# Chapter 10 Eighteen People Were Randomly Chosen For 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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46. Random samples were selected from three populations. The data obtained are shown

below.

Treatment 1

Treatment 2

Treatment 3

45

31

39

41

34

37

37

35

38

40

40

42

a. Compute the overall sample mean

x

.

b. At 90% 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.

47. The manager of Roth Corporation wants to determine whether or not the type of work

schedule for her employees has any effect on their productivity. She has selected 15

production employees at random and then randomly assigned 5 employees to each of the

3 proposed work schedules. The following table shows the units of production (per

week) under each of the work schedules.

Work Schedule (Treatments)

Schedule 1

Schedule 2

Schedule 3

50

60

75

60

65

75

70

65

55

40

58

40

45

57

55

a. Compute the overall sample mean

x

.

b. At 95% confidence, determine if there is a significant difference in the mean weekly

units of production for the three types of work schedules.

48. Six observations were selected from each of three populations. The data obtained is

shown below.

Sample 1

Sample 2

Sample 3

31

31

37

28

32

36

34

33

39

32

30

40

26

32

35

29

34

35

a. Compute the overall sample mean

x

.

b. Test at the = 0.05 level to determine if there is a significant difference in the means

of the three populations.

49. The test scores for selected samples of statistics students who took the course from three

different instructors are shown below.

Instructor A

Instructor B

Instructor C

81

90

85

62

55

90

82

84

90

87

91

95

73

85

80

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

groups. Show the complete ANOVA table.

50. Three universities administer the same comprehensive examination to the recipients of

MS degrees in psychology. From each institution, a random sample of MS recipients was

selected, and these recipients were then given the exam. The following table shows the

scores of the students from each university.

University A

University B

University C

89

60

75

95

95

70

75

89

90

92

80

78

99

66

77

a. Compute the overall sample mean

x

.

b. At = 0.05, test to see if there is any significant difference in the average scores of

the students from the three universities. Set up the complete ANOVA table (Note

that the sample sizes are not equal.)

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

each of the 3 treatments. Part of the ANOVA table is shown below.

ANOVA

Source of Variation

SS

df

MS

F

Between Groups

1500

?

?

?

Within Groups

?

?

?

Total

6000

32

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

b. At 95% confidence, test to determine whether or not the means of the 3 populations

are equal.

52. Wendy, 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

93

76

85

85

74

67

88

60

64

82

70

92

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. Note that the sample sizes are not equal. Show your complete

work and the ANOVA table.

53. In order to compare the life expectancies of three different brands of printers, eight

printers of each brand were randomly selected. Information regarding the three brands is

shown below.

Brand A

Brand B

Brand C

Average life (in months)

62

52

60

Sample variance

36

25

49

Use the above data and test to see if the mean life expectancies of the three brands are the

same. Let = 0.05. Show the complete ANOVA table.

54. Three different models of automobiles (A, B, and C) were compared for gasoline

consumption. For each model of car, ten cars were randomly selected and subjected to

standard driving procedures. The average miles/gallon obtained for each model of car

and sample standard deviations are shown below.

Car A

Car B

Car C

Average Mile/Gallon

42

49

44

Sample Standard Deviation

4

5

3

Use the above data and test to see if the mean gasoline consumption for all three models

of cars is the same. Let = 0.05. Show the complete ANOVA table.

55. At = 0.05, test to determine if the means of the three populations (from which the

following samples are selected) are equal. Show the complete ANOVA table.

Sample 1

Sample 2

Sample 3

60

84

60

78

78

57

72

93

69

66

81

66

56. In order to test to see if there is any significant difference in the mean number of units

produced per week by each of three production methods, the following data were

collected:

Method I

Method II

Method III

182

170

160

170

192

156

185

190

179

a. Compute the overall sample mean

x

.

b. At the = 0.05 level of significance, is there any difference in the mean number of

units produced per week by each method? Show the complete ANOVA table. Note

that the sample sizes are not equal.

57. A dietician wants to see if there is any difference in the effectiveness of three diets.

Eighteen people were randomly chosen for the test. Then each individual was randomly

assigned to one of the three diets. Below you are given the total amount of weight lost in

a six-month period by each person.

Diet A

Diet B

Diet C

14

12

25

18

10

32

20

22

18

12

12

14

20

16

17

18

12

14

a. State the null and alternative hypotheses.

b. Prepare an ANOVA.

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

of the three populations.

58. Ziba Corporation wants to increase the productivity of its line workers. Four different

programs have been suggested to help increase productivity. Twenty employees, making

up a sample, have been randomly assigned to one of the four programs and their output

for a day's work has been recorded. You are given the results below.

Program A

Program B

Program C

Program D

150

150

185

175

130

120

220

150

120

135

190

120

180

160

180

130

145

110

175

175

a. State the null and alternative hypotheses.

b. Construct an ANOVA table.

c. At 95% confidence, test to determine if the means of the three populations are equal.

59. For four populations, the population variances are assumed to be equal. Random samples

from each population provide the following data.

Population

Sample Size

Sample Mean

Sample Variance

1

11

40

23.4

2

11

35

21.6

3

11

39

25.2

4

11

37

24.6

Using a .05 level of significance, test to see if the means for all four populations are the

same. Show the complete ANOVA table.

60. The final examination grades of random samples of students from three different classes

are shown below.

Class A

Class B

Class C

92

91

85

85

85

93

96

90

82

99

86

84

At the = .05 level of significance, is there any difference in the mean grades of the

three classes? Show the complete ANOVA table.

61. Individuals were randomly assigned to three different production processes. The hourly

units of production for the three processes are shown below.

Process 1

Process 2

Process 3

33

33

28

30

35

36

28

30

30

29

38

34

Use the analysis of variance procedure with = 0.05 to determine if there is a significant

difference in the mean hourly units of production for the three types of production

processes. Show the complete ANOVA table.

62. Random samples of employees from three different departments of MNM Corporation

showed the following yearly incomes (in $1,000).

Department A

Department B

Department C

45

46

50

40

41

48

43

43

48

39

33

50

35

41

47

38

42

45

At = .05, test to determine if there is a significant difference among the average

incomes of the employees from the three departments. Show the complete ANOVA

table.

63. The heating bills for a selected sample of houses using various forms of heating are given

below (values are in dollars).

Gas Heated Homes

Central Electric

Heat Pump

83

90

81

80

88

83

82

87

80

83

82

82

82

83

79

At = 0.05, test to see if there is a significant difference among the average bills of the

homes. Show the complete ANOVA table.

64. Three universities in your state decided to administer the same comprehensive

examination to the recipients of MBA degrees from the three institutions. From each

institution, MBA recipients were randomly selected and were given the test. The

following table shows the scores of the students from each university.

Northern

University

Central

University

Southern

University

74

85

79

76

85

80

84

86

83

85

88

78

81

82

84

a. Compute the overall sample mean

x

.

b. At = 0.05, test to see if there is any significant difference in the average scores of

the students from the three universities. (Note that the sample sizes are not equal.)

65. The three major automobile manufacturers have entered their cars in the Indianapolis 500

race. The speeds of the tested cars are given below.

Manufacturer A

Manufacturer B

Manufacturer C

180

177

175

175

180

176

179

167

177

176

172

190

a. Compute the overall sample mean

x

.

b. At = .05, test to see if there is a significant difference in the average speeds of the

cars of the auto manufacturers. Show the complete ANOVA table.

66. Part of an ANOVA table is shown below.

ANOVA

Source of Variation

SS

df

MS

F

Between Groups

90

3

?

?

Within Groups

120

?

?

Total

?

23

a. Determine the missing values and fill in the blanks in the above table. At 95%

confidence, test to determine if there is a significant difference among the means.

b. How many groups have there been in this problem?

c. What has been the total number of observations?

67. Part of an ANOVA table involving 8 groups for a study is shown below.

ANOVA

Source of Variation

SS

df

MS

F

Between Groups

126

?

?

?

Within Groups

240

?

?

Total

?

67

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 eight groups.

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