1

POM 212 Business Statistics

Homework Assignment-4

Note: The homework is due on the day of Test-4.

Chapter-10 Problems:

Problem-1

In order to estimate the difference between the average Miles per Gallon of two different models of

automobiles, samples are taken and the following information is collected.

Model A Model B

Sample Size 50 55

Sample Mean 32 35

Sample Variance 9 10

a. At 95% confidence develop an interval estimate for the difference between the average

Miles per Gallon for the two models.

b. Is there conclusive evidence to indicate that one model gets a higher MPG than the

other? Why or why not? Explain.

Problem-2

Independent random samples taken on two university campuses revealed the following information

concerning the average amount of money spent on textbooks during the fall semester.

University A University B

Sample Size 50 40

Average Purchase $280 $250

Standard Deviation $20 $23

At 95% confidence test to determine if, on the average, students at University A spend more on textbooks

then the students at University B.

Problem-3

Two independent random samples of annual starting salaries for individuals with master’s and bachelor’s

degrees in business were taken. Use the data shown below and provide a 95% confidence interval

estimate for the difference between the salaries of the two groups.

2

Masters Degree Bachelors Degree

Sample Size 14 12

Sample Mean $58,000 $55,000

Sample Standard Deviation $ 2,400 $ 2,000

Problem-4

The following shows the monthly sales in units of six salespersons before and after a bonus plan was

introduced. At 95% confidence, determine whether the bonus plan has increased sales significantly. (For

the following matched samples, let the difference "d" be: d = after - before.)

Monthly Sales

Salesperson After Before

1 94 90

2 82 84

3 90 84

4 76 70

5 79 80

6 85 80

Problem-5

Allied Corporation is trying to sell its new machines to Ajax. Allied claims that the machine will pay for

itself since the time it takes to produce the product using the new machine is significantly less than the

production time using the old machine. To test the claim, independent random samples were taken from

both machines. You are given the following results.

New Machine Old Machine

Sample Mean 25 23

Sample Variance 27 7.56

Sample Size 45 36

As the statistical advisor to Ajax, would you recommend purchasing Allied's machine? Explain your

answer.

3

Chapter-12 Problems:

Problem-6

Before the presidential debates, it was expected that the percentages of registered voters in favor of

various candidates to be as follows.

Percentages

Democrats 48%

Republicans 38%

Independent 4%

Undecided 10%

After the presidential debates, a random sample of 1200 voters showed that 540 favored the Democratic

candidate; 480 were in favor of the Republican candidate; 40 were in favor of the Independent candidate,

and 140 were undecided. At 95% confidence, test to see if the proportion of voters has changed.

Problem-7

Last school year, in the school of Business Administration, 30% were Accounting majors, 24%

Management majors, 26% Marketing majors, and 20% Economics majors. A sample of 300 students

taken from this year's students of the school showed the following number of students in each major:

Accounting 83

Management 68

Marketing 85

Economics 64

Total 300

Has there been any significant change in the number of students in each major between the last school

year and this school year? Use 95% confidence level.

Problem-8

The personnel department of a large corporation reported sixty resignations during the last year. The

following table groups these resignations according to the season in which they occurred:

Season Number of Resignations

Winter 10

Spring 22

Summer 19

Fall 9

Test to see if the number of resignations is uniform over the four seasons. Use 95% confidence level.

4

Problem-9

A group of 2000 individuals from 3 different cities were asked whether they owned a foreign or a

domestic car. The following contingency table shows the results of the survey.

CITY

Type of Car Detroit Atlanta Denver Total

Domestic 80 200 520 800

Foreign 120 600 480 1200

Total 200 800 1000 2000

With 95% confidence level, test to determine if the type of car purchased is independent of the city in

which the purchasers live.

Problem-10

Five hundred randomly selected automobile owners were questioned on the main reason they had

purchased their current automobile. The results are given below.

Styling Engineering Fuel Economy Total

Male 70 130 150 350

Female 30 20 100 150

100 150 250 500

Give your conclusion for this test with 90% confidence level.

Chapter-14 Problems:

Problem-11

The following data represent a company's yearly sales volume and its advertising expenditure over a

period of 8 years.

Year Sales in Millions of Dollars (Y) Advertising in ($10,000) (X)

1994 15 32

1995 16 33

1996 18 35

1997 17 34

1998 16 36

1999 19 37

2000 19 39

2001 24 42

5

a. Develop a scatter diagram of sales versus advertising.

b. Use the method of least squares to compute an estimated regression line between sales

and advertising.

Problem-12

An automobile dealer wants to see if there is a relationship between monthly sales and the interest rate. A

random sample of 4 months was taken. The results of the sample are presented below.

Monthly Sales (Y) Interest Rate (In Percent) (X)

22 9.2

20 7.6

10 10.4

45 5.3

a. Use the method of least squares to compute an estimated regression line.

b. Obtain a measure of how well the estimated regression line fits the data.

Problem-13

Max believes that the sales of coffee at his coffee shop depend upon the weather. He has taken a sample

of 5 days. Below you are given the results of the sample.

Cups of Coffee Sold Temperature

350 50

200 60

210 70

100 80

60 90

40 100

a. Which variable is the dependent variable?

b. Compute the least squares estimated line.

c. Compute the correlation coefficient between temperature and the sales of coffee.

d. Predict sales of a 90 degree day.

6

Problem-14

Researchers have collected data on the hours of television watched in a day and the age of a person. You

are given the data below.

Hours of Television Age

1 45

3 30

4 22

3 25

6 15

a. Determine which variable is the dependent variable.

b. Compute the least squares estimated line.

c. Compute the coefficient of determination. How would you interpret this value?

POM 212 Business Statistics

Homework Assignment-4

Note: The homework is due on the day of Test-4.

Chapter-10 Problems:

Problem-1

In order to estimate the difference between the average Miles per Gallon of two different models of

automobiles, samples are taken and the following information is collected.

Model A Model B

Sample Size 50 55

Sample Mean 32 35

Sample Variance 9 10

a. At 95% confidence develop an interval estimate for the difference between the average

Miles per Gallon for the two models.

b. Is there conclusive evidence to indicate that one model gets a higher MPG than the

other? Why or why not? Explain.

Problem-2

Independent random samples taken on two university campuses revealed the following information

concerning the average amount of money spent on textbooks during the fall semester.

University A University B

Sample Size 50 40

Average Purchase $280 $250

Standard Deviation $20 $23

At 95% confidence test to determine if, on the average, students at University A spend more on textbooks

then the students at University B.

Problem-3

Two independent random samples of annual starting salaries for individuals with master’s and bachelor’s

degrees in business were taken. Use the data shown below and provide a 95% confidence interval

estimate for the difference between the salaries of the two groups.

2

Masters Degree Bachelors Degree

Sample Size 14 12

Sample Mean $58,000 $55,000

Sample Standard Deviation $ 2,400 $ 2,000

Problem-4

The following shows the monthly sales in units of six salespersons before and after a bonus plan was

introduced. At 95% confidence, determine whether the bonus plan has increased sales significantly. (For

the following matched samples, let the difference "d" be: d = after - before.)

Monthly Sales

Salesperson After Before

1 94 90

2 82 84

3 90 84

4 76 70

5 79 80

6 85 80

Problem-5

Allied Corporation is trying to sell its new machines to Ajax. Allied claims that the machine will pay for

itself since the time it takes to produce the product using the new machine is significantly less than the

production time using the old machine. To test the claim, independent random samples were taken from

both machines. You are given the following results.

New Machine Old Machine

Sample Mean 25 23

Sample Variance 27 7.56

Sample Size 45 36

As the statistical advisor to Ajax, would you recommend purchasing Allied's machine? Explain your

answer.

3

Chapter-12 Problems:

Problem-6

Before the presidential debates, it was expected that the percentages of registered voters in favor of

various candidates to be as follows.

Percentages

Democrats 48%

Republicans 38%

Independent 4%

Undecided 10%

After the presidential debates, a random sample of 1200 voters showed that 540 favored the Democratic

candidate; 480 were in favor of the Republican candidate; 40 were in favor of the Independent candidate,

and 140 were undecided. At 95% confidence, test to see if the proportion of voters has changed.

Problem-7

Last school year, in the school of Business Administration, 30% were Accounting majors, 24%

Management majors, 26% Marketing majors, and 20% Economics majors. A sample of 300 students

taken from this year's students of the school showed the following number of students in each major:

Accounting 83

Management 68

Marketing 85

Economics 64

Total 300

Has there been any significant change in the number of students in each major between the last school

year and this school year? Use 95% confidence level.

Problem-8

The personnel department of a large corporation reported sixty resignations during the last year. The

following table groups these resignations according to the season in which they occurred:

Season Number of Resignations

Winter 10

Spring 22

Summer 19

Fall 9

Test to see if the number of resignations is uniform over the four seasons. Use 95% confidence level.

4

Problem-9

A group of 2000 individuals from 3 different cities were asked whether they owned a foreign or a

domestic car. The following contingency table shows the results of the survey.

CITY

Type of Car Detroit Atlanta Denver Total

Domestic 80 200 520 800

Foreign 120 600 480 1200

Total 200 800 1000 2000

With 95% confidence level, test to determine if the type of car purchased is independent of the city in

which the purchasers live.

Problem-10

Five hundred randomly selected automobile owners were questioned on the main reason they had

purchased their current automobile. The results are given below.

Styling Engineering Fuel Economy Total

Male 70 130 150 350

Female 30 20 100 150

100 150 250 500

Give your conclusion for this test with 90% confidence level.

Chapter-14 Problems:

Problem-11

The following data represent a company's yearly sales volume and its advertising expenditure over a

period of 8 years.

Year Sales in Millions of Dollars (Y) Advertising in ($10,000) (X)

1994 15 32

1995 16 33

1996 18 35

1997 17 34

1998 16 36

1999 19 37

2000 19 39

2001 24 42

5

a. Develop a scatter diagram of sales versus advertising.

b. Use the method of least squares to compute an estimated regression line between sales

and advertising.

Problem-12

An automobile dealer wants to see if there is a relationship between monthly sales and the interest rate. A

random sample of 4 months was taken. The results of the sample are presented below.

Monthly Sales (Y) Interest Rate (In Percent) (X)

22 9.2

20 7.6

10 10.4

45 5.3

a. Use the method of least squares to compute an estimated regression line.

b. Obtain a measure of how well the estimated regression line fits the data.

Problem-13

Max believes that the sales of coffee at his coffee shop depend upon the weather. He has taken a sample

of 5 days. Below you are given the results of the sample.

Cups of Coffee Sold Temperature

350 50

200 60

210 70

100 80

60 90

40 100

a. Which variable is the dependent variable?

b. Compute the least squares estimated line.

c. Compute the correlation coefficient between temperature and the sales of coffee.

d. Predict sales of a 90 degree day.

6

Problem-14

Researchers have collected data on the hours of television watched in a day and the age of a person. You

are given the data below.

Hours of Television Age

1 45

3 30

4 22

3 25

6 15

a. Determine which variable is the dependent variable.

b. Compute the least squares estimated line.

c. Compute the coefficient of determination. How would you interpret this value?