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

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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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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This post was last modified on 19 February 2020