40, 5, 16, 24,
22, 31, 30, 16, 15. Draw a systematic sample of size 5. Find out its
mean.
BTL -3 Applying
20. How large sample is useful in estimation and testing BTL -4 Analyzing
PART -B
1(a).
A random sample of 700 units from a large consignment showed
that 200 were damaged. Find (i) 95% (ii) 99% confidence limits
for the proportion of damaged units in the consignment.
BTL -3 Applying
1(b).
A random sample of size 9 is obtained from a Normal population
with mean 25 and if the variance 100 find the probability that the
sample mean exceeds 31.2.
BTL -4 Analyzing
2(a).
In a normally distributed population, average income per
household is Rs.20,000 with a standard deviation of Rs. 1,600.
Find the probability that the sample mean will be between
Rs.19,600 and Rs.20,200 in a survey of a random sample of 100
households.
BTL -6 Creating
2(b).
A university wants to determine the percentage of students who
would accept proposed fees hike for improving facilities. The
university wants to be 90% confident that the percentage is
within2% of the true value. Find the sample size to achieve the
accuracy regardless of the true percentage assuming the percentage
of students accepting the increase in tuition fees to be 0.5.
BTL -6 Creating
3(a).
A bank has kept records of the checking balances of its customers
and determined that the average daily balances of its customers is
Rs.300 with a standard deviation of Rs. 48. A random sample of
144 checking accounts is selected.
(i) What is the probability that the sample mean will be more
than Rs. 306.60?
(ii) What is the probability that the sample mean will be less
than Rs. 308?
BTL -6 Creating
3(b).
From the question 3(a)
(i) What is probability that the sample mean will between Rs.
302 and Rs. 308?
(ii) What is probability that the sample mean will be atleast
Rs. 296?
BTL -6 Creating
4(a).
Explain Stratified sampling technique and discuss how it is better
than simple random sampling in a particular situation.
BTL -4
Analyzing
4(b). Discuss the standard error of proportion BTL-2 Understanding
5.
Explain the methods of drawing simple random sample from a
finite population.
BTL -4 Analyzing
8
6(a).
In a sample of 1000 citizens of India, 540 are wheat eaters and the
rest are rice eaters. Can we assume that both rice and wheat
equally popular in India at 1 % level of significance?
BTL-5
Evaluating
6(b).
A simple random sample of 144 items resulted in a sample mean
of 1257.85 and standard deviation of 480. Develop a 95%
confidence interval for the population mean
BTL -6
Creating
7(a).
A car dealer wants to estimate the proportion of customers who
still own the cars they purchased 5 years earlier. A random sample
of 500 customers selected from the dealer?s records indicate that
315 customers still own cars that they were purchased 5 years
earlier. Set up 95% confidence interval estimation of the
population proportion of all the customers who still own the cars 5
years after they were purchased.
BTL-2
Understanding
7(b).
A movie maker sampled 55 fans who viewed his master piece
movie and asked them whether they had planned to see it again.
Only 10 of them believed that the movie was worthy of a second
look. Find the standard error of the population of fans who will
view the film a second time. Construct a 90% confidence interval
for this population.
BTL -5 Evaluating
8(a).
From a population of size 600, a sample of 60 individuals revealed
mean and standard deviation as 6.2 and 1.45 respectively. (i) Find
the estimated standard error (ii) Construct 96% confidence
interval for the mean.
BTL -3 Applying
8(b).
The age of employees in a company follows normal distribution
with its mean and variance as 40 years and 121 years respectively.
If a random sample of 36 employees is taken from a finite normal
population of size 1000, what is the probability that the sample
mean is
(i) less than 45
(ii) greater than 42 and
(iii) between 40 and 42?
BTL -6
Creating
9(a).
A firm wishes to estimate with an error of not more than 0.03 and
a level of confidence of 98%, the proportion of consumers that
prefer its brand of household detergent. Sales report indicate the
about 0.20 of all consumers prefer the firm?s brand. What is the
requisite sample size?
BTL -5 Evaluating
9(b).
A random sample of 700 units from a large consignment should
that 200 were damaged.
Find (i) 95%
(ii) 99% confidence limits for the proportion of damaged
units in the consignment
BTL -3 Applying
10(a).
From a population of 500 items with a mean of 100 gms and
standard deviation of 12.5 gms, 65 items were chosen. (i) What is
the standard error? (ii) Find P(99.5 < X < 101.5).
BTL -6 Creating
10(b).
A non-normal distribution representing the number of trips
BTL -6 Creating
9
performed by lorries per week in a coal field has a mean of 100
trips and variance of 121 trips. A random sample of 36 lorries is
taken from the non-normal population. What is the probability that
the sample mean is
(i) greater than 105
(ii) less than 102
(iii) between 101 and 103 trips?
11.
Test the significance of the difference between the means of the
sample from the following data
Size of sample Mean SD
Sample A 100 61 4
Sample B 200 63 6
BTL -4 Analyzing
12(a).
A cigarete manufacturing firm claims that its brand. A outsells
brand B by 8%. If it is found that 42 out of a sample of 200
smokers prefer brand a and 18 out of another sample of 100
smokers prefer brand B, test whether the 8% difference is a valid
claim(use 5% level of significance).
BTL -4
Analyzing
12(b).
In an automotive safety test conducted by the North Carolina
Highway Safety Research center, the average tyre pressure in a
sample of 62 tyres was found to be 24 pounds per square inch, and
the standard deviation was 2.1 pounds per square inch.
(i) What is the estimated population standard deviation for this
population
(ii) Calculate the estimated standard error of the mean
(iii) Construct a 95% confidence interval for the population mean.
BTL -3 Applying
13(a).
The manager of a shop selling beverages wants to estimate the
actual amount of beverages in one litre bottles from a nationally
known manufacturer. As per manufacturer?s specifications, the
standard deviation of the volume of the beverage is 0.02 litre. The
average amount of beverage per 1 litre bottle is found to be 0.995
litre on checking 50 bottles. Setup 99% confidence interval
estimate of the true population average amount of beverage in a 1
liter bottle. Check whether the manufacturer is genuine in filling
the beverage.
BTL -6
Creating
13(b).
In a batch chemical process used for etching printed circuit boards,
two different catalysts are being compared to determine whether
they require different emersion times for removal of identical
quantities of photo resist material. Twelve batch were run with
catalyst 1, resulting in a sample mean emersion time of 24.6
minutes and sample standard deviation of 0.85 minutes. Fifteen
batches were run with catalyst 2, resulting in a mean emersion time
of 22.1 minutes and a standard deviation of 0.98 minutes. Find a
95% confidence interval on the difference in means, assuming that
2
2
2
1
? ? ? .
BTL -3 Applying
10
14.
In a random sample of 75 axle shafts. 12 have a surface finish that
is rougher than the specifications will allow. Suppose that a
modification is made in the surface finishing process and
subsequently a second random sample of 85 axle shafts is
obtained. The number of defective shafts in this second sample is
10. Obtain an approximate 95% confidence interval on the
difference in the proportions of defectives produced under the two
processes
BTL -5 Evaluating
PART-C
1.
In a sample of 25 observations from a Normal distribution with
mean 98.6 and standard deviation 17.2.
(i)What is P(92<102)
(ii)Find the corresponding probability given a sample of 36.
BTL -6 Creating
2.
Mary, an auditor for a large credit card company, knows that, on
average, the monthly balance of any customer is Rs.112, and the
standard deviation is Rs.56. If Mary audits 50 randomly selected
accounts, What is the probability that the sample average balance
is
(i) Below Rs. 100
(ii)Between Rs.100 and Rs.130
BTL -6 Creating
3(a).
Write the type of sampling methods and the uses of standard error?
BTL -1 Remembering
3(b).
From a population of 540, a sample of 60 individual is taken. From
this sample, the mean is found to 6.2 and the standard deviation
1.368
(i) Find the estimated standard error of the mean.
(ii) Construct a 96 % confidence interval for the mean.
BTL-2 Understanding
4(a).
Explain the properties of good point estimator.
BTL -4 Analyzing
4(b).
What do you mean by interval estimation? Give examples
BTL-6 Creating
UNIT III - TESTS OF HYPOTHESIS- PARAMETRIC TESTS
SYLLABUS: Hypothesis testing: one sample and two sample tests for means and proportions of large samples (z-test),
one sample and two sample tests for means of small samples (t-test), F-test for two sample standard deviations. ANOVA
one and two way.
PART-A
Q.
No.
Question
Bloom?s
Taxonomy
Level
Domain
1. Define Test of Significance. BTL-1 Remembering
2. What are the Type I and Type II errors? BTL-6 Creating
3. What do you mean by one tail test? BTL-6 Creating
4. State the applications of Z-test and t-test. BTL-4 Analyzing
5. Define critical region BTL-1 Remembering
6. Distinguish between one tail and two tail tests BTL-2 Understanding
7. What is the aim of design of experiments? BTL-6 Creating
8. Distinguish between one-way and two-way analysis of variance. BTL-2 Understanding
9. When does the Z-test apply? BTL-1 Remembering
10. Explain SSB , SSW and SSY
and relationship in ANOVA. BTL-4 Analyzing
11
11. Describe any two applications of t-distribution BTL-1 Remembering
12. Write the uses of F-test? BTL-6 Creating
13. Define the level of significance. BTL-1 Remembering
14. Write the properties of t-distribution? BTL-6 Creating
15. What is the role of standard error? BTL-6 Creating
16. Mention any four applications of t-distribution in tests of hypothesis. BTL-1 Remembering
17. Mention any four uses of Chi-square distribution in test of hypothesis. BTL-1 Remembering
18. Define null hypothesis ? Explain. BTL-6 Creating
19.
Estimate the standard error of difference between two proportion if
p
1
=0.10,p
2=
0.133 and n
1
=50,n
2
=75.
BTL-6 Creating
20.
Mention any two assumptions made in analysis of variance
techniques.
BTL-1 Remembering
PART-B
1(a).
A study compares the effect of four 1-month point-of-purchase
promotions on sales. The unit sales for five stores using all four
promotions in different months follow.
Free Sample
78 87 81 89 58
One-pack gift
94 91 87 90 88
Cents off
73 73 78 69 83
76Refund by mail
79 83 78 69 81
(i)Compute the mean unit sales for each promotion and then
determine the grand mean.
(ii)Estimate the population variance using the between column
variance.
BTL-5 Evaluating
1(b).
From the question 1(a)
(i)Estimate the population variance using the within-column variance
computed from the variance within the samples.
(ii)Calculate the F ratio. At the 0.01 level of significance, do the
promotions produce different effects on sales.
BTL-2 Understanding
2(a).
In a low cost Toy production system, the molding machine has been
set with standard of 1% defective. The 80 sample units produced from
this machine shows defective of one unit. Is it necessary to stop the
product for corrective mechanism? Test at 5% level of significance
BTL-5 Evaluating
2(b).
Block Enterprises, a manufacturer of chips for computers. Is in the
process of deciding whether to replace its current semi automated
assembly line with a fully automated assembly line. Block has
gathered some preliminary test data about hourly chip production,
which is summarized in the following table, and it would like to know
whether it should upgrade its assembly line. State (and test at a =0.02)
appropriate hypothesis to help Block decide.
BTL-5 Evaluating
3(a).
Three samples below have been obtained from normal population
with equal variance. Test the hypothesis that the means are equal.
Sample I : 10 12 18 15 16
Sample II : 7 15 10 12 8
Sample III : 12 8 15 16 15
BTL-5 Evaluating
3(b). The I.Q.s of 16 students from one class of an showed a BTL-2 Understanding
12
mean of 107 with a standard deviation of 10, while the I.Q.s of 14
students from another class showed a mean of 112 with a standard
deviation of 8. Check whether there is an appreciable difference
between the I.Q.s of the two groups at (i) 0.01and (ii) 0.05 level of
significance
4(a).
The following is the information obtained from a random sample of 5
observations. Assume the population has a normal distribution.
30 31 27 32 28
To test if the sample was drawn from a normal distribution with mean
less than 30, (i)State the null and alternative hypotheses
(ii)Compute the standard error.
BTL-2 Understanding
4(b).
From the question 4(a)
(i)Determine the test statistic.
(ii)Decide at 10% level whether or not the mean value could be
greater than 30
BTL-2 Understanding
5.
The following data relate to the number of units produced per week by
three methods.
Method 1 : 170 192 190 120
Method 2 : 160 165 170 172
Method 3 : 182 190 170 178 185
Prepare ANOVA table and write your comments
BTL-6 Creating
6(a).
Test if the following samples could have come from two populations
with the same means, assuming the population variances are equal.
Sample I Sample II
Sample size 12 10
Sample Mean 40.5 43.8
Sample variance 2.6 3.2
BTL-5 Evaluating
6(b).
The weights of 10 people of a locality are found to be
70,67,62,68,61,68,70,64,64,66 kilograms. Is it reasonable to believe
that the average weights of the people of locality is greater than 64
kg? Test at 5%level of significance.
BTL-5 Evaluating
7(a).
In Town A, there were 850 birds of which 52% was males, while in
Town A and Town B combined, the proportion of males in a total of
1200 birds was 0.49. Is there any significance difference in the
proportions of male birds in the two Towns?
BTL-2
Understanding
7(b).
IQ test result of randomly selected five employees in an organization
is given below. Test whether minimum requirement of average IQ
level 87 is maintained in that company or not.
Employee code 234 232 121 343 111
IQ test 85 95 90 93 87
BTL-4 Analyzing
8(a).
The weights of 8 persons are found to be 60, 65, 70, 68, 62, 63, 60,
and 66 kgs. The weights of another group of 12 persons are found to
be 70, 60, 58, 56, 50, 48, 52, 56, 52, 50, 54, and 50. Can we conclude
that both samples have come from populations with same variances?
BTL -4 Analyzing
13
8(b).
ATMs must be stocked with enough cash to meet the requirements of
customers over a week, but excess cash results in loss of income as
investment opportunities could not be utilized. In an ATM, the
average transaction per customer in a week is Rs.8000 with a standard
deviation of Rs.1500. If a random sample of 36 customer transactions
is examined and it is observed that the sample mean with drawl is
Rs.8600, check the belief that the true average withdrawal is no longer
Rs.8000. Assume 0.05 level of significance
BTL -3 Applying
9.
Apply ANOVA technique and write your comment regarding the
sales(in Rs. Lakhs)
Area
Representatives
1 2 3 4
A 12 16 20 18
B 15 10 12 16
C 10 08 16 15
BTL -3 Applying
10(a).
A farmer wishes to determine whether there is a difference in yields
between two different varieties of wheat I and II. The following data
shows the production of wheat per unit area using the two varieties.
Can the farmer conclude at significance levels of
(i) 0.05
(ii) 0.01 that a difference exists?
BTL -4 Analyzing
10(b).
Test if the samples could have come from equal population means.
Sample A Sample B
Size 200 400
Mean 154.8 164.3
Variance 15.2 18.2
BTL-5 Evaluating
11(a).
The number of accidents per week in a city are as follows:
12, 8, 20, 2, 14, 10, 15, 6, 9 and 4. Are these frequencies in agreement
with the belief that accident conditions were the same during this 10
weeks period?
BTL -4
Analyzing
11(b).
Two samples are drawn from two normal population. From the
following data, Test whether the two samples have the same variance
5% level of significance.
Sample 1 60 65 69 74 76 82 85 87
Sample 2 61 66 67 85 78 63 85 86 88 91
BTL -3 Applying
12(a).
Given a sample mean of 83, a sample standard deviation of 12.5 and a
sample size of 22, test the hypothesis that the value of the population
mean is 70 against alternative that it is more than 70. Use the 0.025
significance level.
BTL-2
Understanding
12(b).
The following table shows the lifetimes in hours of samples from
three different types of television tables manufactured by a company.
Determine whether there is a difference between the three types at
significance level of 0.01.
Table:
BTL-2
Understanding
14
Sample 1 407 411 409
Sample 2 404 406 408 405 402
Sample 3 410 408 406 408
13.
The following table shows the yields per acre of hour different plants
crops grown on lots treated with three different types of fertilizer.
Determine at the 5% significance level whether there is a difference in
yield per acre.
(i) due to the fertilizers and
(ii) due to the crops
Table:
Crop -I Crop -II Crop -III Crop -IV
Fertilizer A 4.5 6.4 7.2 6.7
Fertilizer B 8.8 7.8 9.6 7.0
Fertilizer C 5.9 6.8 5.7 5.2
BTL-2
Understanding
14.
Time of 6 machine operator (in minute) in making product is given
below. Use paired t-test for training effectiveness.
Machine operator 1 2 3 4 5 6
Before training 12 23 4 5 16 17
After training 2 3 10 8 12 6
BTL -3 Applying
PART C
1(a).
What are non-parametric tests? Point out their advantages and
disadvantages?
BTL -6 Creating
1(b).
The success of a sales engineer in adopting the proven sales technique
was found to be 12 out of 30 occasions. Hence he tried a novel
technique and achieved success at a rate of 23 out of 40 occasions.
Check whether the novel technique is effective at 5% level of
significance.
BTL-2 Understanding
2(a).
The following are the final examination marks of three groups of
students who were taught computer by three difference methods.
First method: 94 88 91 74 87 97
Second method: 85 82 79 84 61 72 80
Third method: 89 67 72 76 69
BTL -5 Evaluating
2(b).
A consumer product manufacturing company was selling one of its
leading products through a large number of retail shops. Before a
heavy advertisement campaign, the average sale per week per shop
was 140 dozens. After the campaign, a sample of 26 shops was taken
and the mean sales improved to 147 dozens with a standard deviation
of 16. Check the effectiveness of the advertisement campaign at 5%
level of significance
BTL-2
Understanding
3.
Discuss the test procedure to test hypothesized population proportion
using single sample proportion.
BTL-1 Understanding
15
4.
(i)Write the application testing of hypothesis in statistics. (ii)What is
t-test? When should we apply a t-test?
BTL -3 Applying
UNIT IV: NON-PARAMETRIC TESTS
SYLLABUS: Chi-square test for single sample standard deviation. Chi-square tests for independence ofattributes and
goodness of fit. Sign test for paired data. Rank sum test. Kolmogorov-Smirnov ? test for goodness of fit, comparing two
populations. Mann ? Whitney U test and Kruskal Wallis test. One sample run test.
PART-A
Q.
No.
Question
Bloom?s
Taxonomy
Level
Domain
1. Define Rank Correlation test. BTL-1 Remembering
2. Write the formula in chi square test and any two uses. BTL-1 Remembering
3. Define Rank-Sum test. BTL-1 Remembering
4. Mention the advantages of Nonparametric Tests. BTL-1 Remembering
5. What is the other name or non-parametric test? Why? BTL-6 Creating
6. When are non parametric tests used? BTL-1 Remembering
7. What is the null hypothesis framed in Mann-Whitney test? BTL-6 Creating
8.
Write down the working rule for Mann-Whitney U-test and Kruskal-
Wallis test.
BTL-1 Remembering
9. Explain sign test. BTL-4 Analyzing
10. Define one sample run test? BTL-1 Remembering
11. When is Krushkal-Wallis test used? BTL-1 Remembering
12. Distinguish between Mann-Whitney U-test and Krushkal-Wallis test. BTL-2 Understanding
13. Write the contingency 2*2 table for
test. BTL-5 Evaluating
14.
Write down the formula to calculate rank correlation coefficient
(including tie values).
BTL-1 Remembering
15.
Two HR managers (A and B) ranked five candidates for a new
position. Their rankings of the candidates are show below:
Candidate Rank by A Rank by B
Nancy 2 1
Mary 1 3
John 3 4
Lynda 5 5
Steve 4 2
Compute the Spearman rank correlation.
BTL-6 Creating
16. Define rank correlation co-efficient. BTL-1 Remembering
17.
The following are the ranks obtained by 10 students in Statistics and
Mathematics. Find out the rank correlation coefficient.
Statistics 1 2 3 4 5 6 7
Mathematics 2 5 1 6 7 4 3
BTL-4 Analyzing
18. Explain Kolmogorov-Smirnov Test for one sample problem. BTL-4 Analyzing
19. What adjustment is to be done for tie values to find rank correlation. BTL-6 Creating
20. Mention the properties of linear coefficient of correlation. BTL-1 Remembering
PART -B
1(a).
The scores of a written examination of 24 students, who were trained
by using three different methods, are given below.
Video cassette A 74 88 82 93 55 70 65
BTL-3 Applying
16
Audio cassette B 78 80 65 57 89 85 78 70
Class Room C 68 83 50 91 84 77 94 81 92
Use Krushkal-Wallis test at ? = 5% level of significance, whether the
three methods of training yield the same results.
1(b). Explain Rank sum tests and its applications
2(a).
The production volume of units assembled by three different
operators during 9 shifts is summarized below. Check whether there
is significant difference between the production volumes of units
assembled by the three operators using Krushkal-Wallis test at a
significant level of 0.05.
Operator I 29 34 34 20 32 45 42 24 35
Operator II 30 21 23 25 44 37 34 19 38
Operator III 26 36 41 48 27 39 28 46 15
BTL-3
Applying
2(b).
Two faculty members ranked 12 candidates for scholarships.
Calculate the spearman rank-correlation coefficient and test it for
significance. Use 0.02level of significance.
Candidate Rank by Professor A Rank by Professor B
1 6 5
2 10 11
3 2 6
4 1 3
5 5 4
6 11 12
7 4 2
8 3 1
9 7 7
10 12 10
11 9 8
12 8 9
BTL-3
Applying
3(a).
In a study of sedimentary rocks, the following data were obtained
from samples of 32 grains from two kinds of sand :
Apply Mann-Whitney U test with suitable null and alternative
hypotheses.
Sand I 63 17 35 49 18 43 12 20 47
? 136 51 45 84 32 40 44 25
Sand II 113 54 96 26 39 88 92 53 101
? 48 89 107 111 58 62
BTL -3 Applying
3(b).
The Molisa?s shop has 3 mall locations. She keeps a daily record for
each locations of the number of the customers who actually make a
purchase. A sample of these data follows. Using Kruskal- Wallis test
can you say that at 5% level of significance that her stores have the
same number of customers who buy.
Eastowin 99 64 101 85 79 88 97 95 90 100
Craborchard 83 102 125 61 91 96 94 89 93 75
Fair forest 89 98 56 105 87 90 87 101 76 89
BTL -3 Applying
4(a)
The following are the prices in Rs. per kg of a commodity from 2
random samples of shops from 2 cities A&B.
BTL -3 Applying
17
City A 2.7 3.8 4.3 3.2 4.7 3.6 3.8 4.1
2.7 2.8 3.2 3.4 3.8 4.4 4.9 3.9 4.7
City B 3.7 5.3 4.7 3.6 4.7 4.8 6.0 4.8 4.9
3.8 3.9 4.8 5.2 6.1 3.6 3.8
Apply the run test to examine whether the distribution of prices of
commodity in the two cities is the same.
4(b)
Distinguish Nonparametric methods over parametric methods.
BTL -2 Understanding
5(a)
From a poll of 800 television viewers, the following data have been
accumulated as to,their levels of education and their performance of
television stations. We are interested in determining if the selection
of Tv station is independent of the level of education.
Education Level
High school Bachelor graduate Total
Public Broadcasting 50 150 80 280
Commercial
stations
150 250 120 520
Total 200 400 200 800
(i) State the null and alternative hypothesis.
(ii) Show the contingency table of the expected
frequencies
BTL -3 Applying
5(b)
From the question 5(a)
(i)Compute the test static
(ii)The null hypothesis to be tested at 95% confidence Determine the
critical value for this test
BTL-6
Creating
6(a)
Apply Mann-Whitney U test to determine if there is a significant
difference in the age distribution of the two groups
Day :26 18 25 27 19 30 34 21 33 31
Evening :32 24 23 30 40 41 42 39 45 35
BTL -3
Applying
6(b)
Apply the K-S test to check that the observed frequencies match with
the expected frequencies which are obtained from Normal
distribution. (Given at n=5).
Test Score 51-60 61-70 71-80 81-90 91-100
Observed Frequency
30 100 440 500 130
Expected Frequency 40 170 500 390 100
BTL -5 Evaluating
7
A research company has designed three different systems to clean up
oil spills. The following table contains the results, measures by how
much surface area (in square meters) is cleaned in one hour. The data
were found by testing each method in several trials. Are there
systems equally effective? Use the 5% level of significance.
Sample A 55 60 63 56 59 55
Sample B 57 53 64 49 62
Sample C 66 52 61 57
BTL -1 Remembering
8(a)
Suppose it is desired to check whether pinholes in electrolytic tin
plate are distributed uniformly across a plated coil on the basis of the
following distances (in inches) of 10 pinholes from one edge of a
BTL -1 Remembering
18
long strip of tin plate 320 inches wide.
4.8 14.8 28.2 23.1 4.4 28.7 19.5 2.4 25.0 6.2
Use Kolmogorov Smirnov test to test the null hypothesis.
8(b) Explain Mann- WhitneyU test with an example BTL-4 Analyzing
9.
Ten competitors in a beauty contest are ranked by 3 judges in the
following order.
A : 1 6 5 3 10 2 4 9 7 8
B : 3 5 8 4 7 10 2 1 6 9
C : 6 4 9 8 1 2 3 10 5 7
Find out which pair of Judges has awarded the ranks to the nearest
common taste of beauty.
BTL -3 Applying
10(a).
Test the association of Age and preference of colour of Toy from the
following data
Age/Colour Below 5 6-10 Above 10 years
Pink 60 40 5
Purple 30 30 30
Red 80 10 10
BTL -4 Analyzing
10(b).
Melisa?s Boutique has three mall locations. Melisa keeps a dairy
record for each location of number of customers who actually make a
purchase. A sample of those data follows. Using the kruskal-wallis
test, can you say at the 0.05 level of significance that her stores have
the same number of customers who busy?
DSF Mall 99 64 101 85 79 88 97 95 90 100
Forest Mall 83 102 125 61 91 96 94 89 98 75
Big-Ben Mall 89 98 56 105 87 90 87 101 76 89
BTL -3 Applying
11(a).
A brand manager is concerned that her brand?s share may he
unevenly distributes through the country. In a survey in which the
country was divided into four geographic regions, a random
sampling of 100 consumers in each region was surveyed, with the
following results:
NE NW SE SW TOTAL
Purchase the brand 40 55 45 50 190
Do not purchase 60 45 55 50 210
Total 100 100 100 100 400
(i) Develop a table of observed and expected frequencies for
this problem.
(ii) Calculate the sample
value.
BTL -6 Creating
11(b).
From the question 11(a)
(i)State the null and alternative hypothesis.
(ii)At test whether brand share is the same across the four
regions
BTL -2 Understanding
12(a).
In 30 tosses of a coin, the following sequence of head and tails is
obtained HTTHTHHHTHHTTHTHTHHTHTTHTHHTHT
(i) Determine the number of runs
BTL -2 Understanding
12(b).
From the question 12(a ) Test at 0.10 level of significance, whether
the sequence is random
BTL -3 Applying
13. An experiment designed to compare three preventative methods BTL -3 Applying
19
against corrosion yielded the following maximum depths of pits ( in
thousandths of an inch) in pieces of wire subjected to the respective
treatments:
Method A: 77 54 67 74 71 66
Method B: 60 41 59 65 62 64 52
Method C: 49 52 69 47 56
Use the Kruskal-Wallis test at the 5% level of significance to test the
null hypothesis that the three samples come from identical
populations.
14.
The number of defects in printed circuit boards in hypothesized to
follow a poisson distribution. A random sample of 60 printed boards
have been collected and the number of defects observed. The
following table gives the results.
Table:
No. of defects Observed Frequency
0 32
1 15
2 9
3 4
Does the assumption of a poisson distribution seem appropriate as a
probability model for this process?
BTL -4
Analyzing
PART C
1. Explain the Mann-Whitney test procedure with appropriate examples BTL-1 Remembering
2.
Write the application of Non parametric test and Sign test in
statictics.
BTL-1 Remembering
3(a).
The sales records of two branches of a department store over the last
12 months are shown below.(sales figures are in thousands of
dollars). We want to use the Mann-Whitney-Wilcoxon test to
determine if there is a significant difference in the sales of the two
branches.
Month Branch A Branch B
1 257 210
2 280 230
3 200 250
4 250 260
5 284 275
6 295 300
7 297 320
8 265 290
9 330 310
10 350 325
11 340 329
12 372 335
(i) Compute the sum of the ranks for branch A
(ii) Compute the mean ?T
BTL-4 Analyzing
3(b).
From the question 3(a)
(i)Compute ?T
BTL -6 Creating
20
(ii)Use and test to determine if there is a significant
difference in the population of the sales of the two branches
4(a).
Independent random samples of ten day students and ten evening
students at a university showed the following age distributions. We
want to use the Mann-Whitney-Wilcoxon test to determine if there is
a significant different in the age distribution of the two groups.
Day Evening
26 32
18 24
25 23
27 30
19 40
30 41
34 42
21 39
33 45
31 35
(i) Compute the sum of the ranks for the day students.
(ii) Compute the mean ?
BTL-2 Understanding
4(b).
From the question 4(a)
(i)Compute ?
(ii)Use and test for any significant difference in the age
distribution of the two populations
BTL -4
Analyzing
UNIT ? V CORRELATION AND REGRESSION
SYLLABUS: Correlation ? Coefficient of Determination ? Rank Correlation ? Regression ? Estimation of Regression line
? Method of Least Squares ? Standard Error of estimate.
PART ? A
Q.No. Question
Bloom?s
Taxonomy
Level
Domain
1. Define regression coefficient?. BTL -1 Remembering
2. Define Linear Relationship of Correlation. BTL -6 Creating
3. Write the Properties of Correlation Coefficient? BTL -1 Remembering
4. What is the angle between the regression lines? BTL -1 Remembering
5. When is linear regression used? BTL -1 Remembering
6. Distinguish between correlation and regression BTL -2 Understanding
7. What is regression analysis? BTL -6 Creating
8. What do you interpret if the r = 0 , r = + 1 and r = -1? BTL -1 Remembering
9. Specify the range of correlation. BTL -6 Creating
10. Briefly explain how a scatter diagram benefits the researcher? BTL -4 Analyzing
11. Define correlation coefficient between two variables. BTL -1 Remembering
12. What is a scatter diagram and write its benefits? BTL -6 Creating
21
13.
If the equations of the regression lines are x+2y=5 and 2x+3y=8, find
the correlation coefficient between x and y.
BTL -3 Applying
14. Find the mean values of regression lines are 2y-x =50 and 3y-2x =10. BTL -1 Remembering
15. Write the correlation coefficient in terms of regression coefficients. BTL -6 Creating
16. Write the Equations of Regression lines. BTL -1 Remembering
17.
Explain the difference between the coefficient of determination and
the coefficient of correlation.
BTL -1 Remembering
18. What are the various methods in correlation? BTL -1 Remembering
19.
If the equations of the regression lines are x+2y=5 and 2x+3y=8, find
the correlation coefficient between x and y? Use the equations to find
the mean of X and Y. If the variance of X is 12, calculate the variance
of Y?
BTL -1 Remembering
20. What is positive and negative correlation? BTL -1 Remembering
PART-B
1(a).
The following data pertains of X = Revenue (in ?000 of rupees) generated at
a Corporate Hospital and Y = Number of Patients (in ?00) arrived for the last
ten years.
X 86 95 75 85 90 98 112 74 100 110
Y 21 24 18 24 22 30 27 18 25 28
Find the Karl Pearson?s coefficient of correlation and give your comment.
BTL -4
Analyzing
1(b).
Obtain the two regression lines:
X 45 48 50 55 65 70 75 72 80 85
y 25 30 35 30 40 50 45 55 60 65
BTL-5 Evaluating
2(a).
The revenue generated at a unit and is given below. Fit the trend
line using least squares method and estimate the revenue for the year 2013.
Year 2005 2006 2007 2008 2009 2010 2011 2012
Revenue
(Rs. 00)
268 209 390 290 280 450 350 455
BTL -2 Understanding
2(b).
The following table presents the results of a survey of 8 randomly selected
families:
Annual income (in 000 Rs.):
8 12 9 24 13 37 10 16
Percent allocation for investment
36 25 33 15 28 19 20 22
Find the Karl Pearson?s correlation and spearman?s rank correlation methods
for the above data.
BTL -4
Analyzing
3(a).
Given below are the figures of production (in thousand quintals) of a sugar
factory.
Year 1992 1993 1994 1995 1996 1997 1998
Production 75 80 95 85 95 100 105
Fit a straight line trend by the least squares method and tabulate the trend
values.
BTL -3 Applying
3(b).
Promotional expenses and sales data for an equipment manufacturer are as
follows. Calculate the correlation coefficient and comment.
BTL -3 Applying
22
Promotional expenses in Lakhs
7 10 9 4 11 5 3
Sales in units 12 14 13 5 15 7 4
4(a).
Data on rainfall and crop production for the past seven years are as follows:
Rainfall in inches 20 22 24 26 28 30 32
Crop production 30 35 40 50 60 60 55
Find the correlation coefficient and comment on the relationship.
BTL -3 Applying
4(b).
The percentage of students getting dream placements in campus selection in
a leading technical during the past five years are as follows:
Year 2008 2009 2010 2011 2012
Percentage 7.3 8.7 10.2 7.6 7.4
Find the linear equation that describes the data. Also calculate the percentage
of trend
BTL -4
Analyzing
5(a).
Let
be two independent variables with mean 5 and 10 and S.D 2
and 3 respectively. Obtain
where
BTL -1 Remembering
5(b).
The following data represent the number of flash drivers sold per day at a
local computer shop and their prices.
Price(x) Units sold(y)
34 3
36 4
32 6
35 5
30 9
38 2
40 1
(i) Develop a least squares regression line and explain what the slope of the line
indicates. Compute the coefficient of determination and comment on the
strength of relationship between x and y. Compute the sample correlation
coefficient between the prices and the number of flash drives sold.
(ii) Use to test the relationship between x and Y.
BTL -6 Creating
6(a).
What are the assumptions made by the regression model in estimating the
parameters and in significance testing?
BTL -6 Creating
6(b).
The equations of two variables X and Y as follows 3X+2Y-26 =0, 6X+Y-
31=0 Find the means, regression coefficient & coefficient of correlation.
BTL -4 Analyzing
7.
Promotional expenses and sales data for an equipment manufacturer are as
follows. Calculate the correlation coefficient and comment
Promotional expenses in Lakhs 7 10 9 4 11 5 3
Sales in Units 12 14 13 5 15 7 4
BTL -3 Applying
8(a).
A gas company has supplied 18,20,21,25 and 26 billion cubic feet f gas,
respectively, for the years 2004 to 2008.
(i) Find the estimating equation that best describes these data.
(ii) Calculate the percentage of trend.
BTL -3 Applying
8(b).
From the question 8(a)
(i)Calculate the relative cyclical residuals
(ii)Find the year in which the fluctuation is maximum
BTL-5 Evaluating
9.
Given that
? ? ? ? ?
? ? ? ? ? 3467. XY and 5506, Y 220, Y 2288, X 130, X
2 2
BTL -6 Creating
FirstRanker.com - FirstRanker's Choice
1
(An
Ka ttankulathur ?
DEPARTMENT OF MATHEMATICS
QUESTION BANK
I SEMESTER
1918108 ? STATISTICS FOR MANAGEMENT
Regulation ? 2019
Academic Year 2019 - 2020
Prepared by
Ms. B. Vasuki, Assistant Professor/Mathematics
Ms.B.Elakkiavani, Assistant Professor/Mathematics
2
(An
? .
DEPARTMENT OF MATHEMATICS
QUESTION BANK
SUBJECT : 1918108 ? STATISTICS FOR MANAGEMENT
SEM / YEAR : I Semester / I Year
UNIT I - INTRODUCTION
SYLLABUS: Basic definitions and rules for probability, conditional probability independence of events, Baye?s
theorem, and random variables, Probability distributions: Binomial, Poisson, Uniform and Normal distributions.
PART- A
S.NO QUESTIONS
BT Level
COMPETENCE
PART ? A
1. Define Statistics. BTL -6 Creating
2. What is the addition and multiplication theorem on probability. BTL -1 Remembering
3. Distinguish between a priori and posterior probability?. BTL -6 Creating
4.
The price of the selected stock over a five day period shown as 170, 110,
130, 170 and 160. Compute mean , median and mode.
BTL -6 Creating
5.
A car travels 25 miles at 25 mph, 25 miles at 50 mph and 25 miles at 75
mph. Find the harmonic of three velocities?
BTL -4 Analyse
6.
A ball is drawn at random from a box containg 6 red balls, 4 white balls
and 5 blue balls. Find the probability that the ball drawn is not red.
BTL -4 Analyse
7.
Find the median and mode for the weights (kgs) of 15 persons given as
68, 85, 70, 65, 71, 67, 65, 55, 80, 62, 65, 64, 70, 60, 56.
BTL -3 Applying
8. Name few measures of dispersion. BTL -1 Remembering
9. write the common measures of central tendency? BTL -1 Remembering
10. Define continuous and discrete variables examples. BTL -1 Remembering
11.
Let X be the lifetime in years of a mechanical part. Assume that X has
the cdf F(x) = 1- e
-x
, x ? 0. Find P[1< X ? 3].
BTL -1 Remembering
12. Define independent events. BTL -1 Remembering
13. State the theorem of total probability BTL -1 Remembering
14. What is the use of Baye?s theorem? BTL -6 Creating
15. Mention the properties of a discrete probability distribution. BTL -1 Remembering
16. Define a Poisson distribution and mention its mean and variance. BTL -1 Remembering
17. If the mean and variance of a binomial distribution are respectively 6 BTL -3 Applying
3
and 2.4, find P(x=2).
18.
If x is a Poisson distribution such that P(x=1)=4P(x=2). Find its
mean and variance.
BTL -3 Applying
19.
Suppose that X has a Poisson distribution with parameter ? = 2.
Compute P[X ? 1].
BTL -1 Remembering
20. Define mutually exclusive events. BTL -1 Remembering
PART-B
1(a).
Calculate the mean and standard deviation for the following table
giving the age distribution of 542 members.
Age
20-30 30-40 40-50 50-60 60-70 70-80 80-90
No 3 61 132 153 140 51 2
BTL-2 Understanding
1(b).
Find the geometric mean for the following data:
Group
2-4 4-6 6-8 8-10
Frequency 200 400 300 100
BTL-2
Understanding
2(a).
Find the mean, median and modal ages of married women at first
child birth
Age at the
birth of
first child
13
14
15
16
17
18
19
20
21
22
23
24
25
No of
married
women
37
162
343
390
256
433
161
355
65
85
49
46
40
BTL -6 Creating
2(b).
If A and B are independent event with P(A)=2/5, and P(B)=3/5,
find P(A ?B). Let S= {1,2,3,4,5,6} if A = {2,4,6} then find the
probability of A complement.
BTL -3 Applying
3(a).
Given: The probabilities of three events A, B and C occurring are
P(A) = 0.35, P(B) = 0.45 and P(C) = 0.2. Assuming that A, B, or
C has occurred, the probabilities of another event X occurring are
P(X/A) = 0.8, P(X/B) = 0.65 and P(X/C) = 0.3. Find P(A/X),
P(B/X) and P(C/X).
BTL -6 Creating
3(b).
4 cards are drawn from a well shuffled pack of cards. Find the
probability that
(i) All the four are queens
(ii) There is one card from each suit.
(iii) Two cards are diamonds and two are spades
All the four cards are hearts and one of them is jack
BTL -6 Creating
4(a).
Three machines all turn out non ferrous castings. Machine A
produces 1% defective and Machine B- 2% and machine C ? 5%.
Each machine produces 1/3 of the output. An inspector examines
a single casting, which he determines as non defective. Estimate
the probabilities of its having been produced by each machine.
BTL -6 Creating
4(b).
If the random variable X takes values 1, 2, 3, 4 such that
2P(X = 1) = 3P(X = 2) = P( X=3) = 5P(X = 4), find the
probability distribution and cumulative distribution of X.
BTL-2 Understanding
5(a).
Two dice are thrown together once. Find the probabilities for
BTL -3 Applying
4
getting the sum of the two numbers (i) equal to 5, (ii) multiple of
3, (iii) divisible by 4.
5(b).
Given ? = 4.2, for a poisson distribution. Find (a) P(X ? 2) (b)
P(X ? 5) (c) P(X = 8).
BTL -6 Creating
6(a).
An urn contains 5 balls. Two balls are drawn and found to be
white. What is the probability that all the balls are white?
BTL-1 Remembering
6(b).
The contents of urns I, II, III are as follows:
1 white, 2 black and 3 red balls;
2 white, 1 black and 1 red balls;
4 white, 5 black and 3 red balls;
One urn is chosen at random and two balls drawn. They happen to
be white and red. What is the probability that they come from
urns I, II, III?
BTL -3 Applying
7(a).
In 1989, there were three candidates for the position of principal
Mr. Chatterji, Mr. Ayangar and Dr. Singh. Whose chances of
getting the appointment are in the proportion 4:2:3 respectively.
The probability that Mr. Chatterji is selected, would introduce co-
education in the is 0.3. The probabilities of Mr. Ayangar
and Dr. Singh doing the same are respectively 0.5 and .08. What
is the probability that there was co-education in the in
1990?
BTL -3
Applying
7(b).
Find the probability that atmost 5 defective bolts will be found in
a box of 200 bolts, if it is known that 2% of such bolts are
expected to be defective. (e
-4
= 0.0183)
BTL -6 Creating
8(a).
A coin is tossed 6 times what is the probability of obtaining (a) 4
heads (b) 5 heads (c) 6 heads (d) getting 4 or more heads.
BTL -3 Applying
8(b).
In a bolt factory machines A, B, C manufacture respectively 25%,
35% and 40% of the total of their output 5, 4, 2 percent are
defective bolts. If A bolt is drawn at random from the product and
is found to be defective, what are the probabilities that is was
manufactured by machines A, B and C?
BTL -6 Creating
9(a).
In a test of 2000 electric blubs it was found that the life of a
particular make was normally distributed with an average life of
2040 hours and S. D. of 60 hours. Estimate the number of blubs
likely to burn for
(1) More than 2150 hours
(2) Less than 1950 hours
(3) More than 1920 hours but less than 2160 hours.
BTL -3 Applying
9(b).
The latest nationwide political poll indicates that for Americans
who are randomly selected, the probability that they are
conservative is 0.55, the probability that they are liberal is 0.30
and the probability that they are middle of the road is 0.15.
Assuming these probabilities are accurate, answer the following
BTL -4 Analyzing
5
questions from a randomly chosen group of 10 Americans
(a) What the probability that 4 are liberal?
(b) What the probability that none are conservative
(c) What the probability that two are middle of the road
(d) What the probability that a least 8 are liberal
10.
If X follows a normal distribution with mean 12 and variance 16
cm, find the probabilities for (i) X ? 20 (ii) X ? 20, and (iii) 0 ? X
? 12.
BTL -3 Applying
11.
A discerete random variable X has the probability function given
below:
Value of X=x: 0 1 2 3 4 5 6 7
P(X=x) : 0 k 2k 2k 3k k
2
2k
2
7k
2
+k
Find (1) The value of k
(2) P(1.5 < X < 4.5 / X > 2)
(3) P(X < 6), P(X ? 5), P( 0 < X < 4)
(4) The distribution of X.
BTL -3 Applying
12.
X is a normal variable with mean 30 and standard deviation of 5.
Find (i) P[26 ? X ? 40] (ii) P [X?45] (iii) P [ ?X - 30 ?> 5] use
normal distribution tables
BTL -4 Analyzing
13.
In an intelligence test administered on 1000 students, the average
was 42 and standard deviation 24, find (i) the number of students
exceeding a score 50. (ii) the number of students lying between
30 and 54(iii) the value of score exceeded by top 100 students.
BTL -4 Analyzing
14(a).
The probability that an entering student will graduate is 0.4
Determine the probability that out of 5 students atleast one will
graduate.
BTL-5
Evaluating
14(b).
Fit a Poisson Distribution to the following data which gives the
number of doddens in a sample of clover seeds
No 0 1 2 3 4 5 6 7 8
f 56 156 132 92 37 22 4 0 1
.
BTL -4 Analyzing
PART-C
1(a).
A disciplinary committee is formed from the staff of XYZ
Company which has three departments Marketing, Finance and
Production of the 10,5,20 members respectively. All departments
have two female staff each. A department is selected at random
and from which two matters are selected for the committee,
What is the probability that both the team members are female?
BTL-6 Creating
6
1(b).
In a bolt factory machines A, B, C manufacture respectively 25,
35 and 40 percent of the total. Of their output 5, 4 and 2 percent
are defective bolts respectively. A bolt is drawn at random from
the product and is found o be defective. What are the probabilities
that it was manufactured by machines A, B or C?
BTL-2
Understanding
2(a). State Bayes theorem and brief about its applications. BTL-2 Understanding
2(b).
Out of 800 families with 4 children each, how many families
would be expected to have (i) 2 boys and 2 girls (ii) at least 1 boy
(iii) at most 2 girls (iv) children of both sexes? Assume equal
probabilities for boys and girls.
BTL-1 Remembering
3. Describe the classifications of probability ? BTL-1 Remembering
4. What are the applications of Normal distribution in statistics? BTL-6 Creating
UNIT ?II- SAMPLING DISTRIBUTION & ESTIMATION.
SYLLABUS: Introduction to sampling distributions, sampling distribution of mean and proportion, application of central
limit theorem, sampling techniques. Estimation: Point and Interval estimates for population parameters of large sample and
small samples, determining the sample size.
PART - A
S.N
O
QUESTIONS
BT Level
COMPETENCE
1. Define Sampling distribution of proportion. BTL -1 Remembering
2. Define Probable standard error. BTL -1 Remembering
3. Define standard error and mention its importance BTL -1 Remembering
4. Define central limit theorem BTL -1 Remembering
5.
What is the role of central limit theorem in estimation and testing
problems
BTL -6 Creating
6. Define stratified sampling technique BTL -1 Remembering
7. Briefly describe the significance level. BTL -1 Remembering
8. Distinguish between parameter and statistic. BTL -2 Understanding
9. Define estimator, estimate and estimation. BTL -1 Remembering
10. Distinguish between point estimation and interval estimation BTL -2 Understanding
11. Mention the properties of a good estimator. BTL -1 Remembering
12. Define confidence coefficient. BTL -1 Remembering
13. What is the level of significance in testing of hypothesis BTL -6 Creating
14. Define confidence limits for a parameter BTL -1 Remembering
15.
State the conditions under which a binomial distribution becomes a
normal distribution
BTL -4 Analyzing
16.
If the random sample comes from a normal population, what can
be said about the sampling distribution of the mean.
BTL -5 Evaluating
17.
An automobile repair shop has taken a random sample of 40
services that the average service time on an automobile is 130
minutes with a standard deviation of 26 minutes. Compute the
standard error of the mean.
BTL -6 Creating
7
18. What is a random number? How it is useful in sampling? BTL -6 Creating
19.
A population has the numbers: 12, 8, 10, 30, 12, 16, 40, 5, 16, 24,
22, 31, 30, 16, 15. Draw a systematic sample of size 5. Find out its
mean.
BTL -3 Applying
20. How large sample is useful in estimation and testing BTL -4 Analyzing
PART -B
1(a).
A random sample of 700 units from a large consignment showed
that 200 were damaged. Find (i) 95% (ii) 99% confidence limits
for the proportion of damaged units in the consignment.
BTL -3 Applying
1(b).
A random sample of size 9 is obtained from a Normal population
with mean 25 and if the variance 100 find the probability that the
sample mean exceeds 31.2.
BTL -4 Analyzing
2(a).
In a normally distributed population, average income per
household is Rs.20,000 with a standard deviation of Rs. 1,600.
Find the probability that the sample mean will be between
Rs.19,600 and Rs.20,200 in a survey of a random sample of 100
households.
BTL -6 Creating
2(b).
A university wants to determine the percentage of students who
would accept proposed fees hike for improving facilities. The
university wants to be 90% confident that the percentage is
within2% of the true value. Find the sample size to achieve the
accuracy regardless of the true percentage assuming the percentage
of students accepting the increase in tuition fees to be 0.5.
BTL -6 Creating
3(a).
A bank has kept records of the checking balances of its customers
and determined that the average daily balances of its customers is
Rs.300 with a standard deviation of Rs. 48. A random sample of
144 checking accounts is selected.
(i) What is the probability that the sample mean will be more
than Rs. 306.60?
(ii) What is the probability that the sample mean will be less
than Rs. 308?
BTL -6 Creating
3(b).
From the question 3(a)
(i) What is probability that the sample mean will between Rs.
302 and Rs. 308?
(ii) What is probability that the sample mean will be atleast
Rs. 296?
BTL -6 Creating
4(a).
Explain Stratified sampling technique and discuss how it is better
than simple random sampling in a particular situation.
BTL -4
Analyzing
4(b). Discuss the standard error of proportion BTL-2 Understanding
5.
Explain the methods of drawing simple random sample from a
finite population.
BTL -4 Analyzing
8
6(a).
In a sample of 1000 citizens of India, 540 are wheat eaters and the
rest are rice eaters. Can we assume that both rice and wheat
equally popular in India at 1 % level of significance?
BTL-5
Evaluating
6(b).
A simple random sample of 144 items resulted in a sample mean
of 1257.85 and standard deviation of 480. Develop a 95%
confidence interval for the population mean
BTL -6
Creating
7(a).
A car dealer wants to estimate the proportion of customers who
still own the cars they purchased 5 years earlier. A random sample
of 500 customers selected from the dealer?s records indicate that
315 customers still own cars that they were purchased 5 years
earlier. Set up 95% confidence interval estimation of the
population proportion of all the customers who still own the cars 5
years after they were purchased.
BTL-2
Understanding
7(b).
A movie maker sampled 55 fans who viewed his master piece
movie and asked them whether they had planned to see it again.
Only 10 of them believed that the movie was worthy of a second
look. Find the standard error of the population of fans who will
view the film a second time. Construct a 90% confidence interval
for this population.
BTL -5 Evaluating
8(a).
From a population of size 600, a sample of 60 individuals revealed
mean and standard deviation as 6.2 and 1.45 respectively. (i) Find
the estimated standard error (ii) Construct 96% confidence
interval for the mean.
BTL -3 Applying
8(b).
The age of employees in a company follows normal distribution
with its mean and variance as 40 years and 121 years respectively.
If a random sample of 36 employees is taken from a finite normal
population of size 1000, what is the probability that the sample
mean is
(i) less than 45
(ii) greater than 42 and
(iii) between 40 and 42?
BTL -6
Creating
9(a).
A firm wishes to estimate with an error of not more than 0.03 and
a level of confidence of 98%, the proportion of consumers that
prefer its brand of household detergent. Sales report indicate the
about 0.20 of all consumers prefer the firm?s brand. What is the
requisite sample size?
BTL -5 Evaluating
9(b).
A random sample of 700 units from a large consignment should
that 200 were damaged.
Find (i) 95%
(ii) 99% confidence limits for the proportion of damaged
units in the consignment
BTL -3 Applying
10(a).
From a population of 500 items with a mean of 100 gms and
standard deviation of 12.5 gms, 65 items were chosen. (i) What is
the standard error? (ii) Find P(99.5 < X < 101.5).
BTL -6 Creating
10(b).
A non-normal distribution representing the number of trips
BTL -6 Creating
9
performed by lorries per week in a coal field has a mean of 100
trips and variance of 121 trips. A random sample of 36 lorries is
taken from the non-normal population. What is the probability that
the sample mean is
(i) greater than 105
(ii) less than 102
(iii) between 101 and 103 trips?
11.
Test the significance of the difference between the means of the
sample from the following data
Size of sample Mean SD
Sample A 100 61 4
Sample B 200 63 6
BTL -4 Analyzing
12(a).
A cigarete manufacturing firm claims that its brand. A outsells
brand B by 8%. If it is found that 42 out of a sample of 200
smokers prefer brand a and 18 out of another sample of 100
smokers prefer brand B, test whether the 8% difference is a valid
claim(use 5% level of significance).
BTL -4
Analyzing
12(b).
In an automotive safety test conducted by the North Carolina
Highway Safety Research center, the average tyre pressure in a
sample of 62 tyres was found to be 24 pounds per square inch, and
the standard deviation was 2.1 pounds per square inch.
(i) What is the estimated population standard deviation for this
population
(ii) Calculate the estimated standard error of the mean
(iii) Construct a 95% confidence interval for the population mean.
BTL -3 Applying
13(a).
The manager of a shop selling beverages wants to estimate the
actual amount of beverages in one litre bottles from a nationally
known manufacturer. As per manufacturer?s specifications, the
standard deviation of the volume of the beverage is 0.02 litre. The
average amount of beverage per 1 litre bottle is found to be 0.995
litre on checking 50 bottles. Setup 99% confidence interval
estimate of the true population average amount of beverage in a 1
liter bottle. Check whether the manufacturer is genuine in filling
the beverage.
BTL -6
Creating
13(b).
In a batch chemical process used for etching printed circuit boards,
two different catalysts are being compared to determine whether
they require different emersion times for removal of identical
quantities of photo resist material. Twelve batch were run with
catalyst 1, resulting in a sample mean emersion time of 24.6
minutes and sample standard deviation of 0.85 minutes. Fifteen
batches were run with catalyst 2, resulting in a mean emersion time
of 22.1 minutes and a standard deviation of 0.98 minutes. Find a
95% confidence interval on the difference in means, assuming that
2
2
2
1
? ? ? .
BTL -3 Applying
10
14.
In a random sample of 75 axle shafts. 12 have a surface finish that
is rougher than the specifications will allow. Suppose that a
modification is made in the surface finishing process and
subsequently a second random sample of 85 axle shafts is
obtained. The number of defective shafts in this second sample is
10. Obtain an approximate 95% confidence interval on the
difference in the proportions of defectives produced under the two
processes
BTL -5 Evaluating
PART-C
1.
In a sample of 25 observations from a Normal distribution with
mean 98.6 and standard deviation 17.2.
(i)What is P(92<102)
(ii)Find the corresponding probability given a sample of 36.
BTL -6 Creating
2.
Mary, an auditor for a large credit card company, knows that, on
average, the monthly balance of any customer is Rs.112, and the
standard deviation is Rs.56. If Mary audits 50 randomly selected
accounts, What is the probability that the sample average balance
is
(i) Below Rs. 100
(ii)Between Rs.100 and Rs.130
BTL -6 Creating
3(a).
Write the type of sampling methods and the uses of standard error?
BTL -1 Remembering
3(b).
From a population of 540, a sample of 60 individual is taken. From
this sample, the mean is found to 6.2 and the standard deviation
1.368
(i) Find the estimated standard error of the mean.
(ii) Construct a 96 % confidence interval for the mean.
BTL-2 Understanding
4(a).
Explain the properties of good point estimator.
BTL -4 Analyzing
4(b).
What do you mean by interval estimation? Give examples
BTL-6 Creating
UNIT III - TESTS OF HYPOTHESIS- PARAMETRIC TESTS
SYLLABUS: Hypothesis testing: one sample and two sample tests for means and proportions of large samples (z-test),
one sample and two sample tests for means of small samples (t-test), F-test for two sample standard deviations. ANOVA
one and two way.
PART-A
Q.
No.
Question
Bloom?s
Taxonomy
Level
Domain
1. Define Test of Significance. BTL-1 Remembering
2. What are the Type I and Type II errors? BTL-6 Creating
3. What do you mean by one tail test? BTL-6 Creating
4. State the applications of Z-test and t-test. BTL-4 Analyzing
5. Define critical region BTL-1 Remembering
6. Distinguish between one tail and two tail tests BTL-2 Understanding
7. What is the aim of design of experiments? BTL-6 Creating
8. Distinguish between one-way and two-way analysis of variance. BTL-2 Understanding
9. When does the Z-test apply? BTL-1 Remembering
10. Explain SSB , SSW and SSY
and relationship in ANOVA. BTL-4 Analyzing
11
11. Describe any two applications of t-distribution BTL-1 Remembering
12. Write the uses of F-test? BTL-6 Creating
13. Define the level of significance. BTL-1 Remembering
14. Write the properties of t-distribution? BTL-6 Creating
15. What is the role of standard error? BTL-6 Creating
16. Mention any four applications of t-distribution in tests of hypothesis. BTL-1 Remembering
17. Mention any four uses of Chi-square distribution in test of hypothesis. BTL-1 Remembering
18. Define null hypothesis ? Explain. BTL-6 Creating
19.
Estimate the standard error of difference between two proportion if
p
1
=0.10,p
2=
0.133 and n
1
=50,n
2
=75.
BTL-6 Creating
20.
Mention any two assumptions made in analysis of variance
techniques.
BTL-1 Remembering
PART-B
1(a).
A study compares the effect of four 1-month point-of-purchase
promotions on sales. The unit sales for five stores using all four
promotions in different months follow.
Free Sample
78 87 81 89 58
One-pack gift
94 91 87 90 88
Cents off
73 73 78 69 83
76Refund by mail
79 83 78 69 81
(i)Compute the mean unit sales for each promotion and then
determine the grand mean.
(ii)Estimate the population variance using the between column
variance.
BTL-5 Evaluating
1(b).
From the question 1(a)
(i)Estimate the population variance using the within-column variance
computed from the variance within the samples.
(ii)Calculate the F ratio. At the 0.01 level of significance, do the
promotions produce different effects on sales.
BTL-2 Understanding
2(a).
In a low cost Toy production system, the molding machine has been
set with standard of 1% defective. The 80 sample units produced from
this machine shows defective of one unit. Is it necessary to stop the
product for corrective mechanism? Test at 5% level of significance
BTL-5 Evaluating
2(b).
Block Enterprises, a manufacturer of chips for computers. Is in the
process of deciding whether to replace its current semi automated
assembly line with a fully automated assembly line. Block has
gathered some preliminary test data about hourly chip production,
which is summarized in the following table, and it would like to know
whether it should upgrade its assembly line. State (and test at a =0.02)
appropriate hypothesis to help Block decide.
BTL-5 Evaluating
3(a).
Three samples below have been obtained from normal population
with equal variance. Test the hypothesis that the means are equal.
Sample I : 10 12 18 15 16
Sample II : 7 15 10 12 8
Sample III : 12 8 15 16 15
BTL-5 Evaluating
3(b). The I.Q.s of 16 students from one class of an showed a BTL-2 Understanding
12
mean of 107 with a standard deviation of 10, while the I.Q.s of 14
students from another class showed a mean of 112 with a standard
deviation of 8. Check whether there is an appreciable difference
between the I.Q.s of the two groups at (i) 0.01and (ii) 0.05 level of
significance
4(a).
The following is the information obtained from a random sample of 5
observations. Assume the population has a normal distribution.
30 31 27 32 28
To test if the sample was drawn from a normal distribution with mean
less than 30, (i)State the null and alternative hypotheses
(ii)Compute the standard error.
BTL-2 Understanding
4(b).
From the question 4(a)
(i)Determine the test statistic.
(ii)Decide at 10% level whether or not the mean value could be
greater than 30
BTL-2 Understanding
5.
The following data relate to the number of units produced per week by
three methods.
Method 1 : 170 192 190 120
Method 2 : 160 165 170 172
Method 3 : 182 190 170 178 185
Prepare ANOVA table and write your comments
BTL-6 Creating
6(a).
Test if the following samples could have come from two populations
with the same means, assuming the population variances are equal.
Sample I Sample II
Sample size 12 10
Sample Mean 40.5 43.8
Sample variance 2.6 3.2
BTL-5 Evaluating
6(b).
The weights of 10 people of a locality are found to be
70,67,62,68,61,68,70,64,64,66 kilograms. Is it reasonable to believe
that the average weights of the people of locality is greater than 64
kg? Test at 5%level of significance.
BTL-5 Evaluating
7(a).
In Town A, there were 850 birds of which 52% was males, while in
Town A and Town B combined, the proportion of males in a total of
1200 birds was 0.49. Is there any significance difference in the
proportions of male birds in the two Towns?
BTL-2
Understanding
7(b).
IQ test result of randomly selected five employees in an organization
is given below. Test whether minimum requirement of average IQ
level 87 is maintained in that company or not.
Employee code 234 232 121 343 111
IQ test 85 95 90 93 87
BTL-4 Analyzing
8(a).
The weights of 8 persons are found to be 60, 65, 70, 68, 62, 63, 60,
and 66 kgs. The weights of another group of 12 persons are found to
be 70, 60, 58, 56, 50, 48, 52, 56, 52, 50, 54, and 50. Can we conclude
that both samples have come from populations with same variances?
BTL -4 Analyzing
13
8(b).
ATMs must be stocked with enough cash to meet the requirements of
customers over a week, but excess cash results in loss of income as
investment opportunities could not be utilized. In an ATM, the
average transaction per customer in a week is Rs.8000 with a standard
deviation of Rs.1500. If a random sample of 36 customer transactions
is examined and it is observed that the sample mean with drawl is
Rs.8600, check the belief that the true average withdrawal is no longer
Rs.8000. Assume 0.05 level of significance
BTL -3 Applying
9.
Apply ANOVA technique and write your comment regarding the
sales(in Rs. Lakhs)
Area
Representatives
1 2 3 4
A 12 16 20 18
B 15 10 12 16
C 10 08 16 15
BTL -3 Applying
10(a).
A farmer wishes to determine whether there is a difference in yields
between two different varieties of wheat I and II. The following data
shows the production of wheat per unit area using the two varieties.
Can the farmer conclude at significance levels of
(i) 0.05
(ii) 0.01 that a difference exists?
BTL -4 Analyzing
10(b).
Test if the samples could have come from equal population means.
Sample A Sample B
Size 200 400
Mean 154.8 164.3
Variance 15.2 18.2
BTL-5 Evaluating
11(a).
The number of accidents per week in a city are as follows:
12, 8, 20, 2, 14, 10, 15, 6, 9 and 4. Are these frequencies in agreement
with the belief that accident conditions were the same during this 10
weeks period?
BTL -4
Analyzing
11(b).
Two samples are drawn from two normal population. From the
following data, Test whether the two samples have the same variance
5% level of significance.
Sample 1 60 65 69 74 76 82 85 87
Sample 2 61 66 67 85 78 63 85 86 88 91
BTL -3 Applying
12(a).
Given a sample mean of 83, a sample standard deviation of 12.5 and a
sample size of 22, test the hypothesis that the value of the population
mean is 70 against alternative that it is more than 70. Use the 0.025
significance level.
BTL-2
Understanding
12(b).
The following table shows the lifetimes in hours of samples from
three different types of television tables manufactured by a company.
Determine whether there is a difference between the three types at
significance level of 0.01.
Table:
BTL-2
Understanding
14
Sample 1 407 411 409
Sample 2 404 406 408 405 402
Sample 3 410 408 406 408
13.
The following table shows the yields per acre of hour different plants
crops grown on lots treated with three different types of fertilizer.
Determine at the 5% significance level whether there is a difference in
yield per acre.
(i) due to the fertilizers and
(ii) due to the crops
Table:
Crop -I Crop -II Crop -III Crop -IV
Fertilizer A 4.5 6.4 7.2 6.7
Fertilizer B 8.8 7.8 9.6 7.0
Fertilizer C 5.9 6.8 5.7 5.2
BTL-2
Understanding
14.
Time of 6 machine operator (in minute) in making product is given
below. Use paired t-test for training effectiveness.
Machine operator 1 2 3 4 5 6
Before training 12 23 4 5 16 17
After training 2 3 10 8 12 6
BTL -3 Applying
PART C
1(a).
What are non-parametric tests? Point out their advantages and
disadvantages?
BTL -6 Creating
1(b).
The success of a sales engineer in adopting the proven sales technique
was found to be 12 out of 30 occasions. Hence he tried a novel
technique and achieved success at a rate of 23 out of 40 occasions.
Check whether the novel technique is effective at 5% level of
significance.
BTL-2 Understanding
2(a).
The following are the final examination marks of three groups of
students who were taught computer by three difference methods.
First method: 94 88 91 74 87 97
Second method: 85 82 79 84 61 72 80
Third method: 89 67 72 76 69
BTL -5 Evaluating
2(b).
A consumer product manufacturing company was selling one of its
leading products through a large number of retail shops. Before a
heavy advertisement campaign, the average sale per week per shop
was 140 dozens. After the campaign, a sample of 26 shops was taken
and the mean sales improved to 147 dozens with a standard deviation
of 16. Check the effectiveness of the advertisement campaign at 5%
level of significance
BTL-2
Understanding
3.
Discuss the test procedure to test hypothesized population proportion
using single sample proportion.
BTL-1 Understanding
15
4.
(i)Write the application testing of hypothesis in statistics. (ii)What is
t-test? When should we apply a t-test?
BTL -3 Applying
UNIT IV: NON-PARAMETRIC TESTS
SYLLABUS: Chi-square test for single sample standard deviation. Chi-square tests for independence ofattributes and
goodness of fit. Sign test for paired data. Rank sum test. Kolmogorov-Smirnov ? test for goodness of fit, comparing two
populations. Mann ? Whitney U test and Kruskal Wallis test. One sample run test.
PART-A
Q.
No.
Question
Bloom?s
Taxonomy
Level
Domain
1. Define Rank Correlation test. BTL-1 Remembering
2. Write the formula in chi square test and any two uses. BTL-1 Remembering
3. Define Rank-Sum test. BTL-1 Remembering
4. Mention the advantages of Nonparametric Tests. BTL-1 Remembering
5. What is the other name or non-parametric test? Why? BTL-6 Creating
6. When are non parametric tests used? BTL-1 Remembering
7. What is the null hypothesis framed in Mann-Whitney test? BTL-6 Creating
8.
Write down the working rule for Mann-Whitney U-test and Kruskal-
Wallis test.
BTL-1 Remembering
9. Explain sign test. BTL-4 Analyzing
10. Define one sample run test? BTL-1 Remembering
11. When is Krushkal-Wallis test used? BTL-1 Remembering
12. Distinguish between Mann-Whitney U-test and Krushkal-Wallis test. BTL-2 Understanding
13. Write the contingency 2*2 table for
test. BTL-5 Evaluating
14.
Write down the formula to calculate rank correlation coefficient
(including tie values).
BTL-1 Remembering
15.
Two HR managers (A and B) ranked five candidates for a new
position. Their rankings of the candidates are show below:
Candidate Rank by A Rank by B
Nancy 2 1
Mary 1 3
John 3 4
Lynda 5 5
Steve 4 2
Compute the Spearman rank correlation.
BTL-6 Creating
16. Define rank correlation co-efficient. BTL-1 Remembering
17.
The following are the ranks obtained by 10 students in Statistics and
Mathematics. Find out the rank correlation coefficient.
Statistics 1 2 3 4 5 6 7
Mathematics 2 5 1 6 7 4 3
BTL-4 Analyzing
18. Explain Kolmogorov-Smirnov Test for one sample problem. BTL-4 Analyzing
19. What adjustment is to be done for tie values to find rank correlation. BTL-6 Creating
20. Mention the properties of linear coefficient of correlation. BTL-1 Remembering
PART -B
1(a).
The scores of a written examination of 24 students, who were trained
by using three different methods, are given below.
Video cassette A 74 88 82 93 55 70 65
BTL-3 Applying
16
Audio cassette B 78 80 65 57 89 85 78 70
Class Room C 68 83 50 91 84 77 94 81 92
Use Krushkal-Wallis test at ? = 5% level of significance, whether the
three methods of training yield the same results.
1(b). Explain Rank sum tests and its applications
2(a).
The production volume of units assembled by three different
operators during 9 shifts is summarized below. Check whether there
is significant difference between the production volumes of units
assembled by the three operators using Krushkal-Wallis test at a
significant level of 0.05.
Operator I 29 34 34 20 32 45 42 24 35
Operator II 30 21 23 25 44 37 34 19 38
Operator III 26 36 41 48 27 39 28 46 15
BTL-3
Applying
2(b).
Two faculty members ranked 12 candidates for scholarships.
Calculate the spearman rank-correlation coefficient and test it for
significance. Use 0.02level of significance.
Candidate Rank by Professor A Rank by Professor B
1 6 5
2 10 11
3 2 6
4 1 3
5 5 4
6 11 12
7 4 2
8 3 1
9 7 7
10 12 10
11 9 8
12 8 9
BTL-3
Applying
3(a).
In a study of sedimentary rocks, the following data were obtained
from samples of 32 grains from two kinds of sand :
Apply Mann-Whitney U test with suitable null and alternative
hypotheses.
Sand I 63 17 35 49 18 43 12 20 47
? 136 51 45 84 32 40 44 25
Sand II 113 54 96 26 39 88 92 53 101
? 48 89 107 111 58 62
BTL -3 Applying
3(b).
The Molisa?s shop has 3 mall locations. She keeps a daily record for
each locations of the number of the customers who actually make a
purchase. A sample of these data follows. Using Kruskal- Wallis test
can you say that at 5% level of significance that her stores have the
same number of customers who buy.
Eastowin 99 64 101 85 79 88 97 95 90 100
Craborchard 83 102 125 61 91 96 94 89 93 75
Fair forest 89 98 56 105 87 90 87 101 76 89
BTL -3 Applying
4(a)
The following are the prices in Rs. per kg of a commodity from 2
random samples of shops from 2 cities A&B.
BTL -3 Applying
17
City A 2.7 3.8 4.3 3.2 4.7 3.6 3.8 4.1
2.7 2.8 3.2 3.4 3.8 4.4 4.9 3.9 4.7
City B 3.7 5.3 4.7 3.6 4.7 4.8 6.0 4.8 4.9
3.8 3.9 4.8 5.2 6.1 3.6 3.8
Apply the run test to examine whether the distribution of prices of
commodity in the two cities is the same.
4(b)
Distinguish Nonparametric methods over parametric methods.
BTL -2 Understanding
5(a)
From a poll of 800 television viewers, the following data have been
accumulated as to,their levels of education and their performance of
television stations. We are interested in determining if the selection
of Tv station is independent of the level of education.
Education Level
High school Bachelor graduate Total
Public Broadcasting 50 150 80 280
Commercial
stations
150 250 120 520
Total 200 400 200 800
(i) State the null and alternative hypothesis.
(ii) Show the contingency table of the expected
frequencies
BTL -3 Applying
5(b)
From the question 5(a)
(i)Compute the test static
(ii)The null hypothesis to be tested at 95% confidence Determine the
critical value for this test
BTL-6
Creating
6(a)
Apply Mann-Whitney U test to determine if there is a significant
difference in the age distribution of the two groups
Day :26 18 25 27 19 30 34 21 33 31
Evening :32 24 23 30 40 41 42 39 45 35
BTL -3
Applying
6(b)
Apply the K-S test to check that the observed frequencies match with
the expected frequencies which are obtained from Normal
distribution. (Given at n=5).
Test Score 51-60 61-70 71-80 81-90 91-100
Observed Frequency
30 100 440 500 130
Expected Frequency 40 170 500 390 100
BTL -5 Evaluating
7
A research company has designed three different systems to clean up
oil spills. The following table contains the results, measures by how
much surface area (in square meters) is cleaned in one hour. The data
were found by testing each method in several trials. Are there
systems equally effective? Use the 5% level of significance.
Sample A 55 60 63 56 59 55
Sample B 57 53 64 49 62
Sample C 66 52 61 57
BTL -1 Remembering
8(a)
Suppose it is desired to check whether pinholes in electrolytic tin
plate are distributed uniformly across a plated coil on the basis of the
following distances (in inches) of 10 pinholes from one edge of a
BTL -1 Remembering
18
long strip of tin plate 320 inches wide.
4.8 14.8 28.2 23.1 4.4 28.7 19.5 2.4 25.0 6.2
Use Kolmogorov Smirnov test to test the null hypothesis.
8(b) Explain Mann- WhitneyU test with an example BTL-4 Analyzing
9.
Ten competitors in a beauty contest are ranked by 3 judges in the
following order.
A : 1 6 5 3 10 2 4 9 7 8
B : 3 5 8 4 7 10 2 1 6 9
C : 6 4 9 8 1 2 3 10 5 7
Find out which pair of Judges has awarded the ranks to the nearest
common taste of beauty.
BTL -3 Applying
10(a).
Test the association of Age and preference of colour of Toy from the
following data
Age/Colour Below 5 6-10 Above 10 years
Pink 60 40 5
Purple 30 30 30
Red 80 10 10
BTL -4 Analyzing
10(b).
Melisa?s Boutique has three mall locations. Melisa keeps a dairy
record for each location of number of customers who actually make a
purchase. A sample of those data follows. Using the kruskal-wallis
test, can you say at the 0.05 level of significance that her stores have
the same number of customers who busy?
DSF Mall 99 64 101 85 79 88 97 95 90 100
Forest Mall 83 102 125 61 91 96 94 89 98 75
Big-Ben Mall 89 98 56 105 87 90 87 101 76 89
BTL -3 Applying
11(a).
A brand manager is concerned that her brand?s share may he
unevenly distributes through the country. In a survey in which the
country was divided into four geographic regions, a random
sampling of 100 consumers in each region was surveyed, with the
following results:
NE NW SE SW TOTAL
Purchase the brand 40 55 45 50 190
Do not purchase 60 45 55 50 210
Total 100 100 100 100 400
(i) Develop a table of observed and expected frequencies for
this problem.
(ii) Calculate the sample
value.
BTL -6 Creating
11(b).
From the question 11(a)
(i)State the null and alternative hypothesis.
(ii)At test whether brand share is the same across the four
regions
BTL -2 Understanding
12(a).
In 30 tosses of a coin, the following sequence of head and tails is
obtained HTTHTHHHTHHTTHTHTHHTHTTHTHHTHT
(i) Determine the number of runs
BTL -2 Understanding
12(b).
From the question 12(a ) Test at 0.10 level of significance, whether
the sequence is random
BTL -3 Applying
13. An experiment designed to compare three preventative methods BTL -3 Applying
19
against corrosion yielded the following maximum depths of pits ( in
thousandths of an inch) in pieces of wire subjected to the respective
treatments:
Method A: 77 54 67 74 71 66
Method B: 60 41 59 65 62 64 52
Method C: 49 52 69 47 56
Use the Kruskal-Wallis test at the 5% level of significance to test the
null hypothesis that the three samples come from identical
populations.
14.
The number of defects in printed circuit boards in hypothesized to
follow a poisson distribution. A random sample of 60 printed boards
have been collected and the number of defects observed. The
following table gives the results.
Table:
No. of defects Observed Frequency
0 32
1 15
2 9
3 4
Does the assumption of a poisson distribution seem appropriate as a
probability model for this process?
BTL -4
Analyzing
PART C
1. Explain the Mann-Whitney test procedure with appropriate examples BTL-1 Remembering
2.
Write the application of Non parametric test and Sign test in
statictics.
BTL-1 Remembering
3(a).
The sales records of two branches of a department store over the last
12 months are shown below.(sales figures are in thousands of
dollars). We want to use the Mann-Whitney-Wilcoxon test to
determine if there is a significant difference in the sales of the two
branches.
Month Branch A Branch B
1 257 210
2 280 230
3 200 250
4 250 260
5 284 275
6 295 300
7 297 320
8 265 290
9 330 310
10 350 325
11 340 329
12 372 335
(i) Compute the sum of the ranks for branch A
(ii) Compute the mean ?T
BTL-4 Analyzing
3(b).
From the question 3(a)
(i)Compute ?T
BTL -6 Creating
20
(ii)Use and test to determine if there is a significant
difference in the population of the sales of the two branches
4(a).
Independent random samples of ten day students and ten evening
students at a university showed the following age distributions. We
want to use the Mann-Whitney-Wilcoxon test to determine if there is
a significant different in the age distribution of the two groups.
Day Evening
26 32
18 24
25 23
27 30
19 40
30 41
34 42
21 39
33 45
31 35
(i) Compute the sum of the ranks for the day students.
(ii) Compute the mean ?
BTL-2 Understanding
4(b).
From the question 4(a)
(i)Compute ?
(ii)Use and test for any significant difference in the age
distribution of the two populations
BTL -4
Analyzing
UNIT ? V CORRELATION AND REGRESSION
SYLLABUS: Correlation ? Coefficient of Determination ? Rank Correlation ? Regression ? Estimation of Regression line
? Method of Least Squares ? Standard Error of estimate.
PART ? A
Q.No. Question
Bloom?s
Taxonomy
Level
Domain
1. Define regression coefficient?. BTL -1 Remembering
2. Define Linear Relationship of Correlation. BTL -6 Creating
3. Write the Properties of Correlation Coefficient? BTL -1 Remembering
4. What is the angle between the regression lines? BTL -1 Remembering
5. When is linear regression used? BTL -1 Remembering
6. Distinguish between correlation and regression BTL -2 Understanding
7. What is regression analysis? BTL -6 Creating
8. What do you interpret if the r = 0 , r = + 1 and r = -1? BTL -1 Remembering
9. Specify the range of correlation. BTL -6 Creating
10. Briefly explain how a scatter diagram benefits the researcher? BTL -4 Analyzing
11. Define correlation coefficient between two variables. BTL -1 Remembering
12. What is a scatter diagram and write its benefits? BTL -6 Creating
21
13.
If the equations of the regression lines are x+2y=5 and 2x+3y=8, find
the correlation coefficient between x and y.
BTL -3 Applying
14. Find the mean values of regression lines are 2y-x =50 and 3y-2x =10. BTL -1 Remembering
15. Write the correlation coefficient in terms of regression coefficients. BTL -6 Creating
16. Write the Equations of Regression lines. BTL -1 Remembering
17.
Explain the difference between the coefficient of determination and
the coefficient of correlation.
BTL -1 Remembering
18. What are the various methods in correlation? BTL -1 Remembering
19.
If the equations of the regression lines are x+2y=5 and 2x+3y=8, find
the correlation coefficient between x and y? Use the equations to find
the mean of X and Y. If the variance of X is 12, calculate the variance
of Y?
BTL -1 Remembering
20. What is positive and negative correlation? BTL -1 Remembering
PART-B
1(a).
The following data pertains of X = Revenue (in ?000 of rupees) generated at
a Corporate Hospital and Y = Number of Patients (in ?00) arrived for the last
ten years.
X 86 95 75 85 90 98 112 74 100 110
Y 21 24 18 24 22 30 27 18 25 28
Find the Karl Pearson?s coefficient of correlation and give your comment.
BTL -4
Analyzing
1(b).
Obtain the two regression lines:
X 45 48 50 55 65 70 75 72 80 85
y 25 30 35 30 40 50 45 55 60 65
BTL-5 Evaluating
2(a).
The revenue generated at a unit and is given below. Fit the trend
line using least squares method and estimate the revenue for the year 2013.
Year 2005 2006 2007 2008 2009 2010 2011 2012
Revenue
(Rs. 00)
268 209 390 290 280 450 350 455
BTL -2 Understanding
2(b).
The following table presents the results of a survey of 8 randomly selected
families:
Annual income (in 000 Rs.):
8 12 9 24 13 37 10 16
Percent allocation for investment
36 25 33 15 28 19 20 22
Find the Karl Pearson?s correlation and spearman?s rank correlation methods
for the above data.
BTL -4
Analyzing
3(a).
Given below are the figures of production (in thousand quintals) of a sugar
factory.
Year 1992 1993 1994 1995 1996 1997 1998
Production 75 80 95 85 95 100 105
Fit a straight line trend by the least squares method and tabulate the trend
values.
BTL -3 Applying
3(b).
Promotional expenses and sales data for an equipment manufacturer are as
follows. Calculate the correlation coefficient and comment.
BTL -3 Applying
22
Promotional expenses in Lakhs
7 10 9 4 11 5 3
Sales in units 12 14 13 5 15 7 4
4(a).
Data on rainfall and crop production for the past seven years are as follows:
Rainfall in inches 20 22 24 26 28 30 32
Crop production 30 35 40 50 60 60 55
Find the correlation coefficient and comment on the relationship.
BTL -3 Applying
4(b).
The percentage of students getting dream placements in campus selection in
a leading technical during the past five years are as follows:
Year 2008 2009 2010 2011 2012
Percentage 7.3 8.7 10.2 7.6 7.4
Find the linear equation that describes the data. Also calculate the percentage
of trend
BTL -4
Analyzing
5(a).
Let
be two independent variables with mean 5 and 10 and S.D 2
and 3 respectively. Obtain
where
BTL -1 Remembering
5(b).
The following data represent the number of flash drivers sold per day at a
local computer shop and their prices.
Price(x) Units sold(y)
34 3
36 4
32 6
35 5
30 9
38 2
40 1
(i) Develop a least squares regression line and explain what the slope of the line
indicates. Compute the coefficient of determination and comment on the
strength of relationship between x and y. Compute the sample correlation
coefficient between the prices and the number of flash drives sold.
(ii) Use to test the relationship between x and Y.
BTL -6 Creating
6(a).
What are the assumptions made by the regression model in estimating the
parameters and in significance testing?
BTL -6 Creating
6(b).
The equations of two variables X and Y as follows 3X+2Y-26 =0, 6X+Y-
31=0 Find the means, regression coefficient & coefficient of correlation.
BTL -4 Analyzing
7.
Promotional expenses and sales data for an equipment manufacturer are as
follows. Calculate the correlation coefficient and comment
Promotional expenses in Lakhs 7 10 9 4 11 5 3
Sales in Units 12 14 13 5 15 7 4
BTL -3 Applying
8(a).
A gas company has supplied 18,20,21,25 and 26 billion cubic feet f gas,
respectively, for the years 2004 to 2008.
(i) Find the estimating equation that best describes these data.
(ii) Calculate the percentage of trend.
BTL -3 Applying
8(b).
From the question 8(a)
(i)Calculate the relative cyclical residuals
(ii)Find the year in which the fluctuation is maximum
BTL-5 Evaluating
9.
Given that
? ? ? ? ?
? ? ? ? ? 3467. XY and 5506, Y 220, Y 2288, X 130, X
2 2
BTL -6 Creating
23
Compute correlation coefficient and regression equation of X on Y.
10.
(i) This no. of faculty-owned person computer at the University of Ohm
increased dramatically between 1993 & 1995
(ii) Year : 1990 1991 1992 1993 1994 1995
(iii) No. of PCs : 50 110 550 1020 1950 3710
(iv) i. Develop a linear estimating equation that best describes these data
(v) ii. Develop a second-degree estimating equation that best describes these
data.
(vi) iii. Estimate the no. of PCs that will be in use at the university in 1999, using
both equation.
iv. If there are 8000 faculty members at the university, which equation is the
better predictor? Why?
BTL -4 Analyzing
11.
Campus stores has been selling the believe it or not. Wonders of statistics
study guide for 12 semesters and would like to estimate the relationship
between sales and no. of sections of elementary statistics taught in each
semester. The following data have been collection:
Sales(un
its)
33 38 24 61 52 45 65 82 29 63 50 79
No. of
sections
3 7 6 6 19 12 12 13 12 13 14 15
i. Develop the estimating equation that best fits the data.
Calculate the sample coefficient of determination and the sample coefficient
of correlation
BTL -6 Creating
12(a).
A coffee shop owner believes that the sales of coffee at his coffee shop
depend upon the weather. He has taken a sample of 6 days. The results of the
sample are given below
Cups of Coffee sold Temperature
350 50
200 60
210 70
100 80
60 90
40 100
(i) Which variable is the dependent variable?
(ii) Compute the least square estimated line
(iii) Compute the correlation coefficient between temperature and the sales of
coffee. Predict sales of a 90 degree day.
BTL -3 Applying
12(b).
From the question 12(a)
(i)Compute the correlation coefficient between temperature and the sales of
coffee.
(ii)Predict sales of a 90 degree day.
BTL -6 Creating
13.
X independent variable 80 120 90 240 130 370 100 160
Y independent variable 36 25 33 15 28 19 20 22
(i) Develop a regression equation that best describes this data.
(ii) Calculate karl-pearson correlation coefficient.
BTL -3 Applying
14.
From the following data, find the equations of the regression lines
Marks in Maths Marks in English
Mean 62.5 39
S.D 9.5 10
BTL -2 Understanding
FirstRanker.com - FirstRanker's Choice
1
(An
Ka ttankulathur ?
DEPARTMENT OF MATHEMATICS
QUESTION BANK
I SEMESTER
1918108 ? STATISTICS FOR MANAGEMENT
Regulation ? 2019
Academic Year 2019 - 2020
Prepared by
Ms. B. Vasuki, Assistant Professor/Mathematics
Ms.B.Elakkiavani, Assistant Professor/Mathematics
2
(An
? .
DEPARTMENT OF MATHEMATICS
QUESTION BANK
SUBJECT : 1918108 ? STATISTICS FOR MANAGEMENT
SEM / YEAR : I Semester / I Year
UNIT I - INTRODUCTION
SYLLABUS: Basic definitions and rules for probability, conditional probability independence of events, Baye?s
theorem, and random variables, Probability distributions: Binomial, Poisson, Uniform and Normal distributions.
PART- A
S.NO QUESTIONS
BT Level
COMPETENCE
PART ? A
1. Define Statistics. BTL -6 Creating
2. What is the addition and multiplication theorem on probability. BTL -1 Remembering
3. Distinguish between a priori and posterior probability?. BTL -6 Creating
4.
The price of the selected stock over a five day period shown as 170, 110,
130, 170 and 160. Compute mean , median and mode.
BTL -6 Creating
5.
A car travels 25 miles at 25 mph, 25 miles at 50 mph and 25 miles at 75
mph. Find the harmonic of three velocities?
BTL -4 Analyse
6.
A ball is drawn at random from a box containg 6 red balls, 4 white balls
and 5 blue balls. Find the probability that the ball drawn is not red.
BTL -4 Analyse
7.
Find the median and mode for the weights (kgs) of 15 persons given as
68, 85, 70, 65, 71, 67, 65, 55, 80, 62, 65, 64, 70, 60, 56.
BTL -3 Applying
8. Name few measures of dispersion. BTL -1 Remembering
9. write the common measures of central tendency? BTL -1 Remembering
10. Define continuous and discrete variables examples. BTL -1 Remembering
11.
Let X be the lifetime in years of a mechanical part. Assume that X has
the cdf F(x) = 1- e
-x
, x ? 0. Find P[1< X ? 3].
BTL -1 Remembering
12. Define independent events. BTL -1 Remembering
13. State the theorem of total probability BTL -1 Remembering
14. What is the use of Baye?s theorem? BTL -6 Creating
15. Mention the properties of a discrete probability distribution. BTL -1 Remembering
16. Define a Poisson distribution and mention its mean and variance. BTL -1 Remembering
17. If the mean and variance of a binomial distribution are respectively 6 BTL -3 Applying
3
and 2.4, find P(x=2).
18.
If x is a Poisson distribution such that P(x=1)=4P(x=2). Find its
mean and variance.
BTL -3 Applying
19.
Suppose that X has a Poisson distribution with parameter ? = 2.
Compute P[X ? 1].
BTL -1 Remembering
20. Define mutually exclusive events. BTL -1 Remembering
PART-B
1(a).
Calculate the mean and standard deviation for the following table
giving the age distribution of 542 members.
Age
20-30 30-40 40-50 50-60 60-70 70-80 80-90
No 3 61 132 153 140 51 2
BTL-2 Understanding
1(b).
Find the geometric mean for the following data:
Group
2-4 4-6 6-8 8-10
Frequency 200 400 300 100
BTL-2
Understanding
2(a).
Find the mean, median and modal ages of married women at first
child birth
Age at the
birth of
first child
13
14
15
16
17
18
19
20
21
22
23
24
25
No of
married
women
37
162
343
390
256
433
161
355
65
85
49
46
40
BTL -6 Creating
2(b).
If A and B are independent event with P(A)=2/5, and P(B)=3/5,
find P(A ?B). Let S= {1,2,3,4,5,6} if A = {2,4,6} then find the
probability of A complement.
BTL -3 Applying
3(a).
Given: The probabilities of three events A, B and C occurring are
P(A) = 0.35, P(B) = 0.45 and P(C) = 0.2. Assuming that A, B, or
C has occurred, the probabilities of another event X occurring are
P(X/A) = 0.8, P(X/B) = 0.65 and P(X/C) = 0.3. Find P(A/X),
P(B/X) and P(C/X).
BTL -6 Creating
3(b).
4 cards are drawn from a well shuffled pack of cards. Find the
probability that
(i) All the four are queens
(ii) There is one card from each suit.
(iii) Two cards are diamonds and two are spades
All the four cards are hearts and one of them is jack
BTL -6 Creating
4(a).
Three machines all turn out non ferrous castings. Machine A
produces 1% defective and Machine B- 2% and machine C ? 5%.
Each machine produces 1/3 of the output. An inspector examines
a single casting, which he determines as non defective. Estimate
the probabilities of its having been produced by each machine.
BTL -6 Creating
4(b).
If the random variable X takes values 1, 2, 3, 4 such that
2P(X = 1) = 3P(X = 2) = P( X=3) = 5P(X = 4), find the
probability distribution and cumulative distribution of X.
BTL-2 Understanding
5(a).
Two dice are thrown together once. Find the probabilities for
BTL -3 Applying
4
getting the sum of the two numbers (i) equal to 5, (ii) multiple of
3, (iii) divisible by 4.
5(b).
Given ? = 4.2, for a poisson distribution. Find (a) P(X ? 2) (b)
P(X ? 5) (c) P(X = 8).
BTL -6 Creating
6(a).
An urn contains 5 balls. Two balls are drawn and found to be
white. What is the probability that all the balls are white?
BTL-1 Remembering
6(b).
The contents of urns I, II, III are as follows:
1 white, 2 black and 3 red balls;
2 white, 1 black and 1 red balls;
4 white, 5 black and 3 red balls;
One urn is chosen at random and two balls drawn. They happen to
be white and red. What is the probability that they come from
urns I, II, III?
BTL -3 Applying
7(a).
In 1989, there were three candidates for the position of principal
Mr. Chatterji, Mr. Ayangar and Dr. Singh. Whose chances of
getting the appointment are in the proportion 4:2:3 respectively.
The probability that Mr. Chatterji is selected, would introduce co-
education in the is 0.3. The probabilities of Mr. Ayangar
and Dr. Singh doing the same are respectively 0.5 and .08. What
is the probability that there was co-education in the in
1990?
BTL -3
Applying
7(b).
Find the probability that atmost 5 defective bolts will be found in
a box of 200 bolts, if it is known that 2% of such bolts are
expected to be defective. (e
-4
= 0.0183)
BTL -6 Creating
8(a).
A coin is tossed 6 times what is the probability of obtaining (a) 4
heads (b) 5 heads (c) 6 heads (d) getting 4 or more heads.
BTL -3 Applying
8(b).
In a bolt factory machines A, B, C manufacture respectively 25%,
35% and 40% of the total of their output 5, 4, 2 percent are
defective bolts. If A bolt is drawn at random from the product and
is found to be defective, what are the probabilities that is was
manufactured by machines A, B and C?
BTL -6 Creating
9(a).
In a test of 2000 electric blubs it was found that the life of a
particular make was normally distributed with an average life of
2040 hours and S. D. of 60 hours. Estimate the number of blubs
likely to burn for
(1) More than 2150 hours
(2) Less than 1950 hours
(3) More than 1920 hours but less than 2160 hours.
BTL -3 Applying
9(b).
The latest nationwide political poll indicates that for Americans
who are randomly selected, the probability that they are
conservative is 0.55, the probability that they are liberal is 0.30
and the probability that they are middle of the road is 0.15.
Assuming these probabilities are accurate, answer the following
BTL -4 Analyzing
5
questions from a randomly chosen group of 10 Americans
(a) What the probability that 4 are liberal?
(b) What the probability that none are conservative
(c) What the probability that two are middle of the road
(d) What the probability that a least 8 are liberal
10.
If X follows a normal distribution with mean 12 and variance 16
cm, find the probabilities for (i) X ? 20 (ii) X ? 20, and (iii) 0 ? X
? 12.
BTL -3 Applying
11.
A discerete random variable X has the probability function given
below:
Value of X=x: 0 1 2 3 4 5 6 7
P(X=x) : 0 k 2k 2k 3k k
2
2k
2
7k
2
+k
Find (1) The value of k
(2) P(1.5 < X < 4.5 / X > 2)
(3) P(X < 6), P(X ? 5), P( 0 < X < 4)
(4) The distribution of X.
BTL -3 Applying
12.
X is a normal variable with mean 30 and standard deviation of 5.
Find (i) P[26 ? X ? 40] (ii) P [X?45] (iii) P [ ?X - 30 ?> 5] use
normal distribution tables
BTL -4 Analyzing
13.
In an intelligence test administered on 1000 students, the average
was 42 and standard deviation 24, find (i) the number of students
exceeding a score 50. (ii) the number of students lying between
30 and 54(iii) the value of score exceeded by top 100 students.
BTL -4 Analyzing
14(a).
The probability that an entering student will graduate is 0.4
Determine the probability that out of 5 students atleast one will
graduate.
BTL-5
Evaluating
14(b).
Fit a Poisson Distribution to the following data which gives the
number of doddens in a sample of clover seeds
No 0 1 2 3 4 5 6 7 8
f 56 156 132 92 37 22 4 0 1
.
BTL -4 Analyzing
PART-C
1(a).
A disciplinary committee is formed from the staff of XYZ
Company which has three departments Marketing, Finance and
Production of the 10,5,20 members respectively. All departments
have two female staff each. A department is selected at random
and from which two matters are selected for the committee,
What is the probability that both the team members are female?
BTL-6 Creating
6
1(b).
In a bolt factory machines A, B, C manufacture respectively 25,
35 and 40 percent of the total. Of their output 5, 4 and 2 percent
are defective bolts respectively. A bolt is drawn at random from
the product and is found o be defective. What are the probabilities
that it was manufactured by machines A, B or C?
BTL-2
Understanding
2(a). State Bayes theorem and brief about its applications. BTL-2 Understanding
2(b).
Out of 800 families with 4 children each, how many families
would be expected to have (i) 2 boys and 2 girls (ii) at least 1 boy
(iii) at most 2 girls (iv) children of both sexes? Assume equal
probabilities for boys and girls.
BTL-1 Remembering
3. Describe the classifications of probability ? BTL-1 Remembering
4. What are the applications of Normal distribution in statistics? BTL-6 Creating
UNIT ?II- SAMPLING DISTRIBUTION & ESTIMATION.
SYLLABUS: Introduction to sampling distributions, sampling distribution of mean and proportion, application of central
limit theorem, sampling techniques. Estimation: Point and Interval estimates for population parameters of large sample and
small samples, determining the sample size.
PART - A
S.N
O
QUESTIONS
BT Level
COMPETENCE
1. Define Sampling distribution of proportion. BTL -1 Remembering
2. Define Probable standard error. BTL -1 Remembering
3. Define standard error and mention its importance BTL -1 Remembering
4. Define central limit theorem BTL -1 Remembering
5.
What is the role of central limit theorem in estimation and testing
problems
BTL -6 Creating
6. Define stratified sampling technique BTL -1 Remembering
7. Briefly describe the significance level. BTL -1 Remembering
8. Distinguish between parameter and statistic. BTL -2 Understanding
9. Define estimator, estimate and estimation. BTL -1 Remembering
10. Distinguish between point estimation and interval estimation BTL -2 Understanding
11. Mention the properties of a good estimator. BTL -1 Remembering
12. Define confidence coefficient. BTL -1 Remembering
13. What is the level of significance in testing of hypothesis BTL -6 Creating
14. Define confidence limits for a parameter BTL -1 Remembering
15.
State the conditions under which a binomial distribution becomes a
normal distribution
BTL -4 Analyzing
16.
If the random sample comes from a normal population, what can
be said about the sampling distribution of the mean.
BTL -5 Evaluating
17.
An automobile repair shop has taken a random sample of 40
services that the average service time on an automobile is 130
minutes with a standard deviation of 26 minutes. Compute the
standard error of the mean.
BTL -6 Creating
7
18. What is a random number? How it is useful in sampling? BTL -6 Creating
19.
A population has the numbers: 12, 8, 10, 30, 12, 16, 40, 5, 16, 24,
22, 31, 30, 16, 15. Draw a systematic sample of size 5. Find out its
mean.
BTL -3 Applying
20. How large sample is useful in estimation and testing BTL -4 Analyzing
PART -B
1(a).
A random sample of 700 units from a large consignment showed
that 200 were damaged. Find (i) 95% (ii) 99% confidence limits
for the proportion of damaged units in the consignment.
BTL -3 Applying
1(b).
A random sample of size 9 is obtained from a Normal population
with mean 25 and if the variance 100 find the probability that the
sample mean exceeds 31.2.
BTL -4 Analyzing
2(a).
In a normally distributed population, average income per
household is Rs.20,000 with a standard deviation of Rs. 1,600.
Find the probability that the sample mean will be between
Rs.19,600 and Rs.20,200 in a survey of a random sample of 100
households.
BTL -6 Creating
2(b).
A university wants to determine the percentage of students who
would accept proposed fees hike for improving facilities. The
university wants to be 90% confident that the percentage is
within2% of the true value. Find the sample size to achieve the
accuracy regardless of the true percentage assuming the percentage
of students accepting the increase in tuition fees to be 0.5.
BTL -6 Creating
3(a).
A bank has kept records of the checking balances of its customers
and determined that the average daily balances of its customers is
Rs.300 with a standard deviation of Rs. 48. A random sample of
144 checking accounts is selected.
(i) What is the probability that the sample mean will be more
than Rs. 306.60?
(ii) What is the probability that the sample mean will be less
than Rs. 308?
BTL -6 Creating
3(b).
From the question 3(a)
(i) What is probability that the sample mean will between Rs.
302 and Rs. 308?
(ii) What is probability that the sample mean will be atleast
Rs. 296?
BTL -6 Creating
4(a).
Explain Stratified sampling technique and discuss how it is better
than simple random sampling in a particular situation.
BTL -4
Analyzing
4(b). Discuss the standard error of proportion BTL-2 Understanding
5.
Explain the methods of drawing simple random sample from a
finite population.
BTL -4 Analyzing
8
6(a).
In a sample of 1000 citizens of India, 540 are wheat eaters and the
rest are rice eaters. Can we assume that both rice and wheat
equally popular in India at 1 % level of significance?
BTL-5
Evaluating
6(b).
A simple random sample of 144 items resulted in a sample mean
of 1257.85 and standard deviation of 480. Develop a 95%
confidence interval for the population mean
BTL -6
Creating
7(a).
A car dealer wants to estimate the proportion of customers who
still own the cars they purchased 5 years earlier. A random sample
of 500 customers selected from the dealer?s records indicate that
315 customers still own cars that they were purchased 5 years
earlier. Set up 95% confidence interval estimation of the
population proportion of all the customers who still own the cars 5
years after they were purchased.
BTL-2
Understanding
7(b).
A movie maker sampled 55 fans who viewed his master piece
movie and asked them whether they had planned to see it again.
Only 10 of them believed that the movie was worthy of a second
look. Find the standard error of the population of fans who will
view the film a second time. Construct a 90% confidence interval
for this population.
BTL -5 Evaluating
8(a).
From a population of size 600, a sample of 60 individuals revealed
mean and standard deviation as 6.2 and 1.45 respectively. (i) Find
the estimated standard error (ii) Construct 96% confidence
interval for the mean.
BTL -3 Applying
8(b).
The age of employees in a company follows normal distribution
with its mean and variance as 40 years and 121 years respectively.
If a random sample of 36 employees is taken from a finite normal
population of size 1000, what is the probability that the sample
mean is
(i) less than 45
(ii) greater than 42 and
(iii) between 40 and 42?
BTL -6
Creating
9(a).
A firm wishes to estimate with an error of not more than 0.03 and
a level of confidence of 98%, the proportion of consumers that
prefer its brand of household detergent. Sales report indicate the
about 0.20 of all consumers prefer the firm?s brand. What is the
requisite sample size?
BTL -5 Evaluating
9(b).
A random sample of 700 units from a large consignment should
that 200 were damaged.
Find (i) 95%
(ii) 99% confidence limits for the proportion of damaged
units in the consignment
BTL -3 Applying
10(a).
From a population of 500 items with a mean of 100 gms and
standard deviation of 12.5 gms, 65 items were chosen. (i) What is
the standard error? (ii) Find P(99.5 < X < 101.5).
BTL -6 Creating
10(b).
A non-normal distribution representing the number of trips
BTL -6 Creating
9
performed by lorries per week in a coal field has a mean of 100
trips and variance of 121 trips. A random sample of 36 lorries is
taken from the non-normal population. What is the probability that
the sample mean is
(i) greater than 105
(ii) less than 102
(iii) between 101 and 103 trips?
11.
Test the significance of the difference between the means of the
sample from the following data
Size of sample Mean SD
Sample A 100 61 4
Sample B 200 63 6
BTL -4 Analyzing
12(a).
A cigarete manufacturing firm claims that its brand. A outsells
brand B by 8%. If it is found that 42 out of a sample of 200
smokers prefer brand a and 18 out of another sample of 100
smokers prefer brand B, test whether the 8% difference is a valid
claim(use 5% level of significance).
BTL -4
Analyzing
12(b).
In an automotive safety test conducted by the North Carolina
Highway Safety Research center, the average tyre pressure in a
sample of 62 tyres was found to be 24 pounds per square inch, and
the standard deviation was 2.1 pounds per square inch.
(i) What is the estimated population standard deviation for this
population
(ii) Calculate the estimated standard error of the mean
(iii) Construct a 95% confidence interval for the population mean.
BTL -3 Applying
13(a).
The manager of a shop selling beverages wants to estimate the
actual amount of beverages in one litre bottles from a nationally
known manufacturer. As per manufacturer?s specifications, the
standard deviation of the volume of the beverage is 0.02 litre. The
average amount of beverage per 1 litre bottle is found to be 0.995
litre on checking 50 bottles. Setup 99% confidence interval
estimate of the true population average amount of beverage in a 1
liter bottle. Check whether the manufacturer is genuine in filling
the beverage.
BTL -6
Creating
13(b).
In a batch chemical process used for etching printed circuit boards,
two different catalysts are being compared to determine whether
they require different emersion times for removal of identical
quantities of photo resist material. Twelve batch were run with
catalyst 1, resulting in a sample mean emersion time of 24.6
minutes and sample standard deviation of 0.85 minutes. Fifteen
batches were run with catalyst 2, resulting in a mean emersion time
of 22.1 minutes and a standard deviation of 0.98 minutes. Find a
95% confidence interval on the difference in means, assuming that
2
2
2
1
? ? ? .
BTL -3 Applying
10
14.
In a random sample of 75 axle shafts. 12 have a surface finish that
is rougher than the specifications will allow. Suppose that a
modification is made in the surface finishing process and
subsequently a second random sample of 85 axle shafts is
obtained. The number of defective shafts in this second sample is
10. Obtain an approximate 95% confidence interval on the
difference in the proportions of defectives produced under the two
processes
BTL -5 Evaluating
PART-C
1.
In a sample of 25 observations from a Normal distribution with
mean 98.6 and standard deviation 17.2.
(i)What is P(92<102)
(ii)Find the corresponding probability given a sample of 36.
BTL -6 Creating
2.
Mary, an auditor for a large credit card company, knows that, on
average, the monthly balance of any customer is Rs.112, and the
standard deviation is Rs.56. If Mary audits 50 randomly selected
accounts, What is the probability that the sample average balance
is
(i) Below Rs. 100
(ii)Between Rs.100 and Rs.130
BTL -6 Creating
3(a).
Write the type of sampling methods and the uses of standard error?
BTL -1 Remembering
3(b).
From a population of 540, a sample of 60 individual is taken. From
this sample, the mean is found to 6.2 and the standard deviation
1.368
(i) Find the estimated standard error of the mean.
(ii) Construct a 96 % confidence interval for the mean.
BTL-2 Understanding
4(a).
Explain the properties of good point estimator.
BTL -4 Analyzing
4(b).
What do you mean by interval estimation? Give examples
BTL-6 Creating
UNIT III - TESTS OF HYPOTHESIS- PARAMETRIC TESTS
SYLLABUS: Hypothesis testing: one sample and two sample tests for means and proportions of large samples (z-test),
one sample and two sample tests for means of small samples (t-test), F-test for two sample standard deviations. ANOVA
one and two way.
PART-A
Q.
No.
Question
Bloom?s
Taxonomy
Level
Domain
1. Define Test of Significance. BTL-1 Remembering
2. What are the Type I and Type II errors? BTL-6 Creating
3. What do you mean by one tail test? BTL-6 Creating
4. State the applications of Z-test and t-test. BTL-4 Analyzing
5. Define critical region BTL-1 Remembering
6. Distinguish between one tail and two tail tests BTL-2 Understanding
7. What is the aim of design of experiments? BTL-6 Creating
8. Distinguish between one-way and two-way analysis of variance. BTL-2 Understanding
9. When does the Z-test apply? BTL-1 Remembering
10. Explain SSB , SSW and SSY
and relationship in ANOVA. BTL-4 Analyzing
11
11. Describe any two applications of t-distribution BTL-1 Remembering
12. Write the uses of F-test? BTL-6 Creating
13. Define the level of significance. BTL-1 Remembering
14. Write the properties of t-distribution? BTL-6 Creating
15. What is the role of standard error? BTL-6 Creating
16. Mention any four applications of t-distribution in tests of hypothesis. BTL-1 Remembering
17. Mention any four uses of Chi-square distribution in test of hypothesis. BTL-1 Remembering
18. Define null hypothesis ? Explain. BTL-6 Creating
19.
Estimate the standard error of difference between two proportion if
p
1
=0.10,p
2=
0.133 and n
1
=50,n
2
=75.
BTL-6 Creating
20.
Mention any two assumptions made in analysis of variance
techniques.
BTL-1 Remembering
PART-B
1(a).
A study compares the effect of four 1-month point-of-purchase
promotions on sales. The unit sales for five stores using all four
promotions in different months follow.
Free Sample
78 87 81 89 58
One-pack gift
94 91 87 90 88
Cents off
73 73 78 69 83
76Refund by mail
79 83 78 69 81
(i)Compute the mean unit sales for each promotion and then
determine the grand mean.
(ii)Estimate the population variance using the between column
variance.
BTL-5 Evaluating
1(b).
From the question 1(a)
(i)Estimate the population variance using the within-column variance
computed from the variance within the samples.
(ii)Calculate the F ratio. At the 0.01 level of significance, do the
promotions produce different effects on sales.
BTL-2 Understanding
2(a).
In a low cost Toy production system, the molding machine has been
set with standard of 1% defective. The 80 sample units produced from
this machine shows defective of one unit. Is it necessary to stop the
product for corrective mechanism? Test at 5% level of significance
BTL-5 Evaluating
2(b).
Block Enterprises, a manufacturer of chips for computers. Is in the
process of deciding whether to replace its current semi automated
assembly line with a fully automated assembly line. Block has
gathered some preliminary test data about hourly chip production,
which is summarized in the following table, and it would like to know
whether it should upgrade its assembly line. State (and test at a =0.02)
appropriate hypothesis to help Block decide.
BTL-5 Evaluating
3(a).
Three samples below have been obtained from normal population
with equal variance. Test the hypothesis that the means are equal.
Sample I : 10 12 18 15 16
Sample II : 7 15 10 12 8
Sample III : 12 8 15 16 15
BTL-5 Evaluating
3(b). The I.Q.s of 16 students from one class of an showed a BTL-2 Understanding
12
mean of 107 with a standard deviation of 10, while the I.Q.s of 14
students from another class showed a mean of 112 with a standard
deviation of 8. Check whether there is an appreciable difference
between the I.Q.s of the two groups at (i) 0.01and (ii) 0.05 level of
significance
4(a).
The following is the information obtained from a random sample of 5
observations. Assume the population has a normal distribution.
30 31 27 32 28
To test if the sample was drawn from a normal distribution with mean
less than 30, (i)State the null and alternative hypotheses
(ii)Compute the standard error.
BTL-2 Understanding
4(b).
From the question 4(a)
(i)Determine the test statistic.
(ii)Decide at 10% level whether or not the mean value could be
greater than 30
BTL-2 Understanding
5.
The following data relate to the number of units produced per week by
three methods.
Method 1 : 170 192 190 120
Method 2 : 160 165 170 172
Method 3 : 182 190 170 178 185
Prepare ANOVA table and write your comments
BTL-6 Creating
6(a).
Test if the following samples could have come from two populations
with the same means, assuming the population variances are equal.
Sample I Sample II
Sample size 12 10
Sample Mean 40.5 43.8
Sample variance 2.6 3.2
BTL-5 Evaluating
6(b).
The weights of 10 people of a locality are found to be
70,67,62,68,61,68,70,64,64,66 kilograms. Is it reasonable to believe
that the average weights of the people of locality is greater than 64
kg? Test at 5%level of significance.
BTL-5 Evaluating
7(a).
In Town A, there were 850 birds of which 52% was males, while in
Town A and Town B combined, the proportion of males in a total of
1200 birds was 0.49. Is there any significance difference in the
proportions of male birds in the two Towns?
BTL-2
Understanding
7(b).
IQ test result of randomly selected five employees in an organization
is given below. Test whether minimum requirement of average IQ
level 87 is maintained in that company or not.
Employee code 234 232 121 343 111
IQ test 85 95 90 93 87
BTL-4 Analyzing
8(a).
The weights of 8 persons are found to be 60, 65, 70, 68, 62, 63, 60,
and 66 kgs. The weights of another group of 12 persons are found to
be 70, 60, 58, 56, 50, 48, 52, 56, 52, 50, 54, and 50. Can we conclude
that both samples have come from populations with same variances?
BTL -4 Analyzing
13
8(b).
ATMs must be stocked with enough cash to meet the requirements of
customers over a week, but excess cash results in loss of income as
investment opportunities could not be utilized. In an ATM, the
average transaction per customer in a week is Rs.8000 with a standard
deviation of Rs.1500. If a random sample of 36 customer transactions
is examined and it is observed that the sample mean with drawl is
Rs.8600, check the belief that the true average withdrawal is no longer
Rs.8000. Assume 0.05 level of significance
BTL -3 Applying
9.
Apply ANOVA technique and write your comment regarding the
sales(in Rs. Lakhs)
Area
Representatives
1 2 3 4
A 12 16 20 18
B 15 10 12 16
C 10 08 16 15
BTL -3 Applying
10(a).
A farmer wishes to determine whether there is a difference in yields
between two different varieties of wheat I and II. The following data
shows the production of wheat per unit area using the two varieties.
Can the farmer conclude at significance levels of
(i) 0.05
(ii) 0.01 that a difference exists?
BTL -4 Analyzing
10(b).
Test if the samples could have come from equal population means.
Sample A Sample B
Size 200 400
Mean 154.8 164.3
Variance 15.2 18.2
BTL-5 Evaluating
11(a).
The number of accidents per week in a city are as follows:
12, 8, 20, 2, 14, 10, 15, 6, 9 and 4. Are these frequencies in agreement
with the belief that accident conditions were the same during this 10
weeks period?
BTL -4
Analyzing
11(b).
Two samples are drawn from two normal population. From the
following data, Test whether the two samples have the same variance
5% level of significance.
Sample 1 60 65 69 74 76 82 85 87
Sample 2 61 66 67 85 78 63 85 86 88 91
BTL -3 Applying
12(a).
Given a sample mean of 83, a sample standard deviation of 12.5 and a
sample size of 22, test the hypothesis that the value of the population
mean is 70 against alternative that it is more than 70. Use the 0.025
significance level.
BTL-2
Understanding
12(b).
The following table shows the lifetimes in hours of samples from
three different types of television tables manufactured by a company.
Determine whether there is a difference between the three types at
significance level of 0.01.
Table:
BTL-2
Understanding
14
Sample 1 407 411 409
Sample 2 404 406 408 405 402
Sample 3 410 408 406 408
13.
The following table shows the yields per acre of hour different plants
crops grown on lots treated with three different types of fertilizer.
Determine at the 5% significance level whether there is a difference in
yield per acre.
(i) due to the fertilizers and
(ii) due to the crops
Table:
Crop -I Crop -II Crop -III Crop -IV
Fertilizer A 4.5 6.4 7.2 6.7
Fertilizer B 8.8 7.8 9.6 7.0
Fertilizer C 5.9 6.8 5.7 5.2
BTL-2
Understanding
14.
Time of 6 machine operator (in minute) in making product is given
below. Use paired t-test for training effectiveness.
Machine operator 1 2 3 4 5 6
Before training 12 23 4 5 16 17
After training 2 3 10 8 12 6
BTL -3 Applying
PART C
1(a).
What are non-parametric tests? Point out their advantages and
disadvantages?
BTL -6 Creating
1(b).
The success of a sales engineer in adopting the proven sales technique
was found to be 12 out of 30 occasions. Hence he tried a novel
technique and achieved success at a rate of 23 out of 40 occasions.
Check whether the novel technique is effective at 5% level of
significance.
BTL-2 Understanding
2(a).
The following are the final examination marks of three groups of
students who were taught computer by three difference methods.
First method: 94 88 91 74 87 97
Second method: 85 82 79 84 61 72 80
Third method: 89 67 72 76 69
BTL -5 Evaluating
2(b).
A consumer product manufacturing company was selling one of its
leading products through a large number of retail shops. Before a
heavy advertisement campaign, the average sale per week per shop
was 140 dozens. After the campaign, a sample of 26 shops was taken
and the mean sales improved to 147 dozens with a standard deviation
of 16. Check the effectiveness of the advertisement campaign at 5%
level of significance
BTL-2
Understanding
3.
Discuss the test procedure to test hypothesized population proportion
using single sample proportion.
BTL-1 Understanding
15
4.
(i)Write the application testing of hypothesis in statistics. (ii)What is
t-test? When should we apply a t-test?
BTL -3 Applying
UNIT IV: NON-PARAMETRIC TESTS
SYLLABUS: Chi-square test for single sample standard deviation. Chi-square tests for independence ofattributes and
goodness of fit. Sign test for paired data. Rank sum test. Kolmogorov-Smirnov ? test for goodness of fit, comparing two
populations. Mann ? Whitney U test and Kruskal Wallis test. One sample run test.
PART-A
Q.
No.
Question
Bloom?s
Taxonomy
Level
Domain
1. Define Rank Correlation test. BTL-1 Remembering
2. Write the formula in chi square test and any two uses. BTL-1 Remembering
3. Define Rank-Sum test. BTL-1 Remembering
4. Mention the advantages of Nonparametric Tests. BTL-1 Remembering
5. What is the other name or non-parametric test? Why? BTL-6 Creating
6. When are non parametric tests used? BTL-1 Remembering
7. What is the null hypothesis framed in Mann-Whitney test? BTL-6 Creating
8.
Write down the working rule for Mann-Whitney U-test and Kruskal-
Wallis test.
BTL-1 Remembering
9. Explain sign test. BTL-4 Analyzing
10. Define one sample run test? BTL-1 Remembering
11. When is Krushkal-Wallis test used? BTL-1 Remembering
12. Distinguish between Mann-Whitney U-test and Krushkal-Wallis test. BTL-2 Understanding
13. Write the contingency 2*2 table for
test. BTL-5 Evaluating
14.
Write down the formula to calculate rank correlation coefficient
(including tie values).
BTL-1 Remembering
15.
Two HR managers (A and B) ranked five candidates for a new
position. Their rankings of the candidates are show below:
Candidate Rank by A Rank by B
Nancy 2 1
Mary 1 3
John 3 4
Lynda 5 5
Steve 4 2
Compute the Spearman rank correlation.
BTL-6 Creating
16. Define rank correlation co-efficient. BTL-1 Remembering
17.
The following are the ranks obtained by 10 students in Statistics and
Mathematics. Find out the rank correlation coefficient.
Statistics 1 2 3 4 5 6 7
Mathematics 2 5 1 6 7 4 3
BTL-4 Analyzing
18. Explain Kolmogorov-Smirnov Test for one sample problem. BTL-4 Analyzing
19. What adjustment is to be done for tie values to find rank correlation. BTL-6 Creating
20. Mention the properties of linear coefficient of correlation. BTL-1 Remembering
PART -B
1(a).
The scores of a written examination of 24 students, who were trained
by using three different methods, are given below.
Video cassette A 74 88 82 93 55 70 65
BTL-3 Applying
16
Audio cassette B 78 80 65 57 89 85 78 70
Class Room C 68 83 50 91 84 77 94 81 92
Use Krushkal-Wallis test at ? = 5% level of significance, whether the
three methods of training yield the same results.
1(b). Explain Rank sum tests and its applications
2(a).
The production volume of units assembled by three different
operators during 9 shifts is summarized below. Check whether there
is significant difference between the production volumes of units
assembled by the three operators using Krushkal-Wallis test at a
significant level of 0.05.
Operator I 29 34 34 20 32 45 42 24 35
Operator II 30 21 23 25 44 37 34 19 38
Operator III 26 36 41 48 27 39 28 46 15
BTL-3
Applying
2(b).
Two faculty members ranked 12 candidates for scholarships.
Calculate the spearman rank-correlation coefficient and test it for
significance. Use 0.02level of significance.
Candidate Rank by Professor A Rank by Professor B
1 6 5
2 10 11
3 2 6
4 1 3
5 5 4
6 11 12
7 4 2
8 3 1
9 7 7
10 12 10
11 9 8
12 8 9
BTL-3
Applying
3(a).
In a study of sedimentary rocks, the following data were obtained
from samples of 32 grains from two kinds of sand :
Apply Mann-Whitney U test with suitable null and alternative
hypotheses.
Sand I 63 17 35 49 18 43 12 20 47
? 136 51 45 84 32 40 44 25
Sand II 113 54 96 26 39 88 92 53 101
? 48 89 107 111 58 62
BTL -3 Applying
3(b).
The Molisa?s shop has 3 mall locations. She keeps a daily record for
each locations of the number of the customers who actually make a
purchase. A sample of these data follows. Using Kruskal- Wallis test
can you say that at 5% level of significance that her stores have the
same number of customers who buy.
Eastowin 99 64 101 85 79 88 97 95 90 100
Craborchard 83 102 125 61 91 96 94 89 93 75
Fair forest 89 98 56 105 87 90 87 101 76 89
BTL -3 Applying
4(a)
The following are the prices in Rs. per kg of a commodity from 2
random samples of shops from 2 cities A&B.
BTL -3 Applying
17
City A 2.7 3.8 4.3 3.2 4.7 3.6 3.8 4.1
2.7 2.8 3.2 3.4 3.8 4.4 4.9 3.9 4.7
City B 3.7 5.3 4.7 3.6 4.7 4.8 6.0 4.8 4.9
3.8 3.9 4.8 5.2 6.1 3.6 3.8
Apply the run test to examine whether the distribution of prices of
commodity in the two cities is the same.
4(b)
Distinguish Nonparametric methods over parametric methods.
BTL -2 Understanding
5(a)
From a poll of 800 television viewers, the following data have been
accumulated as to,their levels of education and their performance of
television stations. We are interested in determining if the selection
of Tv station is independent of the level of education.
Education Level
High school Bachelor graduate Total
Public Broadcasting 50 150 80 280
Commercial
stations
150 250 120 520
Total 200 400 200 800
(i) State the null and alternative hypothesis.
(ii) Show the contingency table of the expected
frequencies
BTL -3 Applying
5(b)
From the question 5(a)
(i)Compute the test static
(ii)The null hypothesis to be tested at 95% confidence Determine the
critical value for this test
BTL-6
Creating
6(a)
Apply Mann-Whitney U test to determine if there is a significant
difference in the age distribution of the two groups
Day :26 18 25 27 19 30 34 21 33 31
Evening :32 24 23 30 40 41 42 39 45 35
BTL -3
Applying
6(b)
Apply the K-S test to check that the observed frequencies match with
the expected frequencies which are obtained from Normal
distribution. (Given at n=5).
Test Score 51-60 61-70 71-80 81-90 91-100
Observed Frequency
30 100 440 500 130
Expected Frequency 40 170 500 390 100
BTL -5 Evaluating
7
A research company has designed three different systems to clean up
oil spills. The following table contains the results, measures by how
much surface area (in square meters) is cleaned in one hour. The data
were found by testing each method in several trials. Are there
systems equally effective? Use the 5% level of significance.
Sample A 55 60 63 56 59 55
Sample B 57 53 64 49 62
Sample C 66 52 61 57
BTL -1 Remembering
8(a)
Suppose it is desired to check whether pinholes in electrolytic tin
plate are distributed uniformly across a plated coil on the basis of the
following distances (in inches) of 10 pinholes from one edge of a
BTL -1 Remembering
18
long strip of tin plate 320 inches wide.
4.8 14.8 28.2 23.1 4.4 28.7 19.5 2.4 25.0 6.2
Use Kolmogorov Smirnov test to test the null hypothesis.
8(b) Explain Mann- WhitneyU test with an example BTL-4 Analyzing
9.
Ten competitors in a beauty contest are ranked by 3 judges in the
following order.
A : 1 6 5 3 10 2 4 9 7 8
B : 3 5 8 4 7 10 2 1 6 9
C : 6 4 9 8 1 2 3 10 5 7
Find out which pair of Judges has awarded the ranks to the nearest
common taste of beauty.
BTL -3 Applying
10(a).
Test the association of Age and preference of colour of Toy from the
following data
Age/Colour Below 5 6-10 Above 10 years
Pink 60 40 5
Purple 30 30 30
Red 80 10 10
BTL -4 Analyzing
10(b).
Melisa?s Boutique has three mall locations. Melisa keeps a dairy
record for each location of number of customers who actually make a
purchase. A sample of those data follows. Using the kruskal-wallis
test, can you say at the 0.05 level of significance that her stores have
the same number of customers who busy?
DSF Mall 99 64 101 85 79 88 97 95 90 100
Forest Mall 83 102 125 61 91 96 94 89 98 75
Big-Ben Mall 89 98 56 105 87 90 87 101 76 89
BTL -3 Applying
11(a).
A brand manager is concerned that her brand?s share may he
unevenly distributes through the country. In a survey in which the
country was divided into four geographic regions, a random
sampling of 100 consumers in each region was surveyed, with the
following results:
NE NW SE SW TOTAL
Purchase the brand 40 55 45 50 190
Do not purchase 60 45 55 50 210
Total 100 100 100 100 400
(i) Develop a table of observed and expected frequencies for
this problem.
(ii) Calculate the sample
value.
BTL -6 Creating
11(b).
From the question 11(a)
(i)State the null and alternative hypothesis.
(ii)At test whether brand share is the same across the four
regions
BTL -2 Understanding
12(a).
In 30 tosses of a coin, the following sequence of head and tails is
obtained HTTHTHHHTHHTTHTHTHHTHTTHTHHTHT
(i) Determine the number of runs
BTL -2 Understanding
12(b).
From the question 12(a ) Test at 0.10 level of significance, whether
the sequence is random
BTL -3 Applying
13. An experiment designed to compare three preventative methods BTL -3 Applying
19
against corrosion yielded the following maximum depths of pits ( in
thousandths of an inch) in pieces of wire subjected to the respective
treatments:
Method A: 77 54 67 74 71 66
Method B: 60 41 59 65 62 64 52
Method C: 49 52 69 47 56
Use the Kruskal-Wallis test at the 5% level of significance to test the
null hypothesis that the three samples come from identical
populations.
14.
The number of defects in printed circuit boards in hypothesized to
follow a poisson distribution. A random sample of 60 printed boards
have been collected and the number of defects observed. The
following table gives the results.
Table:
No. of defects Observed Frequency
0 32
1 15
2 9
3 4
Does the assumption of a poisson distribution seem appropriate as a
probability model for this process?
BTL -4
Analyzing
PART C
1. Explain the Mann-Whitney test procedure with appropriate examples BTL-1 Remembering
2.
Write the application of Non parametric test and Sign test in
statictics.
BTL-1 Remembering
3(a).
The sales records of two branches of a department store over the last
12 months are shown below.(sales figures are in thousands of
dollars). We want to use the Mann-Whitney-Wilcoxon test to
determine if there is a significant difference in the sales of the two
branches.
Month Branch A Branch B
1 257 210
2 280 230
3 200 250
4 250 260
5 284 275
6 295 300
7 297 320
8 265 290
9 330 310
10 350 325
11 340 329
12 372 335
(i) Compute the sum of the ranks for branch A
(ii) Compute the mean ?T
BTL-4 Analyzing
3(b).
From the question 3(a)
(i)Compute ?T
BTL -6 Creating
20
(ii)Use and test to determine if there is a significant
difference in the population of the sales of the two branches
4(a).
Independent random samples of ten day students and ten evening
students at a university showed the following age distributions. We
want to use the Mann-Whitney-Wilcoxon test to determine if there is
a significant different in the age distribution of the two groups.
Day Evening
26 32
18 24
25 23
27 30
19 40
30 41
34 42
21 39
33 45
31 35
(i) Compute the sum of the ranks for the day students.
(ii) Compute the mean ?
BTL-2 Understanding
4(b).
From the question 4(a)
(i)Compute ?
(ii)Use and test for any significant difference in the age
distribution of the two populations
BTL -4
Analyzing
UNIT ? V CORRELATION AND REGRESSION
SYLLABUS: Correlation ? Coefficient of Determination ? Rank Correlation ? Regression ? Estimation of Regression line
? Method of Least Squares ? Standard Error of estimate.
PART ? A
Q.No. Question
Bloom?s
Taxonomy
Level
Domain
1. Define regression coefficient?. BTL -1 Remembering
2. Define Linear Relationship of Correlation. BTL -6 Creating
3. Write the Properties of Correlation Coefficient? BTL -1 Remembering
4. What is the angle between the regression lines? BTL -1 Remembering
5. When is linear regression used? BTL -1 Remembering
6. Distinguish between correlation and regression BTL -2 Understanding
7. What is regression analysis? BTL -6 Creating
8. What do you interpret if the r = 0 , r = + 1 and r = -1? BTL -1 Remembering
9. Specify the range of correlation. BTL -6 Creating
10. Briefly explain how a scatter diagram benefits the researcher? BTL -4 Analyzing
11. Define correlation coefficient between two variables. BTL -1 Remembering
12. What is a scatter diagram and write its benefits? BTL -6 Creating
21
13.
If the equations of the regression lines are x+2y=5 and 2x+3y=8, find
the correlation coefficient between x and y.
BTL -3 Applying
14. Find the mean values of regression lines are 2y-x =50 and 3y-2x =10. BTL -1 Remembering
15. Write the correlation coefficient in terms of regression coefficients. BTL -6 Creating
16. Write the Equations of Regression lines. BTL -1 Remembering
17.
Explain the difference between the coefficient of determination and
the coefficient of correlation.
BTL -1 Remembering
18. What are the various methods in correlation? BTL -1 Remembering
19.
If the equations of the regression lines are x+2y=5 and 2x+3y=8, find
the correlation coefficient between x and y? Use the equations to find
the mean of X and Y. If the variance of X is 12, calculate the variance
of Y?
BTL -1 Remembering
20. What is positive and negative correlation? BTL -1 Remembering
PART-B
1(a).
The following data pertains of X = Revenue (in ?000 of rupees) generated at
a Corporate Hospital and Y = Number of Patients (in ?00) arrived for the last
ten years.
X 86 95 75 85 90 98 112 74 100 110
Y 21 24 18 24 22 30 27 18 25 28
Find the Karl Pearson?s coefficient of correlation and give your comment.
BTL -4
Analyzing
1(b).
Obtain the two regression lines:
X 45 48 50 55 65 70 75 72 80 85
y 25 30 35 30 40 50 45 55 60 65
BTL-5 Evaluating
2(a).
The revenue generated at a unit and is given below. Fit the trend
line using least squares method and estimate the revenue for the year 2013.
Year 2005 2006 2007 2008 2009 2010 2011 2012
Revenue
(Rs. 00)
268 209 390 290 280 450 350 455
BTL -2 Understanding
2(b).
The following table presents the results of a survey of 8 randomly selected
families:
Annual income (in 000 Rs.):
8 12 9 24 13 37 10 16
Percent allocation for investment
36 25 33 15 28 19 20 22
Find the Karl Pearson?s correlation and spearman?s rank correlation methods
for the above data.
BTL -4
Analyzing
3(a).
Given below are the figures of production (in thousand quintals) of a sugar
factory.
Year 1992 1993 1994 1995 1996 1997 1998
Production 75 80 95 85 95 100 105
Fit a straight line trend by the least squares method and tabulate the trend
values.
BTL -3 Applying
3(b).
Promotional expenses and sales data for an equipment manufacturer are as
follows. Calculate the correlation coefficient and comment.
BTL -3 Applying
22
Promotional expenses in Lakhs
7 10 9 4 11 5 3
Sales in units 12 14 13 5 15 7 4
4(a).
Data on rainfall and crop production for the past seven years are as follows:
Rainfall in inches 20 22 24 26 28 30 32
Crop production 30 35 40 50 60 60 55
Find the correlation coefficient and comment on the relationship.
BTL -3 Applying
4(b).
The percentage of students getting dream placements in campus selection in
a leading technical during the past five years are as follows:
Year 2008 2009 2010 2011 2012
Percentage 7.3 8.7 10.2 7.6 7.4
Find the linear equation that describes the data. Also calculate the percentage
of trend
BTL -4
Analyzing
5(a).
Let
be two independent variables with mean 5 and 10 and S.D 2
and 3 respectively. Obtain
where
BTL -1 Remembering
5(b).
The following data represent the number of flash drivers sold per day at a
local computer shop and their prices.
Price(x) Units sold(y)
34 3
36 4
32 6
35 5
30 9
38 2
40 1
(i) Develop a least squares regression line and explain what the slope of the line
indicates. Compute the coefficient of determination and comment on the
strength of relationship between x and y. Compute the sample correlation
coefficient between the prices and the number of flash drives sold.
(ii) Use to test the relationship between x and Y.
BTL -6 Creating
6(a).
What are the assumptions made by the regression model in estimating the
parameters and in significance testing?
BTL -6 Creating
6(b).
The equations of two variables X and Y as follows 3X+2Y-26 =0, 6X+Y-
31=0 Find the means, regression coefficient & coefficient of correlation.
BTL -4 Analyzing
7.
Promotional expenses and sales data for an equipment manufacturer are as
follows. Calculate the correlation coefficient and comment
Promotional expenses in Lakhs 7 10 9 4 11 5 3
Sales in Units 12 14 13 5 15 7 4
BTL -3 Applying
8(a).
A gas company has supplied 18,20,21,25 and 26 billion cubic feet f gas,
respectively, for the years 2004 to 2008.
(i) Find the estimating equation that best describes these data.
(ii) Calculate the percentage of trend.
BTL -3 Applying
8(b).
From the question 8(a)
(i)Calculate the relative cyclical residuals
(ii)Find the year in which the fluctuation is maximum
BTL-5 Evaluating
9.
Given that
? ? ? ? ?
? ? ? ? ? 3467. XY and 5506, Y 220, Y 2288, X 130, X
2 2
BTL -6 Creating
23
Compute correlation coefficient and regression equation of X on Y.
10.
(i) This no. of faculty-owned person computer at the University of Ohm
increased dramatically between 1993 & 1995
(ii) Year : 1990 1991 1992 1993 1994 1995
(iii) No. of PCs : 50 110 550 1020 1950 3710
(iv) i. Develop a linear estimating equation that best describes these data
(v) ii. Develop a second-degree estimating equation that best describes these
data.
(vi) iii. Estimate the no. of PCs that will be in use at the university in 1999, using
both equation.
iv. If there are 8000 faculty members at the university, which equation is the
better predictor? Why?
BTL -4 Analyzing
11.
Campus stores has been selling the believe it or not. Wonders of statistics
study guide for 12 semesters and would like to estimate the relationship
between sales and no. of sections of elementary statistics taught in each
semester. The following data have been collection:
Sales(un
its)
33 38 24 61 52 45 65 82 29 63 50 79
No. of
sections
3 7 6 6 19 12 12 13 12 13 14 15
i. Develop the estimating equation that best fits the data.
Calculate the sample coefficient of determination and the sample coefficient
of correlation
BTL -6 Creating
12(a).
A coffee shop owner believes that the sales of coffee at his coffee shop
depend upon the weather. He has taken a sample of 6 days. The results of the
sample are given below
Cups of Coffee sold Temperature
350 50
200 60
210 70
100 80
60 90
40 100
(i) Which variable is the dependent variable?
(ii) Compute the least square estimated line
(iii) Compute the correlation coefficient between temperature and the sales of
coffee. Predict sales of a 90 degree day.
BTL -3 Applying
12(b).
From the question 12(a)
(i)Compute the correlation coefficient between temperature and the sales of
coffee.
(ii)Predict sales of a 90 degree day.
BTL -6 Creating
13.
X independent variable 80 120 90 240 130 370 100 160
Y independent variable 36 25 33 15 28 19 20 22
(i) Develop a regression equation that best describes this data.
(ii) Calculate karl-pearson correlation coefficient.
BTL -3 Applying
14.
From the following data, find the equations of the regression lines
Marks in Maths Marks in English
Mean 62.5 39
S.D 9.5 10
BTL -2 Understanding
24
Coefficient of correlation between marks in Maths & English = 0.60
i. Estimate the marks in English when marks in Maths is 70
ii. Estimate the marks in Maths corresponding to 54 marks in
English
PART C
1.
Given below are five observations collected in a regression study on two
variables, x and y
X 2 3 4 5 6
Y 4 4 3 2 1
(i)Develop the least square estimated regression equation.
(ii)Compute the correlation co-efficienent.
BTL -1 Remembering
2.
What are assumption made by the regression model in estimating the
parameters and in significance testing.
BTL -1
Remembering
3.
In what ways can regression analysis to be used?
BTL-2 Understanding
4.
Find the correlation coefficient of X and Y
X 30 32 35 40 48 50 52 55 57 61
Y 1 0 2 5 2 4 6 5 7 8
BTL -4 Analyzing
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This post was last modified on 29 February 2020