Download GTU (Gujarat Technological University) MBA (Master of Business Administration) 2015 Winter 1st Sem 2810007 Quantitative Analysis I Previous Question Paper

Seat No.: ________ Enrolment No.___________

GUJARAT TECHNOLOGICAL UNIVERSITY

MBA ? SEMESTER 01? ? EXAMINATION ? WINTER 2015

Subject Code:2810007 Date: 28/12/2015

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.

4. Scientific calculator & statistical table (Z, t, F & chi square) are permitted.

Q.1 (a) Answer all the following multiple choice questions. 06

1. When a person collects information from the entire population, this is called a _______.

A. Sample B. Census

C. Statistics D. Parameter

2. The probability of committing a Type I error is called _______.

A. The level of significance B. Beta

C. The power of the test D. Sampling error

3. Which of the following nonrandom sampling technique is similar to stratified sampling?

A. Judgment sampling B. Quota sampling

C. Convenience sampling D. Systematic sampling

4. In a chi-square goodness-of-fit test, actual frequencies are also called _______ frequencies.

A. Calculated B. Expected

C. Theoretical D. Observed

5. In regression analysis, the independent variable is also known as the _______.

A. Decision variable B. Response variable

C. Controlled variable D. Explanatory variable

6. Analysis of variance tests use the _______.

A. t distribution B. Z distribution

C. F distribution D. Exponential distribution

Q.1 (b) Define the following terms. 04

1.

2.

3.

4.

Median

Mutually Exclusive Events

Normal Distribution

Independent Events

Q.1 (c) Explain Chebyshev?s Theorem. 04

Q.2 (a) Kerav Electronics is considering employing one of two training programs. Two groups

were trained for the same task. Group 1 was trained by program A, Group 2, by

program B. For the first group, the times required to train the employees had an

average of 32.11 hours and a variance of 68.09. In the second group, the average was

19.75 hours and the variance was 71.14. Which training program has less relative

variability in its performance?

07

(b) According to the HRD statistics in India, 75 % of the women of 18 to 25 years age

group are student. Suppose 78 % of the women in that age group are married. Suppose

also that 61% of all women of 18 to 25 years age group are married and are student.

What is the probability that a randomly selected woman in that age group is married or

is student? What is the probability that a randomly selected woman in the age group is

07

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Seat No.: ________ Enrolment No.___________

GUJARAT TECHNOLOGICAL UNIVERSITY

MBA ? SEMESTER 01? ? EXAMINATION ? WINTER 2015

Subject Code:2810007 Date: 28/12/2015

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.

4. Scientific calculator & statistical table (Z, t, F & chi square) are permitted.

Q.1 (a) Answer all the following multiple choice questions. 06

1. When a person collects information from the entire population, this is called a _______.

A. Sample B. Census

C. Statistics D. Parameter

2. The probability of committing a Type I error is called _______.

A. The level of significance B. Beta

C. The power of the test D. Sampling error

3. Which of the following nonrandom sampling technique is similar to stratified sampling?

A. Judgment sampling B. Quota sampling

C. Convenience sampling D. Systematic sampling

4. In a chi-square goodness-of-fit test, actual frequencies are also called _______ frequencies.

A. Calculated B. Expected

C. Theoretical D. Observed

5. In regression analysis, the independent variable is also known as the _______.

A. Decision variable B. Response variable

C. Controlled variable D. Explanatory variable

6. Analysis of variance tests use the _______.

A. t distribution B. Z distribution

C. F distribution D. Exponential distribution

Q.1 (b) Define the following terms. 04

1.

2.

3.

4.

Median

Mutually Exclusive Events

Normal Distribution

Independent Events

Q.1 (c) Explain Chebyshev?s Theorem. 04

Q.2 (a) Kerav Electronics is considering employing one of two training programs. Two groups

were trained for the same task. Group 1 was trained by program A, Group 2, by

program B. For the first group, the times required to train the employees had an

average of 32.11 hours and a variance of 68.09. In the second group, the average was

19.75 hours and the variance was 71.14. Which training program has less relative

variability in its performance?

07

(b) According to the HRD statistics in India, 75 % of the women of 18 to 25 years age

group are student. Suppose 78 % of the women in that age group are married. Suppose

also that 61% of all women of 18 to 25 years age group are married and are student.

What is the probability that a randomly selected woman in that age group is married or

is student? What is the probability that a randomly selected woman in the age group is

07

2

married or is student but not both? What is the probability that a randomly selected

woman in that age group is neither married nor student?

OR

(b) In a manufacturing plant, machines A, B, and C all produce the same two parts, W and

M. Of all the parts produced, machine A, produces 35 %, machine B produces 45 %

and machine C produces 20 %. 80 % of the parts made by machine A are part W. 65

% of the parts made by machine B are part W and 30 % of the parts made by machine

C are part W. A part produced by this company is randomly selected and is

determined to be a W part. With the knowledge that it is an W part, revise the

probabilities that the part came from machine A, B or C.

07

Q.3 (a)

1

2

3

4

5

6

7

Classify each of the following as nominal, ordinal, interval and ratio data.

The time required to produce each engine on an assembly line.

The ranking of a company by Fortune 500

Pin code in India

Student enrolment number

The age of each of students

Per capita income of India

Satisfaction level for state transportation service

07

(b) A pendrive company averages 1.2 defective pendrive per packet produced (200

pendrives). The number of defects per packet is Poisson distributed. What is the

probability of selecting a packet and finding no defective pendrives? What is the

probability of finding eight or more defective pendrives in packet? Suppose a

purchaser of these pendrives will quit buying from the company if a packet contains

more than three defective pendrives. What is the probability that a packet contains

more than three defective pendrives?

07

OR

Q.3 (a) Discuss Type I and Type II Errors. 07

(b) Madan Bhatiya, an auditor for a large credit card company, knows that, on average,

the monthly balance of any given customer is Rs. 11200, and the standard deviation is

Rs. 5600. If Mr. Bhatiya audits 50 randomly selected accounts, what is the probability

that the sample average monthly balance is below Rs. 10000? Between Rs. 10000 and

Rs. 13000?

07

Q.4 (a) Explain Co-efficient of Correlation and Co-efficient of Determination. 07

(b) Family transportation costs are usually higher than most people believe because those

costs include various costs. Twenty randomly selected families in four major cities of

Gujarat are asked to use their records to estimate a monthly figure for transportation

cost (in Rs.). Use the data obtained and ANOVA to test whether there is significant

difference in monthly transportation costs for families living in these cities. Use 0.05

significance level.

Ahmedabad 650 480 550 600 675

Baroda 250 525 300 175 500

Surat 850 700 950 780 600

Rajkot 540 450 675 550 600

07

OR

Q.4 (a) Discuss the application of one way analysis of variance with example. 07

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Seat No.: ________ Enrolment No.___________

GUJARAT TECHNOLOGICAL UNIVERSITY

MBA ? SEMESTER 01? ? EXAMINATION ? WINTER 2015

Subject Code:2810007 Date: 28/12/2015

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.

4. Scientific calculator & statistical table (Z, t, F & chi square) are permitted.

Q.1 (a) Answer all the following multiple choice questions. 06

1. When a person collects information from the entire population, this is called a _______.

A. Sample B. Census

C. Statistics D. Parameter

2. The probability of committing a Type I error is called _______.

A. The level of significance B. Beta

C. The power of the test D. Sampling error

3. Which of the following nonrandom sampling technique is similar to stratified sampling?

A. Judgment sampling B. Quota sampling

C. Convenience sampling D. Systematic sampling

4. In a chi-square goodness-of-fit test, actual frequencies are also called _______ frequencies.

A. Calculated B. Expected

C. Theoretical D. Observed

5. In regression analysis, the independent variable is also known as the _______.

A. Decision variable B. Response variable

C. Controlled variable D. Explanatory variable

6. Analysis of variance tests use the _______.

A. t distribution B. Z distribution

C. F distribution D. Exponential distribution

Q.1 (b) Define the following terms. 04

1.

2.

3.

4.

Median

Mutually Exclusive Events

Normal Distribution

Independent Events

Q.1 (c) Explain Chebyshev?s Theorem. 04

Q.2 (a) Kerav Electronics is considering employing one of two training programs. Two groups

were trained for the same task. Group 1 was trained by program A, Group 2, by

program B. For the first group, the times required to train the employees had an

average of 32.11 hours and a variance of 68.09. In the second group, the average was

19.75 hours and the variance was 71.14. Which training program has less relative

variability in its performance?

07

(b) According to the HRD statistics in India, 75 % of the women of 18 to 25 years age

group are student. Suppose 78 % of the women in that age group are married. Suppose

also that 61% of all women of 18 to 25 years age group are married and are student.

What is the probability that a randomly selected woman in that age group is married or

is student? What is the probability that a randomly selected woman in the age group is

07

2

married or is student but not both? What is the probability that a randomly selected

woman in that age group is neither married nor student?

OR

(b) In a manufacturing plant, machines A, B, and C all produce the same two parts, W and

M. Of all the parts produced, machine A, produces 35 %, machine B produces 45 %

and machine C produces 20 %. 80 % of the parts made by machine A are part W. 65

% of the parts made by machine B are part W and 30 % of the parts made by machine

C are part W. A part produced by this company is randomly selected and is

determined to be a W part. With the knowledge that it is an W part, revise the

probabilities that the part came from machine A, B or C.

07

Q.3 (a)

1

2

3

4

5

6

7

Classify each of the following as nominal, ordinal, interval and ratio data.

The time required to produce each engine on an assembly line.

The ranking of a company by Fortune 500

Pin code in India

Student enrolment number

The age of each of students

Per capita income of India

Satisfaction level for state transportation service

07

(b) A pendrive company averages 1.2 defective pendrive per packet produced (200

pendrives). The number of defects per packet is Poisson distributed. What is the

probability of selecting a packet and finding no defective pendrives? What is the

probability of finding eight or more defective pendrives in packet? Suppose a

purchaser of these pendrives will quit buying from the company if a packet contains

more than three defective pendrives. What is the probability that a packet contains

more than three defective pendrives?

07

OR

Q.3 (a) Discuss Type I and Type II Errors. 07

(b) Madan Bhatiya, an auditor for a large credit card company, knows that, on average,

the monthly balance of any given customer is Rs. 11200, and the standard deviation is

Rs. 5600. If Mr. Bhatiya audits 50 randomly selected accounts, what is the probability

that the sample average monthly balance is below Rs. 10000? Between Rs. 10000 and

Rs. 13000?

07

Q.4 (a) Explain Co-efficient of Correlation and Co-efficient of Determination. 07

(b) Family transportation costs are usually higher than most people believe because those

costs include various costs. Twenty randomly selected families in four major cities of

Gujarat are asked to use their records to estimate a monthly figure for transportation

cost (in Rs.). Use the data obtained and ANOVA to test whether there is significant

difference in monthly transportation costs for families living in these cities. Use 0.05

significance level.

Ahmedabad 650 480 550 600 675

Baroda 250 525 300 175 500

Surat 850 700 950 780 600

Rajkot 540 450 675 550 600

07

OR

Q.4 (a) Discuss the application of one way analysis of variance with example. 07

3

(b) A Brand manager of Chocolate company is concerned that his brand?s share may be

unevenly distributed throughout 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. At 0.05 significance level, test

whether brand share is the same across the four regions.

Region

North West East South Total

Purchase the brand 40 55 45 50 190

Do not purchase 60 45 55 50 210

07

Q.5 Dr. Trivedi, the dean of students at KR institute, is wondering about grade distribution

at the institute. He has heard grumblings that the GPAs in the Business School are

about 0.25 lower than those in the institute of Arts and Sciences. A quick random

sampling produced the following GPAs.

Business Institute: 2.86, 2.77, 3.18, 2.80, 3.14, 2.87, 3.19, 3.24, 2.91, 3.00, 2.83

Arts and Sciences: 3.35, 3.32, 3.36, 3.63, 3.41, 3.37, 3.45, 3.43, 3.44, 3.17, 3.26,

Institute 3.18, 3.41

Do these data indicate that there is a factual basis for the grumblings? State and test

appropriate hypotheses at alpha=0.02.

14

OR

Q.5 Recent study reports that the average price for a gallon of self serve regular unleaded

gasoline is Rs. 116. Mr. Gupta believes that the figure is higher in your area of the

country. He decided to test this claim for part of the Maharshtra by randomly calling

gasoline stations. His random survey of 25 stations produces the following prices in

Rs.

127 129 116 120 137 120 123 119 120 124 116 107 127 109 135

115 123 114 105 135 121 114 114 107 110

Assume gasoline prices for a region are normally distributed. Do the data you obtained

provide enough evidence to reject the claim? Use a 1% level of significance.

14

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This post was last modified on 19 February 2020