Within Groups
27
4
Total
Actual p-value = 0.0206
46. Random samples were selected from three populations. The data obtained are shown below.
Treatment 1
Treatment 3
45
39
41
37
37
38
40
42
a.
Compute the overall sample mean .
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.
38.25
b.
Between Groups
Within Groups
Total
value is between 0.025 and 0.05.
Actual p-value = 0.0414
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 3
50
75
60
75
70
55
40
40
45
55
a.
Compute the overall sample mean .
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.
58
b.
Between Groups
Within Groups
Total
Using the F table (2 numerator and 12 denominator degrees of freedom) for F = 0.7412, the
Actual p-value = 0.4971
Since the p-value = 0.05, do not reject H0 (critical F = 3.89).
48. Six observations were selected from each of three populations. The data obtained is shown below.
Sample 1
Sample 3
31
37
28
36
34
39
32
40
26
35
29
35
a.
Compute the overall sample mean .
b.
Test at the = 0.05 level to determine if there is a significant difference in the means of the
three populations.
33
b.
Between Groups
Within Groups
Total
Actual p-value = 0.0002
Since the p-value = 0.05, reject H0 (critical F = 3.68).
49. The test scores for selected samples of statistics students who took the course from three different
instructors are shown below.
Instructor A
Instructor C
81
85
62
90
82
90
87
95
73
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.
Between Groups
Within Groups
Total
14
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 .
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.)
a.
82
b.
Between Groups
2
3.89
Within Groups
Total
value is greater than 0.1.
Actual p-value = 0.1372
Since the p-value = 0.05, do not reject H0.
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.
a.
ANOVA
Source of Variation
Between Groups
3.32
Within Groups
Total
Using the F table (2 numerator and 30 denominator degrees of freedom) for F = 5, the p–
value is between 0.01 and 0.025
Actual p-value = 0.0134
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 3
93
85
85
67
88
64
82
92
a.
Compute the overall sample mean .
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.
78
b.
Between Groups
Within Groups
Total
Using the F table (2 numerator and 9 denominator degrees of freedom) for F = 7.84, the p–
Actual p-value = 0.0107
Since the p-value is = 0.05, reject H0 (critical F = 4.26).
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.
Between Groups
Within Groups
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.
Between Groups
Within Groups
Total
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 3
60
60
78
57
72
69
66
66
Between Groups
Within Groups
Total
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 III
182
160
170
156
185
179
a.
Compute the overall sample mean .
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.
a.
176
b.
Between Groups
2
Within Groups
Total
value is between 0.025 and 0.05.
Actual p-value = 0.0357
Since the p-value is = 0.05, reject H0 (critical F = 5.14).
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 C
14
25
18
32
20
18
12
14
20
17
18
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.
b.
Between Groups
2
Within Groups
Total
value is greater than 0.1.
Actual p-value = 0.169
Since the p-value is = 0.05, do not reject the null (critical F = 3.68).
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 C
Program D
150
185
175
130
220
150
120
190
120
180
180
130
145
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.
b.
Between Groups
Within Groups
Total
value is less than 0.01.
Since the p-value is = 0.05, reject the null (critical F = 3.24).
59. For four populations, the population variances are assumed to be equal. Random samples from each
population provide the following data.
Population
Sample Mean
Sample Variance
1
40
23.4
2
35
21.6
3
39
25.2
4
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.
Between Groups
3
54.08
Within Groups
Total
43
60. The final examination grades of random samples of students from three different classes are shown
below.
Class A
Class C
92
85
85
93
96
82
99
84
At the = .05 level of significance, is there any difference in the mean grades of the three classes?
Show the complete ANOVA table.
Between Groups
Within Groups
9
Total
11
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 3
33
28
30
36
28
30
29
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.
Between Groups
2
Within Groups
Total
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.
Between Groups
Within Groups
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.
Between Groups
Within Groups
Total
132
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 .
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.)
82
b.
Between Groups
Within Groups
Total
Using the F table (2 numerator and 12 denominator degrees of freedom) for F = 4.22, the p–
Actual p-value = 0.0410
Since the p-value is = 0.05, reject H0 (critical F = 3.89).
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 .
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.
177
b.
Between Groups
Within Groups
Total
Using the F table (2 numerator and 9 denominator degrees of freedom) for F = 1.56, the p–
value is greater than 0.10.
Actual p-value = = 0.2616
Since the p-value is = 0.05, do not reject H0 (critical F = 4.26).
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?
a.
Source of Variation
Between Groups
5
Within Groups
6
Total
value is less than 0.01.
Actual p-value = 0.0095
Since the p-value is = 0.05, reject H0 (critical F = 3.10)
b.
4
c.
24
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.
a.
ANOVA
Source of Variation
Between Groups
Within Groups
4
Total
value is less than 0.01.