Download GTU MBA 2015 Winter 1st Sem 810007 Quantitative Analysis Question Paper

Download GTU (Gujarat Technological University) MBA (Master of Business Administration) 2015 Winter 1st Sem 810007 Quantitative Analysis Previous Question Paper

1
Seat No.: ________ Enrolment No.___________

GUJARAT TECHNOLOGICAL UNIVERSITY
MBA - SEMESTER ? I EXAMINATIONS ? WINTER 2015

Subject Code: 810007 Date: 28/12/2015
Subject Name: Quantitative Analysis
Time: 10:30 AM to 1:30 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) Define Statistics. What is the use of statistics in business? 07
(b) Calculate the mean, mode and the variance of the given sample data.
Class Interval Frequency
10 ? 15 6
15 ? 20 22
20 ? 25 35
25 ? 30 29
30 ? 35 16
35 ? 40 8
40 ? 45 4
45 ? 50 2

07

Q.2 (a) In a manufacturing plant, machine A produces 10% of a certain product,
machine B produces 40% of this product, and machine C produces 50% of this
product. Five percent of machine A products are defective, 12% of machine B
products are defective, and 8% of machine C products are defective. The
company inspector has just sampled a product from this plant and has found it
to be defective. Determine the revised probabilities that the sampled product
was produced by machine A, machine B, or machine C.
07
(b) The U.S. Bureau of Economic Statistics reports that the average annual salary in
the metropolitan Boston area is $50,542. Suppose annual salaries in the
metropolitan Boston area are normally distributed with a standard deviation of
$4,246. A Boston worker is randomly selected.
1. What is the probability that the worker?s annual salary is more than
$60,000?
2. What is the probability that the worker?s annual salary is less than
$45,000?
3. What is the probability that the worker?s annual salary is more than
$40,000?
4. What is the probability that the worker?s annual salary is between
$44,000 and $52,000?
07
OR
(b) The following lists the number of fatal accidents by scheduled commercial
airlines over a 17-year period according to the Air Transport Association of
America. Using these data, compute the mean, median, and mode. What is the
value of the third quartile? Determine P11, P35, P58, and P67.
4 4 4 1 4 2 4 3 8 6 4 4 1 4 2 3 3
07

Q.3 (a) Define & explain different random sampling techniques. 07
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1
Seat No.: ________ Enrolment No.___________

GUJARAT TECHNOLOGICAL UNIVERSITY
MBA - SEMESTER ? I EXAMINATIONS ? WINTER 2015

Subject Code: 810007 Date: 28/12/2015
Subject Name: Quantitative Analysis
Time: 10:30 AM to 1:30 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) Define Statistics. What is the use of statistics in business? 07
(b) Calculate the mean, mode and the variance of the given sample data.
Class Interval Frequency
10 ? 15 6
15 ? 20 22
20 ? 25 35
25 ? 30 29
30 ? 35 16
35 ? 40 8
40 ? 45 4
45 ? 50 2

07

Q.2 (a) In a manufacturing plant, machine A produces 10% of a certain product,
machine B produces 40% of this product, and machine C produces 50% of this
product. Five percent of machine A products are defective, 12% of machine B
products are defective, and 8% of machine C products are defective. The
company inspector has just sampled a product from this plant and has found it
to be defective. Determine the revised probabilities that the sampled product
was produced by machine A, machine B, or machine C.
07
(b) The U.S. Bureau of Economic Statistics reports that the average annual salary in
the metropolitan Boston area is $50,542. Suppose annual salaries in the
metropolitan Boston area are normally distributed with a standard deviation of
$4,246. A Boston worker is randomly selected.
1. What is the probability that the worker?s annual salary is more than
$60,000?
2. What is the probability that the worker?s annual salary is less than
$45,000?
3. What is the probability that the worker?s annual salary is more than
$40,000?
4. What is the probability that the worker?s annual salary is between
$44,000 and $52,000?
07
OR
(b) The following lists the number of fatal accidents by scheduled commercial
airlines over a 17-year period according to the Air Transport Association of
America. Using these data, compute the mean, median, and mode. What is the
value of the third quartile? Determine P11, P35, P58, and P67.
4 4 4 1 4 2 4 3 8 6 4 4 1 4 2 3 3
07

Q.3 (a) Define & explain different random sampling techniques. 07
2
(b) What is the first big change that American drivers made due to higher gas
prices? According to an Access America survey, 30% said that it was cutting
recreational driving. However, 27% said that it was consolidating or reducing
errands. If these figures are true for all American drivers and if 20 such drivers
are randomly sampled and asked what is the first big change they made due to
higher gas prices?
1. What is the probability that exactly 8 said that it was consolidating or
reducing errands?
2. What is the probability that none of them said that it was cutting
recreational driving?
3. What is the probability that more than 7 said that it was cutting
recreational driving?
07
OR
Q.3 (a) What is Hypothesis? Explain different types of hypothesis. 07
(b) Use the data given to test the following hypothesis
H0 : ? = 1200 Ha : ? > 1200
Sample Mean = 1215
Size of Sample = 113
Population standard deviation = 100
Level of significance = 0.10
07

Q.4 (a) Develop a one-way ANOVA on the following data.
1 2 3 4
113 120 132 122
121 127 130 118
117 125 129 125
110 129 135 125
Determine the observed F value. Compare it to the critical F value and decide
whether to reject the null hypothesis. Use a 5% level of significance.
07
(b) Explain the steps of hypothesis testing procedure. 07
OR
Q.4 (a) Use a chi-square goodness-of-fit test to determine whether the observed
frequencies are distributed the same as the expected frequencies (a = 0.05).
Category 1 2 3 4 5 6
Fo 53 37 32 28 18 15
Fe 64 42 33 22 10 8

07
(b) A sample of 87 professional working women showed that the average amount
paid annually into a private pension fund per person was $3352. The population
standard deviation is $1100. A sample of 76 professional working men showed
that the average amount paid annually into a private pension fund per person
was $5727, with a population standard deviation of $1700. A women?s activist
group wants to ?prove? that women do not pay as much per year as men into
private pension funds. If they use = 0.01 and these sample data, will they be
able to reject a null hypothesis that women annually pay the same as or more
than men into private pension funds? Use the eight-step hypothesis-testing
process.
07

Q.5 (a) Determine the equation of the regression line for the following data.
X 12 21 28 8 20
Y 17 15 22 19 24

07
(b) Write a short note on Index numbers. 07
OR

Q.5 (a) What is regression analysis? Discuss the application of regression in Business
Decisions.
07
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1
Seat No.: ________ Enrolment No.___________

GUJARAT TECHNOLOGICAL UNIVERSITY
MBA - SEMESTER ? I EXAMINATIONS ? WINTER 2015

Subject Code: 810007 Date: 28/12/2015
Subject Name: Quantitative Analysis
Time: 10:30 AM to 1:30 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) Define Statistics. What is the use of statistics in business? 07
(b) Calculate the mean, mode and the variance of the given sample data.
Class Interval Frequency
10 ? 15 6
15 ? 20 22
20 ? 25 35
25 ? 30 29
30 ? 35 16
35 ? 40 8
40 ? 45 4
45 ? 50 2

07

Q.2 (a) In a manufacturing plant, machine A produces 10% of a certain product,
machine B produces 40% of this product, and machine C produces 50% of this
product. Five percent of machine A products are defective, 12% of machine B
products are defective, and 8% of machine C products are defective. The
company inspector has just sampled a product from this plant and has found it
to be defective. Determine the revised probabilities that the sampled product
was produced by machine A, machine B, or machine C.
07
(b) The U.S. Bureau of Economic Statistics reports that the average annual salary in
the metropolitan Boston area is $50,542. Suppose annual salaries in the
metropolitan Boston area are normally distributed with a standard deviation of
$4,246. A Boston worker is randomly selected.
1. What is the probability that the worker?s annual salary is more than
$60,000?
2. What is the probability that the worker?s annual salary is less than
$45,000?
3. What is the probability that the worker?s annual salary is more than
$40,000?
4. What is the probability that the worker?s annual salary is between
$44,000 and $52,000?
07
OR
(b) The following lists the number of fatal accidents by scheduled commercial
airlines over a 17-year period according to the Air Transport Association of
America. Using these data, compute the mean, median, and mode. What is the
value of the third quartile? Determine P11, P35, P58, and P67.
4 4 4 1 4 2 4 3 8 6 4 4 1 4 2 3 3
07

Q.3 (a) Define & explain different random sampling techniques. 07
2
(b) What is the first big change that American drivers made due to higher gas
prices? According to an Access America survey, 30% said that it was cutting
recreational driving. However, 27% said that it was consolidating or reducing
errands. If these figures are true for all American drivers and if 20 such drivers
are randomly sampled and asked what is the first big change they made due to
higher gas prices?
1. What is the probability that exactly 8 said that it was consolidating or
reducing errands?
2. What is the probability that none of them said that it was cutting
recreational driving?
3. What is the probability that more than 7 said that it was cutting
recreational driving?
07
OR
Q.3 (a) What is Hypothesis? Explain different types of hypothesis. 07
(b) Use the data given to test the following hypothesis
H0 : ? = 1200 Ha : ? > 1200
Sample Mean = 1215
Size of Sample = 113
Population standard deviation = 100
Level of significance = 0.10
07

Q.4 (a) Develop a one-way ANOVA on the following data.
1 2 3 4
113 120 132 122
121 127 130 118
117 125 129 125
110 129 135 125
Determine the observed F value. Compare it to the critical F value and decide
whether to reject the null hypothesis. Use a 5% level of significance.
07
(b) Explain the steps of hypothesis testing procedure. 07
OR
Q.4 (a) Use a chi-square goodness-of-fit test to determine whether the observed
frequencies are distributed the same as the expected frequencies (a = 0.05).
Category 1 2 3 4 5 6
Fo 53 37 32 28 18 15
Fe 64 42 33 22 10 8

07
(b) A sample of 87 professional working women showed that the average amount
paid annually into a private pension fund per person was $3352. The population
standard deviation is $1100. A sample of 76 professional working men showed
that the average amount paid annually into a private pension fund per person
was $5727, with a population standard deviation of $1700. A women?s activist
group wants to ?prove? that women do not pay as much per year as men into
private pension funds. If they use = 0.01 and these sample data, will they be
able to reject a null hypothesis that women annually pay the same as or more
than men into private pension funds? Use the eight-step hypothesis-testing
process.
07

Q.5 (a) Determine the equation of the regression line for the following data.
X 12 21 28 8 20
Y 17 15 22 19 24

07
(b) Write a short note on Index numbers. 07
OR

Q.5 (a) What is regression analysis? Discuss the application of regression in Business
Decisions.
07
3
(b) Use the decision table given below to select decision alternative with below
mention decision making criteria.
Decision
Alternatives

State of Nature
S1 S2 S3
D1 250 175 -25
D2 110 100 70
D3 390 140 -80
(1) Use the maximax criterion to determine which decision alternative to select.
(2) Use the maximin criterion to determine which decision alternative to select.
07


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