# Chapter 10 Samples Were Selected From Three Populations The

Document Type

Test Prep

Book Title

Essentials of Modern Business Statistics 4th (Fourth) Edition By Williams 4th Edition

Authors

J.K

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68. MNM, Inc. has three stores located in three different areas. Random samples of the daily

sales of the three stores (in $1,000) are shown below.

Store 1

Store 2

Store 3

9

10

6

8

11

7

7

10

8

8

13

11

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

the three stores. Show the complete ANOVA table.

69. Ten observations were selected from each of 3 populations, and an analysis of variance

was performed on the data. The following are the results.

ANOVA

Source of Variation

SS

df

MS

F

Between Groups

82

?

?

?

Within Groups

162

?

?

Total

?

?

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

three populations.

70. The following are the results from a completely randomized design consisting of 3

treatments.

ANOVA

Source of Variation

SS

df

MS

F

Between Groups

390

?

?

?

Within Groups

?

?

?

Total

558

23

Using = .05, test to see if there is a significant difference among the means of the three

populations.

71. Eight observations were selected from each of 3 populations (total of 24 observations),

and an analysis of variance was performed on the data. The following are part of the

results.

ANOVA

Source of Variation

SS

df

MS

F

Between Groups

216

?

?

?

Within Groups

252

?

?

Total

?

?

Using = .05, test to see if there is a significant difference among the means of the three

populations.

72. Random samples of individuals from three different cities were asked how much time

they spend per day watching television. The results (in minutes) for the three groups are

shown below.

City I

City II

City III

260

182

211

280

190

190

240

220

247

260

240

300

a. Compute the overall sample mean

x

.

b. At = 0.05, test to see if there is a significant difference in the averages of the three

groups. Show the complete ANOVA table.

73. Three different brands of tires were compared for wear characteristics. From each brand

of tire, ten tires were randomly selected and subjected to standard wear-testing

procedures. The average mileage obtained for each brand of tire and sample variances

(both in 1,000 miles) are shown below.

Brand A

Brand B

Brand C

Average Mileage

37

38

33

Sample variance

3

4

2

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

of the three brands.

74. MOA, Inc. has three stores located in three different areas. Random samples of the sales

of the three stores (In $1,000) are shown below.

Store 1

Store 2

Store 3

46

34

33

47

36

31

45

35

35

42

39

45

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. Show the complete ANOVA table.

75. In a completely randomized experimental design, 11 experimental units were used for

each of the 4 treatments. Part of the ANOVA table is shown below.

ANOVA

Source of Variation

SS

df

MS

F

Between Groups

1500

?

?

?

Within Groups

?

?

?

Total

5500

?

a. Determine all the missing values in the above table and fill in the blanks.

b. Use = 0.05 to determine if there is any significant difference among the means of

the four treatments.

76. Samples were selected from three populations. The data obtained are shown below.

Sample 1

Sample 2

Sample 3

10

16

15

9

14

15

12

13

16

13

14

14

16

10

17

Sample Mean (

j

x

)

11

15

14

Sample Variance (

2

j

s

)

3.33

2.4

5.5

a. Compute the overall sample mean

x

.

b. Set up an ANOVA table for this problem.

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

means of the three populations.

77. In a completely randomized experimental design, 16 experimental units were used for

each of the 4 levels of the factor (i.e., 4 treatments). Part of the ANOVA table is shown

below.

ANOVA

Source of Variation

SS

df

MS

F

Between Groups

?

?

100

?

Within Groups

?

?

?

Total

1560

?

a. Determine all the missing values in the above table and fill in the blanks.

b. Use = 0.05 to determine if there is any significant difference among the means of

the four groups.

78. Independent random samples of Company W employees were taken to compare salaries

between college graduates and high school graduates. Samples of size 30 were taken for

each group. The results follow.

Salary HS ($1000)

Salary College ($1000)

24.1

22.9

24.0

32.4

33.1

26.2

21.2

19.9

23.9

30.9

29.6

28.7

25.7

19.5

29.0

39.2

32.1

31.8

28.8

22.1

24.7

29.6

30.4

28.5

28.6

22.7

24.4

35.5

30.4

32.7

30.2

18.6

23.5

32.0

31.3

28.6

18.4

23.3

30.9

32.0

33.3

33.5

24.3

23.8

27.6

28.3

37.5

41.4

28.3

25.4

32.1

30.8

35.4

28.4

21.7

23.9

23.0

31.2

37.2

27.2

Use Excel to estimate the difference in average salaries between the two groups with a

95% level of confidence.

79. At a particular airport in the United States, independent samples of domestic flights from

two airlines were taken and the amount of time each flight was delayed was measured. The

results follow.

Minutes Delayed

Airline A

Minutes Delayed

Airline B

0.0

33.7

0.0

7.2

25.6

31.8

0.0

34.6

38.9

36.2

0.0

41.6

27.3

24.7

34.8

43.1

44.5

0.0

38.9

39.4

41.8

41.5

42.1

7.8

35.3

23.5

39.5

12.8

34.5

38.1

35.7

33.0

29.0

32.9

41.3

31.8

Use Excel to estimate the difference in average delay time between the two airlines with

a 95% level of confidence.

80. Independent samples of commuters are taken from two cities. The following data

represents the time (in minutes) to drive to work. Use Excel to determine whether the

average commuting times are significantly different between the two cities. Use = .05.

City A

City B

15.25

40.25

12.75

48.75

25.50

50.00

12.50

12.25

18.75

45.00

15.50

10.00

60.25

16.75

22.75

42.00

10.50

18.75

38.75

42.50

10.50

28.50

45.00

12.25

35.75

30.00

81. The following independent samples show the delivery times for two suppliers of raw

materials (in days). A company currently uses Supplier A but will switch to Supplier B if

its average delivery time is less than that for Supplier A. Use Excel to conduct the

appropriate hypothesis test. Use = .10.

Supplier A

Supplier B

10

12

3

6

13

13

15

4

12

14

7

6

14

10

2

4

14

8

18

16

12

8

20

18

10

12

9

4

5

8

82. Starting annual salaries for business school graduates majoring in finance and

management information systems (MIS) were collected in two independent random

samples. Use the following data to develop a 95% confidence interval estimate of the

difference between the starting salaries for the two majors. Based on previous studies,

the population standard deviations for Finance and MIS salaries are estimated to be

$2,100 and $2,600, respectively.

Finance

MIS

n1 = 60

n2 = 50

1

x

= $43,200

2

x

= $46,500

EMBS4-TB10.doc - 64

83. A manager is thinking of providing, on a regular basis, in-house training for employees

preparing for an inventory management certification exam. In the past, some employees

received the in-house training before taking the exam, while others did not. Independent

random samples taken from the company’s records provided the following exam scores

for 10 workers who did not receive in-house training and 8 workers who did receive

training. (The manager is confident that the distributions of both populations’ exam

scores are approximately normal.)

No Training

Training

76

80

80

66

60

71

91

79

73

94

77

74

82

83

68

78

75

86

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

average test scores for the two populations of employees.

b. Using

= .05, test for any difference between the average test scores for the two

populations of employees.

84. A survey was recently conducted to determine if consumers spend more on computer-

related purchases via the Internet or store visits. Assume a sample of 8 respondents

provided the following data on their computer-related purchases during a 30-day period.

Using a .05 level of significance, can we conclude that consumers spend more on

computer-related purchases by way of the Internet than by visiting stores?

Expenditures (dollars)

Respondent

In-Store

Internet

1

132

225

2

90

24

3

119

95

4

16

55

5

85

13

6

248

105

7

64

57

8

49

0

85. Regional Manager Sue Collins would like to know if the mean number of telephone calls

made per 8-hour shift is the same for the telemarketers at her three call centers (Austin,

Las Vegas, and Albuquerque). A simple random sample of 6 telemarketers from each of

the three call centers was taken and the number of telephone calls made in eight hours by

each observed employee is shown below.

Observation

Center 1

Austin

Center 2

Las Vegas

Center 3

Albuquerque

1

82

72

71

2

68

63

81

3

77

74

73

4

80

60

68

5

69

70

76

6

78

73

80

Sample Mean

75.667

68.667

74.833

Sample Variance

33.867

33.467

26.167

Using

= .10, test for any significant difference in the mean number of telephone calls

made at the three call centers.

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