# Download GTU MBA 2018 Summer 1st Sem 2810007 Quantitative Analysis I Question Paper

1

Seat No.: ________ Enrolment No.___________

GUJARAT TECHNOLOGICAL UNIVERSITY
MBA ? SEMESTER I ? EXAMINATION ? SUMMER 2018

Subject Code:2810007 Date:04/05/2018
Subject Name: Quantitative Analysis-I
Time: 10:30 AM to 01:30 PM Total Marks: 70

Instructions:
1. Attempt all questions.
2. Make suitable assumptions wherever necessary.
3. Figures to the right indicate full marks.

Q.1 (a) Answer the following questions 6

1. What is the lowest level of data measurement?
A. Nominal B. Ordinal
C. Interval D. Ratio

2. Which of the following is not a probability assigning technique?
A. Classical method B. Subjective Probability method
C. Relative frequency method D Cumulative frequency method

3. If the standard deviation of a variable is expressed as a percentage of mean, the
measure is called______

A. Relative Variation B. Quartile deviation
C. Coefficient of variation D. Mean Absolute deviation

4.
The value of r
2
for particular situation is 0.81. What is the coefficient of
correlation?

A. Cannot be determined B. 0.81
C. 0.9 D. 0.09

5. A random variable that can assume any numerical value over a range is
A. Classical variable B. Discrete variable
C. Continuous variable D. Independent Variable

6. When a distribution is symmetrical and has one mode, the highest point on the curve
is called:

A. All of these B. Mode
C. Median D. Mean

Q.1
(b) What are independent and mutually exclusive events? Distinguish with
examples
4

Q.1 (c) Explain Central Limit theorem in detail. 4

Q.2 (a) What is statistics? Discuss applications of it in various fields of management. 7
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1

Seat No.: ________ Enrolment No.___________

GUJARAT TECHNOLOGICAL UNIVERSITY
MBA ? SEMESTER I ? EXAMINATION ? SUMMER 2018

Subject Code:2810007 Date:04/05/2018
Subject Name: Quantitative Analysis-I
Time: 10:30 AM to 01:30 PM Total Marks: 70

Instructions:
1. Attempt all questions.
2. Make suitable assumptions wherever necessary.
3. Figures to the right indicate full marks.

Q.1 (a) Answer the following questions 6

1. What is the lowest level of data measurement?
A. Nominal B. Ordinal
C. Interval D. Ratio

2. Which of the following is not a probability assigning technique?
A. Classical method B. Subjective Probability method
C. Relative frequency method D Cumulative frequency method

3. If the standard deviation of a variable is expressed as a percentage of mean, the
measure is called______

A. Relative Variation B. Quartile deviation
C. Coefficient of variation D. Mean Absolute deviation

4.
The value of r
2
for particular situation is 0.81. What is the coefficient of
correlation?

A. Cannot be determined B. 0.81
C. 0.9 D. 0.09

5. A random variable that can assume any numerical value over a range is
A. Classical variable B. Discrete variable
C. Continuous variable D. Independent Variable

6. When a distribution is symmetrical and has one mode, the highest point on the curve
is called:

A. All of these B. Mode
C. Median D. Mean

Q.1
(b) What are independent and mutually exclusive events? Distinguish with
examples
4

Q.1 (c) Explain Central Limit theorem in detail. 4

Q.2 (a) What is statistics? Discuss applications of it in various fields of management. 7
2

(b) Alpha Mall is the target for many shoplifters in the past month, but owing to
increased security precautions, 250 shoplifters have been caught. The data are
tabulated as follow:
Gender
First-Time
Offender
Repeat Offender
Male 60 70
Female 70 50
i. The Probability that shoplifter is both Female and a first time
offender
ii. The Probability that shoplifter is a first time offender, given that he
is a male
iii. The Probability that shoplifter is a female, given that shoplifter is
repeat offender

7
OR

(b) An organization is planning a leisure trip for its employees. The only thing
which can cancel the trip is thunderstorm. The weather service has predicted
Dry conditions with probability 0.2, Moist Conditions with probability 0.45 and
Wet conditions with probability 0.35.If the probability of a thunderstorm given
dry conditions is 0.3, given moist conditions is 0.6, and given wet conditions is
0.8. If a thunderstorm occurs,
(i) What is the probability that moist conditions were in effect?
(ii)What is the probability that wet conditions were in effect?
(iii)What is the probability that dry conditions were in effect? (use Bayesian
Analysis)

7
Q.3 (a) Discuss various types of probability and non probability sampling techniques 7
(b) One of the earliest applications of the Poisson Distribution was in analyzing
incoming calls to a telephone switch-board. Analysts generally believe that
random phone calls are Poisson distributed. Suppose phone calls to a switch-
board arrive at an average rate of 2.4 calls per minute.
a) If an operator wants to take a 1-minute break, what is the probability
that there will be no calls during a 1-minute interval?
b) If an operator can handle at most five calls per minute, what is the
probability that the operator will be unable to handle the calls in any
1-minute interval?
c) What is the probability that exactly three calls will arrive in a 2-
minute interval?
d) What is the probability that one or fewer calls will arrive in a 15-
second interval?

7
OR
Q.3
(a) Explain in detail the characteristics of Uniform and hyper-geometric
distribution
7
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1

Seat No.: ________ Enrolment No.___________

GUJARAT TECHNOLOGICAL UNIVERSITY
MBA ? SEMESTER I ? EXAMINATION ? SUMMER 2018

Subject Code:2810007 Date:04/05/2018
Subject Name: Quantitative Analysis-I
Time: 10:30 AM to 01:30 PM Total Marks: 70

Instructions:
1. Attempt all questions.
2. Make suitable assumptions wherever necessary.
3. Figures to the right indicate full marks.

Q.1 (a) Answer the following questions 6

1. What is the lowest level of data measurement?
A. Nominal B. Ordinal
C. Interval D. Ratio

2. Which of the following is not a probability assigning technique?
A. Classical method B. Subjective Probability method
C. Relative frequency method D Cumulative frequency method

3. If the standard deviation of a variable is expressed as a percentage of mean, the
measure is called______

A. Relative Variation B. Quartile deviation
C. Coefficient of variation D. Mean Absolute deviation

4.
The value of r
2
for particular situation is 0.81. What is the coefficient of
correlation?

A. Cannot be determined B. 0.81
C. 0.9 D. 0.09

5. A random variable that can assume any numerical value over a range is
A. Classical variable B. Discrete variable
C. Continuous variable D. Independent Variable

6. When a distribution is symmetrical and has one mode, the highest point on the curve
is called:

A. All of these B. Mode
C. Median D. Mean

Q.1
(b) What are independent and mutually exclusive events? Distinguish with
examples
4

Q.1 (c) Explain Central Limit theorem in detail. 4

Q.2 (a) What is statistics? Discuss applications of it in various fields of management. 7
2

(b) Alpha Mall is the target for many shoplifters in the past month, but owing to
increased security precautions, 250 shoplifters have been caught. The data are
tabulated as follow:
Gender
First-Time
Offender
Repeat Offender
Male 60 70
Female 70 50
i. The Probability that shoplifter is both Female and a first time
offender
ii. The Probability that shoplifter is a first time offender, given that he
is a male
iii. The Probability that shoplifter is a female, given that shoplifter is
repeat offender

7
OR

(b) An organization is planning a leisure trip for its employees. The only thing
which can cancel the trip is thunderstorm. The weather service has predicted
Dry conditions with probability 0.2, Moist Conditions with probability 0.45 and
Wet conditions with probability 0.35.If the probability of a thunderstorm given
dry conditions is 0.3, given moist conditions is 0.6, and given wet conditions is
0.8. If a thunderstorm occurs,
(i) What is the probability that moist conditions were in effect?
(ii)What is the probability that wet conditions were in effect?
(iii)What is the probability that dry conditions were in effect? (use Bayesian
Analysis)

7
Q.3 (a) Discuss various types of probability and non probability sampling techniques 7
(b) One of the earliest applications of the Poisson Distribution was in analyzing
incoming calls to a telephone switch-board. Analysts generally believe that
random phone calls are Poisson distributed. Suppose phone calls to a switch-
board arrive at an average rate of 2.4 calls per minute.
a) If an operator wants to take a 1-minute break, what is the probability
that there will be no calls during a 1-minute interval?
b) If an operator can handle at most five calls per minute, what is the
probability that the operator will be unable to handle the calls in any
1-minute interval?
c) What is the probability that exactly three calls will arrive in a 2-
minute interval?
d) What is the probability that one or fewer calls will arrive in a 15-
second interval?

7
OR
Q.3
(a) Explain in detail the characteristics of Uniform and hyper-geometric
distribution
7
3

(b) The lifetime of certain kinds of electronic devices have a mean of 300 hours
and the standard deviation of 25 hours. Assuming that the distribution of these
lifetimes which are measured to the nearest hour can be approximated closely
with a normal distribution.

i. What is the probability of lifetime of any one of these devices to be
more than 350 hours?
ii. What percentage will have lifetimes of 300 or less?

iii. What percentage will have lifetimes from 220 to 260 hours?

7

Q.4 (a) What is Hypothesis testing? Discuss steps in detail. 7

(b) A Cable TV network company wants to provide modern facility to its
consumers. The Company has a five year old data, which reveals that the
average household income is Rs 120000. The company believes that the
average income might have changed over the period. To verify the claim, it
takes a sample of 40 households. From the sample, it is observed that the
average income is 125000. From the historical data, population standard
deviation is obtained as 1200. Use alpha as 0.05 to test the claim.
7

OR

Q.4
(a) What are Type I and type II errors? Discuss in relation to level of significance.

7

(b) An electronic goods company arranged a special training programme for its
employees. The company wants to measure the change in the attitude of its
employees after the training. The company selected a random sample of
10employees. The scores by these employees are given in the table. Use ?=
0.10, to determine whether there is a significant change in the attitude of
employees after the training programme.

Employee 1 2 3 4 5 6 7 8 9 10
Before 25 26 28 22 20 30 22 20 21 24
After 32 30 32 34 32 28 25 30 25 28

7

Q.5 The following table gives the number of good and defective parts produced by
each of the three shifts in a factory.

Shift Good Defective Total
Day 900 130 1030
Evening 700 170 870
Night 400 200 600
Total 2000 500 2500

A. Is there any association between the shift and the quality of the parts
produced? Use 0.05 level of significance.
B. Discuss various applications of Chi Square test with illustrations.
14

OR

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1

Seat No.: ________ Enrolment No.___________

GUJARAT TECHNOLOGICAL UNIVERSITY
MBA ? SEMESTER I ? EXAMINATION ? SUMMER 2018

Subject Code:2810007 Date:04/05/2018
Subject Name: Quantitative Analysis-I
Time: 10:30 AM to 01:30 PM Total Marks: 70

Instructions:
1. Attempt all questions.
2. Make suitable assumptions wherever necessary.
3. Figures to the right indicate full marks.

Q.1 (a) Answer the following questions 6

1. What is the lowest level of data measurement?
A. Nominal B. Ordinal
C. Interval D. Ratio

2. Which of the following is not a probability assigning technique?
A. Classical method B. Subjective Probability method
C. Relative frequency method D Cumulative frequency method

3. If the standard deviation of a variable is expressed as a percentage of mean, the
measure is called______

A. Relative Variation B. Quartile deviation
C. Coefficient of variation D. Mean Absolute deviation

4.
The value of r
2
for particular situation is 0.81. What is the coefficient of
correlation?

A. Cannot be determined B. 0.81
C. 0.9 D. 0.09

5. A random variable that can assume any numerical value over a range is
A. Classical variable B. Discrete variable
C. Continuous variable D. Independent Variable

6. When a distribution is symmetrical and has one mode, the highest point on the curve
is called:

A. All of these B. Mode
C. Median D. Mean

Q.1
(b) What are independent and mutually exclusive events? Distinguish with
examples
4

Q.1 (c) Explain Central Limit theorem in detail. 4

Q.2 (a) What is statistics? Discuss applications of it in various fields of management. 7
2

(b) Alpha Mall is the target for many shoplifters in the past month, but owing to
increased security precautions, 250 shoplifters have been caught. The data are
tabulated as follow:
Gender
First-Time
Offender
Repeat Offender
Male 60 70
Female 70 50
i. The Probability that shoplifter is both Female and a first time
offender
ii. The Probability that shoplifter is a first time offender, given that he
is a male
iii. The Probability that shoplifter is a female, given that shoplifter is
repeat offender

7
OR

(b) An organization is planning a leisure trip for its employees. The only thing
which can cancel the trip is thunderstorm. The weather service has predicted
Dry conditions with probability 0.2, Moist Conditions with probability 0.45 and
Wet conditions with probability 0.35.If the probability of a thunderstorm given
dry conditions is 0.3, given moist conditions is 0.6, and given wet conditions is
0.8. If a thunderstorm occurs,
(i) What is the probability that moist conditions were in effect?
(ii)What is the probability that wet conditions were in effect?
(iii)What is the probability that dry conditions were in effect? (use Bayesian
Analysis)

7
Q.3 (a) Discuss various types of probability and non probability sampling techniques 7
(b) One of the earliest applications of the Poisson Distribution was in analyzing
incoming calls to a telephone switch-board. Analysts generally believe that
random phone calls are Poisson distributed. Suppose phone calls to a switch-
board arrive at an average rate of 2.4 calls per minute.
a) If an operator wants to take a 1-minute break, what is the probability
that there will be no calls during a 1-minute interval?
b) If an operator can handle at most five calls per minute, what is the
probability that the operator will be unable to handle the calls in any
1-minute interval?
c) What is the probability that exactly three calls will arrive in a 2-
minute interval?
d) What is the probability that one or fewer calls will arrive in a 15-
second interval?

7
OR
Q.3
(a) Explain in detail the characteristics of Uniform and hyper-geometric
distribution
7
3

(b) The lifetime of certain kinds of electronic devices have a mean of 300 hours
and the standard deviation of 25 hours. Assuming that the distribution of these
lifetimes which are measured to the nearest hour can be approximated closely
with a normal distribution.

i. What is the probability of lifetime of any one of these devices to be
more than 350 hours?
ii. What percentage will have lifetimes of 300 or less?

iii. What percentage will have lifetimes from 220 to 260 hours?

7

Q.4 (a) What is Hypothesis testing? Discuss steps in detail. 7

(b) A Cable TV network company wants to provide modern facility to its
consumers. The Company has a five year old data, which reveals that the
average household income is Rs 120000. The company believes that the
average income might have changed over the period. To verify the claim, it
takes a sample of 40 households. From the sample, it is observed that the
average income is 125000. From the historical data, population standard
deviation is obtained as 1200. Use alpha as 0.05 to test the claim.
7

OR

Q.4
(a) What are Type I and type II errors? Discuss in relation to level of significance.

7

(b) An electronic goods company arranged a special training programme for its
employees. The company wants to measure the change in the attitude of its
employees after the training. The company selected a random sample of
10employees. The scores by these employees are given in the table. Use ?=
0.10, to determine whether there is a significant change in the attitude of
employees after the training programme.

Employee 1 2 3 4 5 6 7 8 9 10
Before 25 26 28 22 20 30 22 20 21 24
After 32 30 32 34 32 28 25 30 25 28

7

Q.5 The following table gives the number of good and defective parts produced by
each of the three shifts in a factory.

Shift Good Defective Total
Day 900 130 1030
Evening 700 170 870
Night 400 200 600
Total 2000 500 2500

A. Is there any association between the shift and the quality of the parts
produced? Use 0.05 level of significance.
B. Discuss various applications of Chi Square test with illustrations.
14

OR

4
Q.5 As the head of the department of a consumer research organization, you have
the responsibility for testing and comparing the lifetime of four brands of
electric bulbs. Suppose you test the lifetime of the three electric bulbs of each
of the four brands. The data is shown below, each entry representing the
lifetime of an electric bulb, measured in hundreds of hours.

Brand
A B C D
20 25 24 23
19 23 20 20
21 21 22 20

A. Use ANOVA to infer, whether the mean lifetimes of the four brands of
electric bulbs are equal? ?=0.05
B. It can be inferred that more the price of the electric bulb, more will be the
life time of it. Discuss the concept of correlation and regression techniques for
finding the relationship between price and lifetime.
14

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