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b. 500

c. 1,687.5

d. 2,250

105. Refer to Exhibit 10-16. The test statistic to test the null hypothesis equals

a. 0.22

b. 0.84

c. 4.22

d. 4.5

106. Refer to Exhibit 10-16. The null hypothesis is to be tested at the 5% level of

significance. The p-value is

a. less than .01

b. between .01 and .025

c. between .025 and .05

d. between .05 and .10

107. Refer to Exhibit 10-16. The null hypothesis

a. should be rejected

b. should not be rejected

c. was designed incorrectly

d. None of these alternatives is correct.

PROBLEMS

1. The following sample information is given concerning the ACT scores of high school

seniors form two local schools.

School A

School B

1

n

= 14

2

n

= 15

1

x

= 25

2

x

= 23

2

1

= 16

2

2

= 10

Develop a 95% confidence interval estimate for the difference between the two

populations.

2. Maxforce, Inc. manufactures racquetball racquets by two different manufacturing processes

(A and B). Because the management of this company is interested in estimating the

difference between the average time it takes each process to produce a racquet, they select

independent samples from each process. The results of the samples are shown below.

Process A

Process B

Sample Size

32

35

Sample Mean (in minutes)

43

47

Population Variance (2)

64

70

a. Develop a 95% confidence interval estimate for the difference between the average

times of the two processes.

b. Is there conclusive evidence to prove that one process takes longer than the other? If

yes, which process? Explain.

3. Consider the following results for two samples randomly taken from two normal

populations with equal variances.

Sample I

Sample II

Sample Size

28

35

Sample Mean

48

44

Population Standard Deviation

9

10

a. Develop a 95% confidence interval for the difference between the two population

means.

b. Is there conclusive evidence that one population has a larger mean? Explain.

4. The business manager of a local health clinic is interested in estimating the difference

between the fees for extended office visits in her center and the fees of a newly opened

group practice. She gathered the following information regarding the two offices.

Health Clinic

Group Practice

Sample Size

50 visits

45 visits

Sample Mean

$21

$19

Population Standard Deviation

$2.75

$3.00

Develop a 95% confidence interval estimate for the difference between the average fees

of the two offices.

5. 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

$260

$250

Population Standard Deviation()

$20

$23

We want to determine if, on the average, students at University A spent more on

textbooks then the students at University B.

a. Compute the test statistic.

b. Compute the p-value.

c. What is your conclusion? Let = .05.

6. The management of Recover Fast Hospital (RFH) claims that the average length of stay in

their hospital after a major surgery is less than the average length of stay at General

Hospital (GH). The following data have been accumulated to test their claim.

RFH

GH

Sample size

45

58

Mean (in days)

4.6

4.9

Population Standard Deviation ()

0.5

0.6

a. Formulate the hypotheses.

b. Compute the test statistic.

c. Using the p-value approach, test to see if the average length of stay in RFH is

significantly less than the average length of stay in GH. Let = 0.05.

7. 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

60

55

Sample Mean

28

25

Sample Variance

16

9

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.

8. Consider the following results for two samples randomly taken from two populations.

Sample A

Sample B

Sample Size

31

35

Sample Mean

106

102

Sample Standard Deviation

8

7

a. Determine the degrees of freedom for the t distribution.

b. Develop a 95% confidence interval for the difference between the two population

means.

9. Consider the following results for two samples randomly taken from two populations.

Sample A

Sample B

Sample Size

25

38

Sample Mean

66

60

Sample Standard Deviation

5

7

a. What are the degrees of freedom for the t distribution?

b. At 95% confidence, compute the margin of error.

c. Develop a 95% confidence interval for the difference between the two population

means.

10. Consider the following results for two samples randomly taken from two populations.

Sample A

Sample B

Sample Size

20

25

Sample Mean

28

22

Sample Standard Deviation

5

6

a. Determine the degrees of freedom for the t distribution.

b. At 95% confidence, what is the margin of error?

c. Develop a 95% confidence interval for the difference between the two population

means.

11. Consider the following results for two samples randomly taken from two populations.

Sample A

Sample B

Sample Size

28

30

Sample Mean

24

22

Sample Standard Deviation

8

6

a. Determine the degrees of freedom for the t distribution.

b. Develop a 95% confidence interval for the difference between the two population

means.

c. Is there conclusive evidence that one population has a larger mean? Explain.

12. The following are the test scores of two samples of students from University A and

University B on a national statistics examination. Develop a 95% confidence interval

estimate for the difference between the mean scores of the two populations.

University A

Scores

University B

Scores

x

86

83

n

64

87

6

8

13. In order to estimate the difference between the average mortgages in the southern states

and the northern states, the following information was gathered.

Southern

Northern

Sample Size

40

45

Sample Mean (in $1,000)

$170

$175

Sample Standard Deviation (in $1,000)

$5

$7

a. Compute the degrees of freedom for the t distribution.

b. Develop an interval estimate for the difference between the average of the mortgages

in the South and North. Let alpha = 0.05.

14. A credit company has gathered information regarding the average amount owed by

people under 30 years old and by people over 30 years. Independent random samples

were taken from both age groups. You are given the following information.

Under 30

Over 30

x

600

550

n

200

300

2

361

400

Construct a 95% confidence interval for the difference between the average amounts

owed by the two age groups.

15. Two independent random samples of annual starting salaries for individuals with masters

and bachelors degrees in business were taken and the results are shown below.

Masters

Degree

Bachelors

Degree

Sample Size

33

30

Sample Mean (in $1,000)

58

54

Sample Standard Deviation (in $1,000)

2.4

2.0

a. What are the degrees of freedom for the t distribution?

b. Provide a 95% confidence interval estimate for the difference between the salaries of

the two groups.

16. Samples of employees of Companies A and B provided the following information

regarding the ages of employees.

Company A

Company B

Sample Size

32

36

Average Age

42

47

Variance

16

36

Develop a 97% confidence interval for the difference between the average ages of the

employees of the two companies.

17. Test scores on a standardized test from samples of students from two universities are

given below.

UA

UB

Sample Size

28

41

Average Test Score

84

82

Variance

64

100

Provide a 98% confidence interval estimate for the difference between the test scores of

the two universities.

18. In order to estimate the difference between the average age of male and female

employees at the Young Corporation, the following information was gathered.

Male

Female

Sample Size

32

36

Sample Mean

25

23

Sample Standard Deviation

4

6

Develop a 95% confidence interval estimate for the difference between the average age

of male and female employees at the Young Corporation.

19. In order to estimate the difference between the average yearly salaries of top managers in

private and governmental organizations, the following information was gathered.

Private

Governmental

Sample Size

50

60

Sample Mean (in $1,000s)

190

180

Sample Standard Deviation (in $1,000s)

6

8

Develop an interval estimate for the difference between the average salaries of the two

sectors. Let = .05.

20. The following information regarding the ages of full-time and part-time students are

given. Using the following data, develop an interval estimate for the difference between

the mean ages of the two populations. Use a 5% level of significance. The degrees of

freedom for the t distribution are 106.

Full-Time

Part-Time

x

27

24

s

1.5

2

n

50

60

21. The following information regarding the number of semester hours taken from random

samples of day and evening students is provided.

Day

Evening

x

16

12

s

4

2

n

140

160

Develop a 95% confidence interval estimate for the difference between the mean

semester hours taken by the two groups of students.

22. A random sample of 89 tourists in the Grand Bahamas showed that they spent an average

of $2,860 (in a week) with a standard deviation of $126; and a sample of 64 tourists in

New Province showed that they spent an average of $2,935 (in a week) with a standard

deviation of $138. We are interested in determining if there is any significant difference

between the average expenditures of those who visited the two islands?

a. Determine the degrees of freedom for this test.

b. Compute the test statistic.

c. Compute the p-value.

d. What is your conclusion? Let = .05.

23. Consider the following hypothesis test:

H0:

1 −

2 0

Ha:

1 −

2 > 0

The following results are for two independent samples taken from two populations.

Sample 1

Sample 2

Sample Size

35

34

Sample Mean

43

37

Sample Variance

140

170

a. Determine the degrees of freedom for the t distribution.

b. Compute the test statistic.

c. Determine the p-value and test the above hypotheses.

24. Recently, a local newspaper reported that part time students are older than full time

students. In order to test the validity of its statement, two independent samples of

students were selected.

Full Time

Part Time

x

26

24

s

2

3

n

42

31

a. Give the hypotheses for the above.

b. Determine the degrees of freedom.

c. Compute the test statistic.

d. At 95% confidence, test to determine whether or not the average age of part time

students is significantly more than full time students.

25. Independent random samples of managers’ yearly salaries (in $1000) taken from

governmental and private organizations provided the following information. At 95%

confidence, test to determine if there is a significant difference between the average

salaries of the managers in the two sectors.

Government

Private

x

80

75

s

9

10

n

28

31

26. Independent random samples taken at two local malls provided the following information

regarding purchases by patrons of the two malls.

Hamilton Place

Eastgate

Sample Size

85

93

Average Purchase

$143

$150

Standard Deviation

$22

$18

We want to determine whether or not there is a significant difference between the average

purchases by the patrons of the two malls.

a. Give the hypotheses for the above.

b. Compute the test statistic.

c. At 95% confidence, test the hypotheses.

27. The Dean of Students at UTC has said that the average grade of UTC students is higher

than that of the students at GSU. Random samples of grades from the two schools are

selected, and the results are shown below.

UTC

GSU

Sample Size

14

12

Sample Mean

2.85

2.61

Sample Standard Deviation

0.40

0.35

Sample Mode

2.5

3.0

a. Give the hypotheses.

b. Compute the test statistic.

c. At a 0.1 level of significance, test the Dean of Students' statement.

28. Zip, Inc. manufactures Zip drives on two different manufacturing processes. Because the

management of this company is interested in determining if process 1 takes less

manufacturing time, they selected independent samples from each process. The results of

the samples are shown below.

Process 1

Process 2

Sample Size

27

22

Sample Mean (in minutes)

10

14

Sample Variance

16

25

a. State the null and alternative hypotheses.

b. Determine the degrees of freedom for the t test.

c. Compute the test statistic

d. At 95% confidence, test to determine if there is sufficient evidence to indicate that

process 1 takes a significantly shorter time to manufacture the Zip drives.

29. A recent Time magazine reported the following information about a sample of workers in

Germany and the United States.

United States

Germany

Average length of workweek (hours)

42

38

Sample Standard Deviation

5

6

Sample Size

600

700

We want to determine whether or not there is a significant difference between the average

workweek in the United States and the average workweek in Germany.

a. State the null and the alternative hypotheses.

b. Compute the test statistic.

c. Compute the p-value. What is your conclusion?

30. Independent random samples taken at two companies provided the following information

regarding annual salaries of the employees.

Marissa, Inc

Jason, Inc.

Sample Size

72

50

Sample Mean (in $1,000)

48

43

Sample Standard Deviation (in $1,000)

12

10

a. We want to determine whether or not there is a significant difference between the

average salaries of the employees at the two companies. Compute the test statistic.

b. Compute the p-value; and at 95% confidence, test the hypotheses.

31. Two independent samples are drawn from two populations, and the following

information is provided.

Population 1

Population 2

n

34

52

x

55

65

s

14

18

We want to test the following hypotheses.

Ho:

1 −

2 0

Ha:

1 −

2 < 0

a. Determine the degrees of freedom.

b. Compute the test statistic.

c. At 95% confidence, test the hypotheses. Assume the two populations are normally

distributed and have equal variances.

32. In order to determine whether or not a driver's education course improves the scores on a

driving exam, a sample of 6 students were given the exam before and after taking the

course. The results are shown below.

Let d = Score After - Score Before.

Score

Score

Student

Before the Course

After the Course

1

83

87

2

89

88

3

93

91

4

77

77

5

86

93

6

79

83

a. Compute the test statistic.

b. At 95% confidence using the p-value approach, test to see if taking the course actually

increased scores on the driving exam.

33. The daily production rates for a sample of factory workers before and after a training

program are shown below. Let d = After – Before.

Worker

Before

After

1

6

9

2

10

12

3

9

10

4

8

11

5

7

9

We want to determine if the training program was effective.

a. Give the hypotheses for this problem.

b. Compute the test statistic.

c. At 95% confidence, test the hypotheses. That is, did the training program actually

increase the production rates?

34. The following data present the number of computer units sold per day by a sample of 6

salespersons before and after a bonus plan was implemented. Let d = before – after.

Salesperson

Before

After

1

3

6

2

7

5

3

6

6

4

8

7

5

7

8

6

9

8

At 95% confidence, test to see if the bonus plan was effective. That is, did the bonus

plan actually increase sales?

35. A test on world history was given to a group of individuals before and also after a film on

the history of the world was presented. The results are given below. We want to

determine if the film significantly increased the test scores. (For the following matched

samples, let the d = after − before.)

Individual

After

Before

1

92

86

2

86

88

3

89

84

4

90

90

5

93

85

6

88

90

7

97

91

a. Give the hypotheses for this problem.

b. Compute the test statistic.

c. At 95% confidence, test the hypotheses.

36. 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

37. Allied Corporation is trying to determine whether to purchase Machine A or B. It has

leased the two machines for a month. A random sample of 5 employees has been taken.

These employees have gone through a training session on both machines. Below you are

given information on their productivity rate on both machines. (Let d = Machine A -

Machine B.)

Productivity Rate

Person

Machine A

Machine B

1

47

52

2

53

58

3

50

47

4

55

60

5

45

53

a. State the null and alternative hypotheses for a two-tailed test.

b. Find the mean and standard deviation for the difference.

c. Compute the test statistic.

d. Test the null hypothesis stated in Part a at the 10% level.

38. A company attempts to evaluate the potential for a new bonus plan by selecting a sample

of 4 salespersons to use the bonus plan for a trial period. The weekly sales volume before

and after implementing the bonus plan is shown below. (For the following matched

samples, let the difference "d" be d = after − before.)

Weekly Sales

Salesperson

Before

After

1

44

48

2

40

48

3

36

38

4

50

44

a. State the hypotheses.

b. Compute the test statistic.

c. Use Alpha = .05 and test to see if the bonus plan will result in an increase in the mean

weekly sales.

39. The following information was obtained from matched samples regarding the

productivity of four individuals using two different methods of production.

Individual

Method 1

Method 2

1

6

8

2

9

5

3

7

6

4

7

5

5

8

6

6

9

5

7

6

3

Let d = Method 1 − Method 2. Is there a significant difference between the productivity

of the two methods? Let = 0.05.

40. Information regarding the ACT scores of samples of students in three different majors is

given below.

Major

Management

Finance

Accounting

28

22

29

26

23

27

25

24

26

27

22

28

21

24

25

19

26

26

27

27

28

17

29

20

17

28

20

23

24

28

28

29

Sums

230

225

338

Means

23

25

26

Variances

18

6.75

9.33

a. Set up the ANOVA table for this problem.

b. At 95% confidence test to determine whether there is a significant difference in the

means of the three populations.

41. Information regarding the ACT scores of samples of students in four different majors is

given below.

Major

Management

Marketing

Finance

Accounting

29

22

29

28

27

22

27

26

21

25

27

25

28

26

28

20

22

27

24

21

28

20

20

19

28

23

20

27

23

25

30

24

28

27

29

21

24

28

23

29

27

31

27

24

Sum

318

245

234

312

Mean

26.50

24.50

26.00

24.00

Variance

10.09

6.94

14.50

9.00

a. Set up the ANOVA table for this problem.

b. At 95% confidence, test to determine whether there is a significant difference in the

means of the three populations.

42. Guitars R. US has three stores located in three different areas. Random samples of the

sales of the three stores (in $1000) are shown below.

Store 1

Store 2

Store 3

80

85

79

75

86

85

76

81

88

89

80

80

a. Compute the overall sample mean

x

.

b. At 95% confidence, test to see if there is a significant difference in the average sales

of the three stores. Set up the complete ANOVA table. Please note that the sample

sizes are not equal.

43. In a completely randomized experimental design, 18 experimental units were used for the

first treatment, 10 experimental units for the second treatment, and 15 experimental units

for the third treatment. Part of the ANOVA table for this experiment is shown below.

ANOVA

Source of Variation

SS

df

MS

F

Between Groups

?

?

?

3

Within Groups

?

?

6

Total

?

?

a. Fill in all the blanks in the above ANOVA table.

b. At 95% confidence, test to see if there is a significant difference among the means.

44. Random samples were selected from three populations. The data obtained are shown

below.

Treatment 1

Treatment 2

Treatment 3

37

43

28

33

39

32

36

35

33

38

38

40

a. Compute the overall sample mean

x

.

b. At 95% confidence, test to see if there is a significant difference in the means of the

three populations. Show the complete ANOVA table. Please note that the sample

sizes are not equal.

45. In a completely randomized experimental design, 7 experimental units were used for the

first treatment, 9 experimental units for the second treatment, and 14 experimental units

for the third treatment. Part of the ANOVA table for this experiment is shown below.

ANOVA

Source of Variation

SS

df

MS

F

Between Groups

?

?

?

4.5

Within Groups

?

?

4

Total

?

?

a. Fill in all the blanks in the above ANOVA table.

b. At 95% confidence, test to see if there is a significant difference among the means.

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