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12 Chapter - Analysis of Variance
Chapter 12
Analysis of Variance
True / False Questions
1. The F distribution's curve is positively skewed.
True False
2. One characteristic of the F distribution is that the computed F can only range between -1
and +1.
True False
3. If the computed value of F is 0.99 and the critical value is 3.89, we would not reject the
null hypothesis.
True False
4. For the hypothesis test,
, with n1 = 10 and n2 = 10, the F-test statistic is
2.56. At the 0.01 level of significance, we would reject the null hypothesis.
True False
5. To employ ANOVA, the populations being studied must be approximately normally
distributed.
True False
6. To employ ANOVA, the populations should have approximately equal standard
deviations.
True False
12-1
Chapter 12 - Analysis of Variance
7. The alternative hypothesis used in ANOVA is
True False
.
8. For an ANOVA test, rejection of the null hypothesis does not identify which treatment
means differ significantly.
True False
9. In an ANOVA table, k represents the total number of sample observations and n represents
the total number of treatments.
True False
10. If a confidence interval for the difference between a pair of treatment means includes 0,
then we reject the null hypothesis that there is no difference in the pair of treatment means.
True False
11. If we want to determine which treatment means differ, we compute a confidence interval
for the difference between each pair of means.
True False
12. When a blocking effect is included in an ANOVA, the result is a larger error sum of
squares.
True False
13. When a blocking effect is included in an ANOVA, the analysis is more likely to detect
differences in the treatment means.
True False
12-2
Chapter 12 - Analysis of Variance
14. In a two-way ANOVA with interaction, there are two factor effects and an interaction
effect.
True False
15. Interaction between two factors occurs when the effect of one factor on the response
variable is the same for any value of another factor.
True False
Multiple Choice Questions
16. An F statistic is:
A. a ratio of two means.
B. a ratio of two variances.
C. the difference between three means.
D. a population parameter.
17. What distribution does the F distribution approach as the sample size increases?
A. Binomial
B. Normal
C. Poisson
D. Exponential
18. Which statement is correct about the F distribution?
A. Cannot be negative
B. Cannot be positive
C. Is the same as the t distribution
D. Is the same as the z distribution
12-3
Chapter 12 - Analysis of Variance
19. Analysis of variance is used to
A. compare nominal data.
B. compute t test.
C. compare population proportions.
D. simultaneously compare several population means.
20. A large department store examined a sample of the 18 credit card sales and recorded the
amounts charged for each of three types of credit cards: MasterCard, Visa and Discover. Six
MasterCard sales, seven Visa and five Discover sales were recorded. The store used an
ANOVA to test if the mean sales for each credit card were equal. What are the degrees of
freedom for the F statistic?
A. 18 in the numerator, 3 in the denominator
B. 3 in the numerator, 18 in the denominator
C. 2 in the numerator, 15 in the denominator
D. 6 in the numerator, 15 in the denominator
21. Suppose that an automobile manufacturer designed a radically new lightweight engine and
wants to recommend the grade of gasoline that will have the best fuel economy. The four
grades are: regular, below regular, premium, and super premium. The test car made three trial
runs on the test track using each of the four grades and the miles per gallon recorded. At the
0.05 level, what is the critical value of F used to test the hypothesis that the miles per gallon
for each fuel is the same?
A. 1.96
B. 4.07
C. 2.33
D. 12.00
12-4
Chapter 12 - Analysis of Variance
22. Three different fertilizers were applied to a field of celery. In computing F, how many
degrees of freedom are there in the numerator?
A. 0
B. 1
C. 2
D. 3
23. Suppose a package delivery company purchased 14 trucks at the same time. Five trucks
were purchased from manufacturer A, four from manufacturer B, and five from manufacturer
C. The cost of maintaining each truck was recorded. The company used ANOVA to test if the
mean maintenance cost of the trucks from each manufacturer were equal. To apply the F test,
how many degrees of freedom must be in the denominator?
A. 2
B. 3
C. 11
D. 14
24. An experiment to determine the most effective way to teach safety principles applied four
different teaching methods. Some employees were given programmed instruction booklets
and worked through the course at their own pace. Other employees attended lectures. A third
group watched a television presentation, and a fourth group was divided into small discussion
groups. A high of 10 was possible. A sample of five tests was selected from each group. The
test grade results were:
At the 0.01 level, what is the critical value?
A. 1.00
B. 1.96
C. 3.24
D. 5.29
12-5
Chapter 12 - Analysis of Variance
25. In ANOVA, an F statistic is used to test a null hypothesis such as:
A. Option A
B. Option B
C. Option C
D. Option D
26. An electronics company wants to compare the quality of their cell phones to the cell
phones from three competitors. They sample 10 phones from each company and count the
number of defects for each phone. If ANOVA were used to compare the average number of
defects, then the treatments would be defined as:
A. The number of cell phones sampled.
B. The average number of defects.
C. The total number of phones.
D. The four companies.
27. Several employees have submitted different methods of assembling a subassembly.
Sample data for each method are:
How many treatments are there?
A. 3
B. 4
C. 12
D. 0
12-6
Chapter 12 - Analysis of Variance
28. If an ANOVA test is conducted and the null hypothesis is rejected, what does this
indicate?
A. Too many degrees of freedom
B. No difference between the population means
C. A difference between at least one pair of population means
D. All population means are different
29. A preliminary study of hourly wages paid to unskilled employees in three metropolitan
areas was conducted. Seven employees were included from Area A, 9 from Area B, and 12
from Area C. The test statistic was computed to be 4.91. What can we conclude at the 0.05
level?
A. Mean hourly wages of unskilled employees of all areas are equal
B. Mean hourly wages in at least 2 metropolitan areas are different
C. More degrees of freedom are needed
D. None of these is correct
30. In ANOVA analysis, when the null hypothesis is rejected, we can test for differences
between treatment means by
A. constructing confidence intervals.
B. adding another treatment.
C. doing an additional ANOVA.
D. doing a t test.
31. When the null hypothesis for an ANOVA analysis comparing four treatment means, is
rejected,
A. 2 comparisons of treatment means can be made.
B. 4 comparisons of treatment means can be made.
C. 6 comparisons of treatment means can be made.
D. 8 comparisons of treatment means can be made.
12-7
Chapter 12 - Analysis of Variance
32. The null hypothesis for an ANOVA analysis comparing four treatment means is rejected.
The four sample means are:
1= 10,
2=12,
3= 15,
4=18. The sample size for each
treatment is the same. If ( 1) is significantly different from zero, then
2
A. 1 is significantly less than 2, 3, and 4.
B. 2 is significantly less than 3 and 4.
C. 3 and 4 are significantly different.
D. 1, 2, 3, and 4 are all equal.
33. When testing for differences between treatment means, the t statistic is based on:
A. The treatment degrees of freedom.
B. The total degrees of freedom.
C. The error degrees of freedom.
D. The ratio of treatment and error degrees of freedom.
34. When testing for differences between treatment means, a confidence interval is based on
A. the mean square error.
B. the standard deviation.
C. the sum of squared errors.
D. the standard error of the mean.
35. When testing for differences between treatment means, the degrees of freedom for the t
statistic are:
A. k
B. (n - 1)
C. (n - k)
D. (1/n1 + 1/n2)
12-8
Chapter 12 - Analysis of Variance
36. A manufacturer of automobile transmissions uses two different processes. Management
ordered a study of the production costs to see if there is a difference among the two processes.
A summary of the findings is shown below.
What is the critical value of F at the 5% level of significance?
A. 19.45
B. 3.00
C. 4.41
D. 4.38
37. A manufacturer of automobile transmissions uses two different processes. Management
ordered a study of the production costs to see if there is a difference between the two
processes. A summary of the findings is shown below.
What is the critical value of F at the 1% level of significance?
A. 9.46
B. 8.29
C. 8.18
D. 4.61
12-9
Chapter 12 - Analysis of Variance
38. A manufacturer of automobile transmissions uses three different processes. Management
ordered a study of the production costs to see if there is a difference among the three
processes. A summary of the findings is shown below.
What are the degrees of freedom for the treatment sum of squares?
A. 2
B. 3
C. 10
D. 27
39. A manufacturer of automobile transmissions uses three different processes. Management
ordered a study of the production costs to see if there is a difference among the three
processes. A summary of the findings is shown below.
What are the degrees of freedom for the error sum of squares?
A. 3
B. 10
C. 27
D. 30
12-10
Chapter 12 - Analysis of Variance
40. A manufacturer of automobile transmissions uses three different processes. Management
ordered a study of the production costs to see if there is a difference among the three
processes. A summary of the findings is shown below.
What are the total degrees of freedom?
A. 27
B. 28
C. 29
D. 30
41. Given the following Analysis of Variance table for three treatments each with six
observations.
What are the degrees of freedom for the treatment and error sum of squares?
A. 3 and 18
B. 2 and 17
C. 3 and 15
D. 2 and 15
42. Given the following Analysis of Variance table for three treatments each with six
observations.
What is the critical value of F at the 5% level of significance?
A. 3.29
B. 3.68
C. 3.59
D. 3.20
12-11
Chapter 12 - Analysis of Variance
43. Given the following Analysis of Variance table for three treatments each with six
observations.
What is the mean square for treatments?
A. 71.2
B. 71.4
C. 558
D. 534
44. Given the following Analysis of Variance table for three treatments each with six
observations.
What is the computed value of F?
A. 7.48
B. 7.84
C. 8.84
D. 8.48
45. Given the following Analysis of Variance table for three treatments each with six
observations.
What is the decision regarding the null hypothesis?
A. Reject H0 - there is a difference in treatment means
B. Fail to reject H0 - there is a difference in treatment means
C. Reject H0 - there is a difference in errors
D. Fail to reject H0 - there is a difference in errors
12-12
Chapter 12 - Analysis of Variance
46. Two accounting professors decided to compare the variance of their grading procedures.
To accomplish this, they each graded the same 10 exams with the following results:
What is H0?
A. Option A
B. Option B
C. Option C
D. Option D
47. Two accounting professors decided to compare the variance of their grading procedures.
To accomplish this, they each graded the same 10 exams with the following results:
What is H1?
A. Option A
B. Option B
C. Option C
D. Option D
12-13
Chapter 12 - Analysis of Variance
48. Two accounting professors decided to compare the variance of their grading procedures.
To accomplish this, they each graded the same 10 exams with the following results:
What are the degrees of freedom for the numerator of the F ratio?
A. 8
B. 9
C. 10
D. 18
49. Two accounting professors decided to compare the variance of their grading procedures.
To accomplish this, they each graded the same 10 exams with the following results:
What are the degrees of freedom for the denominator of the F ratio?
A. 20
B. 18
C. 10
D. 9
50. Two accounting professors decided to compare the variance of their grading procedures.
To accomplish this, they each graded the same 10 exams with the following results:
What is the critical value of F at the 0.01 level of significance?
A. 5.85
B. 5.35
C. 6.51
D. 4.03
12-14
Chapter 12 - Analysis of Variance
51. Two accounting professors decided to compare the variance of their grading procedures.
To accomplish this, they each graded the same 10 exams with the following results:
What is the critical value of F at the 0.05 level of significance?
A. 5.85
B. 5.35
C. 3.18
D. 4.03
52. Two accounting professors decided to compare the variance of their grading procedures.
To accomplish this, they each graded the same 10 exams with the following results:
The calculated F ratio is
A. 3.484
B. 1.867
C. 3.18
D. 5.35
53. Two accounting professors decided to compare the variance of their grading procedures.
To accomplish this, they each graded the same 10 exams with the following results:
At the 1% level of significance, what is the decision?
A. Reject the null hypothesis and conclude the variances are different.
B. Fail to reject the null hypothesis and conclude the variances are different.
C. Reject the null hypothesis and conclude the variances are the same.
D. Fail to reject the null hypothesis and conclude the variances are the same.
12-15
Chapter 12 - Analysis of Variance
54. Two accounting professors decided to compare the variance of their grading procedures.
To accomplish this, they each graded the same 10 exams with the following results:
At the 5% level of significance, what is the decision regarding the null hypothesis?
A. Reject the null hypothesis and conclude the variances are different.
B. Fail to reject the null hypothesis and conclude no significant difference in the variances.
C. Reject the null hypothesis and conclude the variances are the same.
D. Fail to reject the null hypothesis and conclude the variances are the same.
55. A random sample of 30 executives from companies with assets over $1 million was
selected and asked for their annual income and level of education. The ANOVA comparing
the average income among three levels of education rejected the null hypothesis. The Mean
Square Error (MSE) was 243.7. The following table summarized the results:
When comparing the mean annual incomes for executives with Undergraduate and Master's
Degree or more, the following 95% confidence interval can be constructed:
A. 2.0 2.052 * 6.51
B. 2.0 3.182 * 6.51
C. 2.0 2.052 * 42.46
D. 2.0 3.182 * 42.46
12-16
Chapter 12 - Analysis of Variance
56. A random sample of 30 executives from companies with assets over $1 million was
selected and asked for their annual income and level of education. The ANOVA comparing
the average income among three levels of education rejected the null hypothesis. The Mean
Square Error (MSE) was 243.7. The following table summarized the results:
Based on the comparison between the mean annual incomes for executives with
Undergraduate and Master's Degree or more,
A. A confidence interval shows that the mean annual incomes are not significantly different.
B. The ANOVA results show that the mean annual incomes are significantly different.
C. A confidence interval shows that the mean annual incomes are significantly different.
D. The ANOVA results show that the mean annual incomes are not significantly different.
57. A random sample of 30 executives from companies with assets over $1 million was
selected and asked for their annual income and level of education. The ANOVA comparing
the average income among three levels of education rejected the null hypothesis. The Mean
Square Error (MSE) was 243.7. The following table summarized the results:
When comparing the mean annual incomes for executives with a High School education or
less and Undergraduate Degree, the 95% confidence interval shows an interval of 11.7 to 42.7
for the difference. This result indicates that
A. There is no significant difference between the two incomes.
B. The interval contains a difference of zero.
C. Executives with an Undergraduate Degree earn significantly more than executives with a
High School education or less.
D. Executives with an Undergraduate Degree earn significantly less than executives with a
High School education or less.
12-17
Chapter 12 - Analysis of Variance
58. A random sample of 40 companies with assets over $10 million was selected and asked
for their annual computer technology expense and industry. The ANOVA comparing the
average computer technology expense among three industries rejected the null hypothesis.
The Mean Square Error (MSE) was 195. The following table summarized the results:
When comparing the mean annual computer technology expense for companies in the
Education and Tax services industries, the following 95% confidence interval can be
constructed:
A. 13.5 2.026 * 5.78
B. 13.5 2.021 * 5.78
C. 13.5 2.026 * 13.96
D. 13.5 2.021 * 13.96
59. A random sample of 40 companies with assets over $10 million was selected and asked
for their annual computer technology expense and industry. The ANOVA comparing the
average computer technology expense among three industries rejected the null hypothesis.
The Mean Square Error (MSE) was 195. The following table summarized the results:
Based on the comparison between the mean annual computer technology expense for
companies in the Education and Tax services industries,
A. A confidence interval shows that the mean annual computer technology expenses are not
significantly different.
B. The ANOVA results show that the mean annual computer technology expenses are
significantly different.
C. A confidence interval shows that the mean annual computer technology expenses are
significantly different.
D. The ANOVA results show that the mean annual computer technology expenses are not
significantly different.
12-18
Chapter 12 - Analysis of Variance
60. A random sample of 40 companies with assets over $10 million was selected and asked
for their annual computer technology expense and industry. The ANOVA comparing the
average computer technology expense among three industries rejected the null hypothesis.
The Mean Square Error (MSE) was 195. The following table summarized the results:
Based on the comparison between the mean annual computer technology expense for
companies in the Tax Service and Food Service industries, the 95% confidence interval shows
an interval of -14.85 to 5.85 for the difference. This result indicates that
A. There is no significant difference between the two expenses.
B. The interval contains a difference of 20.7.
C. Companies in the Tax Service industry spend significantly less than companies in the Food
Service industry.
D. Companies in the Food Service industry spend significantly less than companies in the Tax
Service industry.
61. A random sample of 16 companies was selected and asked for their annual dividend rate
in three different industries: utilities, banking, and insurance. The ANOVA comparing the
mean annual dividend rate among three industries rejected the null hypothesis. The Mean
Square Error (MSE) was 3.36. The following table summarized the results:
When comparing the mean annual dividend rate for companies in the utilities and insurance
industries, the following 95% confidence interval can be constructed:
A. 5.78 2.160 * 2.40
B. 5.78 2.120 * 2.40
C. 5.78 2.160 * 1.11
D. 5.78 2.120 * 1.11
12-19
Chapter 12 - Analysis of Variance
62. A random sample of 16 companies was selected and asked for their annual dividend rate
in three different industries: utilities, banking, and insurance. The ANOVA comparing the
mean annual dividend rate among three industries rejected the null hypothesis. The Mean
Square Error (MSE) was 3.36. The following table summarized the results:
Based on the comparison between the mean annual dividend rate for companies in the utilities
and insurance industries,
A. A confidence interval shows that the mean annual dividend rates are not significantly
different.
B. The ANOVA results show that the mean annual dividend rates are significantly different.
C. A confidence interval shows that the mean annual dividend rates are significantly different.
D. The ANOVA results show that the mean annual dividend rates are not significantly
different.
63. A random sample of 16 companies was selected and asked for their annual dividend rate
in three different industries: utilities, banking, and insurance. The ANOVA comparing the
mean annual dividend rate among three industries rejected the null hypothesis. The Mean
Square Error (MSE) was 3.36. The following table summarized the results:
Based on the comparison between the mean annual dividend rate for companies in the utilities
and banking, the 95% confidence interval shows an interval of 1.28 to 6.28 for the difference.
This result indicates that
A. There is no significant difference between the two rates.
B. The interval contains a difference of 5.00.
C. The annual dividend rate in the utilities industry is significantly less than the annual
dividend rate in banking industry.
D. The annual dividend rate in banking industry is significantly less than the annual dividend
rate in utilities industry.
12-20
Chapter 12 - Analysis of Variance
64. In a two-way ANOVA, a blocking variable is used to
A. increase the error sum of squares.
B. decrease the error sum of squares.
C. increase the treatment sum of squares.
D. decrease the treatment sum of squares.
65. In a two-way ANOVA, the sources of variation are
A. Total variation and error variation.
B. Total variation, treatment variation, and error variation.
C. Total variation, treatment variation, blocking variation and error variation.
D. Treatment variation and blocking variation.
66. The college of business was interested in comparing the attendance for three different
class times for a business statistics class. The data follow.
What is the blocking variable?
A. Day.
B. Class time.
C. Tuesday.
D. 8:00 am class.
12-21
Chapter 12 - Analysis of Variance
67. The college of business was interested in comparing the attendance for three different
class times for a business statistics class. The data follow.
What is the treatment variable?
A. Day.
B. Class time.
C. Tuesday.
D. 8:00 am class.
68. The college of business was interested in comparing the attendance for three different
class times for a business statistics class. The data follow.
What are the block and treatment degrees of freedom?
A. 5 and 3.
B. 5 and 5.
C. 4 and 2.
D. 3 and 15.
12-22
Chapter 12 - Analysis of Variance
69. The college of business was interested in comparing the attendance for three different
class times for a business statistics class. The data follow.
What is the critical F statistic for testing the hypothesis of equal treatment means at the 0.05
significance level?
A. 1.96.
B. 6.94.
C. 3.84.
D. 4.46.
70. In a two-way ANOVA with interaction, a significant interaction term indicates that
A. the response variable is interactive.
B. a blocking factor is present.
C. both factors are unrelated.
D. both factors have a combined effect on the response variable.
71. A two-way ANOVA with interaction has how many sources of variation?
A. 5.
B. 4.
C. 3.
D. 2.
72. If there are 5 levels of Factor A and 7 levels of Factor B for an ANOVA with interaction,
what are the interaction degrees of freedom?
A. 12.
B. 35.
C. 24.
D. 10.
12-23
Chapter 12 - Analysis of Variance
73. The college of business was interested in comparing the interaction of Academic status
and class time on class attendance. Three different classes were sampled for each cell in the
table. The means for each cell follow.
What are the total degrees of freedom?
A. 44.
B. 14.
C. 4.
D. 2.
74. The college of business was interested in comparing the interaction of Academic status
and class time on class attendance. Three different classes were sampled for each cell in the
table. The means for each cell follow.
What are the error degrees of freedom?
A. 44.
B. 14.
C. 30.
D. 2.
12-24
Chapter 12 - Analysis of Variance
75. The college of business was interested in comparing the interaction of Academic status
and class time on class attendance. Three different classes were sampled for each cell in the
table. The means for each cell follow.
What are the interaction degrees of freedom?
A. 10.
B. 2.
C. 4.
D. 8.
Fill in the Blank Questions
76. The F distribution is a ______________ distribution.
________________________________________
77. What is the shape of the F distribution? ______________________
________________________________________
78. What are the minimum and maximum of values of an F distribution? _______ and
_______
________________________________________
79. All values in an F distribution must be _____________.
________________________________________
12-25
Chapter 12 - Analysis of Variance
80. What test statistic is used to compare two variances? ________________
________________________________________
81. The F-distribution is useful when testing a requirement of two-sample tests of hypothesis.
What is the assumption? ________________
________________________________________
82. ANOVA requires that the populations should be ______, ______, and _____.
________________________________________
83. What statistical technique is used to test the equality of three or more population means?
____________________
________________________________________
84. What is the least number of sources of variation in ANOVA? _________
________________________________________
85. In an one-way ANOVA, what are the degrees of freedom associated with the error sum of
squares? ___________
________________________________________
86. In an one-way ANOVA, how many degrees of freedom are associated with the numerator
of the F ratio? _______
________________________________________
87. What is the sum of squares divided by its corresponding degrees of freedom called?
_________________
________________________________________
12-26
Chapter 12 - Analysis of Variance
88. Assuming that the larger of two variances is in the numerator of an F statistic, in which
tail of the F distribution is the rejection region for analysis of variance? ________
________________________________________
89. In ANOVA, when we do not reject the null hypothesis, what inference do we make about
the population means? ________________
________________________________________
90. What is the null hypothesis for an ANOVA comparing three population means?
____________________
________________________________________
91. When H0 is rejected in ANOVA, _______ _______ are constructed to identify pairs of
means that differ.
________________________________________
92. In a study of protein breakfast bars, five bars from each of three brands were tested to see
if the mean amount of protein per bar differs among the brands. What are the degrees of
freedom for the numerator? ______
________________________________________
93. In a study of protein breakfast bars, five bars from each of three brands were tested to see
if the mean amount of protein per bar differs among the brands. What are the degrees of
freedom for the denominator? ______
________________________________________
94. In a study of protein breakfast bars, five bars from each of three brands were tested to see
if the mean amount of protein per bar differs among the brands. If the sum of squares for the
brands is 0.07, what is the mean square for brands? ______
________________________________________
12-27
Chapter 12 - Analysis of Variance
95. In a study of protein breakfast bars, five bars from each of three brands were tested to see
if the mean amount of protein per bar differs among the brands. If the sum of squares for the
error is 0.09, what is the mean square for the error? ______
________________________________________
96. In a study of protein breakfast bars, five bars from each of three brands were tested to see
if the mean amount of protein per bar differs among the brands. What is the F critical value
for = 0.05? ______
________________________________________
97. In a study of protein breakfast bars, five bars from each of three brands were tested to see
if the mean amount of protein per bar differs among the brands. What is the calculated value
of F, if the brand sum of squares is 0.07 and the error sum of squares is 0.09? ______
________________________________________
98. In a two-way ANOVA table with interaction, what are the error degrees of freedom?
_________
________________________________________
99. When a second source of variance is included in the ANOVA analysis without interaction,
that source is called a _________________.
________________________________________
100. How many mean square errors are summarized in a two-way ANOVA table?
_________
________________________________________
12-28
Chapter 12 - Analysis of Variance
Short Answer Questions
101. A company compared the variance of salaries for employees who have been employed
for 5 years or less with employees who have been employed for 10 years or more. They
randomly selected 21 employees with 5 years or less experience and 15 employees with 10
years or more experience. The standard deviation for the group with 5 years or less experience
was $2,225; the standard deviation for the group with 10 years or more experience is $1,875.
What is the F test statistic for the hypothesis test?
102. A company compared the variance of salaries for employees who have been employed
for 5 years or less with employees who have been employed for 10 years or more. They
randomly selected 21 employees with 5 years or less experience and 15 employees with 10
years or more experience. The standard deviation for the group with 5 years or less experience
was $2,225; the standard deviation for the group with 10 years or more experience is $1,875.
Using the 0.05 significance level, what is the F critical value for the hypothesis test?
12-29
Chapter 12 - Analysis of Variance
103. A company compared the variance of salaries for employees who have been employed
for 5 years or less with employees who have been employed for 10 years or more. They
randomly selected 21 employees with 5 years or less experience and 15 employees with 10
years or more experience. The standard deviation for the group with 5 years or less experience
was $2,225; the standard deviation for the group with 10 years or more experience is $1,875.
Using the 0.05 significance level, what is the decision regarding the null hypothesis?
104. To test the hypothesis that two population variances are equal, a random sample of size
13 was selected from the first population, and a random sample of size 21 was selected from
the second population. What are the degrees of freedom to test the hypothesis?
105. To test the hypothesis that two population variances are equal, a random sample of size
13 was selected from the first population, and a random sample of size 21 was selected from
the second population. Given that the sample standard deviation from the first population is
larger than the sample standard deviation from the second population, what is the F-critical
value using 0.01 as the significance level?
12-30
Chapter 12 - Analysis of Variance
106. A bottle cap manufacturer with four machines and six operators wants to see if variation
in production is due to the machines and/or the operators. The ANOVA table follows.
What are the degrees of freedom for the machines?
107. A bottle cap manufacturer with four machines and six operators wants to see if variation
in production is due to the machines and/or the operators. ANOVA table follows.
What are the degrees of freedom for the operators?
12-31
Chapter 12 - Analysis of Variance
108. A bottle cap manufacturer with four machines and six operators wants to see if variation
in production is due to the machines and/or the operators. ANOVA table follows.
What are the degrees of freedom for the errors?
12-32
Chapter 12 - Analysis of Variance
109. A bottle cap manufacturer with four machines and six operators wants to see if variation
in production is due to the machines and/or the operators. ANOVA table follows.
What is the critical value of F for the machine treatment effect at the 1% level of
significance? ____
110. A bottle cap manufacturer with four machines and six operators wants to see if variation
in production is due to the machines and/or the operators. ANOVA table follows.
What is the critical value of F for the operator block effect at the 1% level of significance?
12-33
Chapter 12 - Analysis of Variance
111. A bottle cap manufacturer with four machines and six operators wants to see if variation
in production is due to the machines and/or the operators. ANOVA table follows.
What is the mean square for machines?
112. A bottle cap manufacturer with four machines and six operators wants to see if variation
in production is due to the machines and/or the operators. ANOVA table follows.
What is the mean square for operators?
12-34
Chapter 12 - Analysis of Variance
113. A bottle cap manufacturer with four machines and six operators wants to see if variation
in production is due to the machines and/or the operators. ANOVA table follows.
What is the mean square for error?
114. A bottle cap manufacturer with four machines and six operators wants to see if variation
in production is due to the machines and/or the operators. ANOVA table follows.
What is the computed value of F for the machines?
12-35
Chapter 12 - Analysis of Variance
115. A bottle cap manufacturer with four machines and six operators wants to see if variation
in production is due to the machines and/or the operators. ANOVA table follows.
What is the computed value of F for the operators? _____
116. A bottle cap manufacturer with four machines and six operators wants to see if variation
in production is due to the machines and/or the operators. ANOVA table follows.
Test the hypothesis that all operators are equally productive. State your decision in terms of
the null hypothesis.
12-36
Chapter 12 - Analysis of Variance
117. An ANOVA showed the following comparison of four treatment means.
Which treatment means are significantly different?
118. An ANOVA comparing the waiting times for four different emergency rooms shows the
following comparison of the four mean waiting times.
Which two pairs of means are significantly different?
12-37
Chapter 12 - Analysis of Variance
119. A random sample of 20 female executives from companies with assets over $1 million
was selected and asked for their annual income and level of education. The ANOVA
comparing the average income among three levels of education rejected the null hypothesis.
The Mean Square Error (MSE) was 250. The following table summarized the results:
To compare the mean annual incomes of female executives with an undergraduate degree and
female executives with a high school or less education, compute the 95% confidence interval.
120. A random sample of 20 female executives from companies with assets over $1 million
was selected and asked for their annual income and level of education. The ANOVA
comparing the average income among three levels of education rejected the null hypothesis.
The Mean Square Error (MSE) was 250. The following table summarized the results:
To compare the mean annual incomes of female executives with an undergraduate degree and
female executives with a Master's degree or more, compute the 99% confidence interval.
12-38
Chapter 12 - Analysis of Variance
121. A random sample of 20 female executives from companies with assets over $1 million
was selected and asked for their annual income and level of education. The ANOVA
comparing the average income among three levels of education rejected the null hypothesis.
The Mean Square Error (MSE) was 250. The following table summarized the results:
To compare the mean annual incomes of female executives with a high school education or
less and female executives with a Master's degree or more, compute the 90% confidence
interval.
122. The human resources department of a software company encourages their employees to
participate in a wellness program. They sampled 16 employees, 2 males and 2 females from
four different workout routines and measured their peak heart rate. The ANOVA for the
research follows.
What is the Interaction sum of squares?
12-39
Chapter 12 - Analysis of Variance
123. The human resources department of a software company encourages their employees to
participate in a wellness program. They sampled 16 employees, 2 males and 2 females from
four different workout routines and measured their peak heart rate. The ANOVA for the
research follows.
What is the Workout mean square?
124. The human resources department of a software company encourages their employees to
participate in a wellness program. They sampled 16 employees, 2 males and 2 females from
four different workout routines and measured their peak heart rate. The ANOVA for the
research follows.
What is the F-statistic for Gender?
12-40
Chapter 12 - Analysis of Variance
125. The human resources department of a software company encourages their employees to
participate in a wellness program. They sampled 16 employees, 2 males and 2 females from
four different workout routines and measured their peak heart rate. The ANOVA for the
research follows.
Which source of variation significantly affects peak heart rate?
Essay Questions
126. What is the purpose of using a blocking variable in a two-way ANOVA?
127. When testing a hypothesis regarding the equality of two population means, what is the
analogy to a blocking variable?
12-41
Chapter 12 - Analysis of Variance
128. In a two-way ANOVA, when is an interaction source of variance included?
129. What is the advantage of using ANOVA to test for differences among treatment means
rather than testing all possible pairs of treatment means?
12-42
Chapter 12 - Analysis of Variance
Chapter 12 Analysis of Variance Answer Key
True / False Questions
1. The F distribution's curve is positively skewed.
TRUE
AACSB: Communication Abilities
Bloom's: Knowledge
Difficulty: Medium
Learning Objective: 12-01 List the characteristics of the F distribution and locate values in an F table.
Topic: F-distribution
2. One characteristic of the F distribution is that the computed F can only range between -1
and +1.
FALSE
AACSB: Communication Abilities
Bloom's: Knowledge
Difficulty: Easy
Learning Objective: 12-01 List the characteristics of the F distribution and locate values in an F table.
Topic: F-distribution
3. If the computed value of F is 0.99 and the critical value is 3.89, we would not reject the
null hypothesis.
TRUE
AACSB: Communication Abilities
Bloom's: Comprehension
Difficulty: Medium
Learning Objective: 12-02 Perform a test of hypothesis to determine whether the variances of two populations are equal.
Topic: Comparing two population variances
12-43
Chapter 12 - Analysis of Variance
4. For the hypothesis test,
, with n1 = 10 and n2 = 10, the F-test statistic is
2.56. At the 0.01 level of significance, we would reject the null hypothesis.
FALSE
AACSB: Analytic Skills
Bloom's: Application
Difficulty: Hard
Learning Objective: 12-02 Perform a test of hypothesis to determine whether the variances of two populations are equal.
Topic: Comparing two population variances
5. To employ ANOVA, the populations being studied must be approximately normally
distributed.
TRUE
AACSB: Communication Abilities
Bloom's: Knowledge
Difficulty: Easy
Learning Objective: 12-03 Describe the ANOVA approach for testing differences in sample means.
Topic: ANOVA Concepts
12-44
Chapter 12 - Analysis of Variance
6. To employ ANOVA, the populations should have approximately equal standard
deviations.
TRUE
AACSB: Communication Abilities
Bloom's: Knowledge
Difficulty: Easy
Learning Objective: 12-03 Describe the ANOVA approach for testing differences in sample means.
Topic: ANOVA Concepts
7. The alternative hypothesis used in ANOVA is
FALSE
.
AACSB: Communication Abilities
Bloom's: Knowledge
Difficulty: Medium
Learning Objective: 12-04 Organize data into appropriate ANOVA tables for analysis.
Topic: ANOVA Hypotheses
8. For an ANOVA test, rejection of the null hypothesis does not identify which treatment
means differ significantly.
TRUE
AACSB: Communication Abilities
Bloom's: Comprehension
Difficulty: Medium
Learning Objective: 12-04 Organize data into appropriate ANOVA tables for analysis.
Topic: ANOVA Hypotheses
9. In an ANOVA table, k represents the total number of sample observations and n represents
the total number of treatments.
FALSE
AACSB: Communication Abilities
Bloom's: Knowledge
Difficulty: Medium
Learning Objective: 12-05 Conduct a test of hypothesis among three or more treatment means and describe the results.
Topic: The ANOVA test
12-45
Chapter 12 - Analysis of Variance
10. If a confidence interval for the difference between a pair of treatment means includes 0,
then we reject the null hypothesis that there is no difference in the pair of treatment means.
FALSE
AACSB: Communication Abilities
Bloom's: Comprehension
Difficulty: Medium
Learning Objective: 12-06 Develop confidence intervals for the differences between treatment means and interpret the results.
Topic: Inferences about pairs of treatment means
11. If we want to determine which treatment means differ, we compute a confidence interval
for the difference between each pair of means.
TRUE
AACSB: Communication Abilities
Bloom's: Comprehension
Difficulty: Easy
Learning Objective: 12-06 Develop confidence intervals for the differences between treatment means and interpret the results.
Topic: Inferences about pairs of treatment means
12. When a blocking effect is included in an ANOVA, the result is a larger error sum of
squares.
FALSE
AACSB: Communication Abilities
Bloom's: Comprehension
Difficulty: Medium
Learning Objective: 12-07 Carry out a test of hypothesis among treatment means using a blocking variable and understand the results.
Topic: Two-way ANOVA
13. When a blocking effect is included in an ANOVA, the analysis is more likely to detect
differences in the treatment means.
TRUE
AACSB: Communication Abilities
Bloom's: Comprehension
Difficulty: Hard
Learning Objective: 12-07 Carry out a test of hypothesis among treatment means using a blocking variable and understand the results.
Topic: Two-way ANOVA
12-46
Chapter 12 - Analysis of Variance
14. In a two-way ANOVA with interaction, there are two factor effects and an interaction
effect.
TRUE
AACSB: Communication Abilities
Bloom's: Comprehension
Difficulty: Easy
Learning Objective: 12-08 Perform a two-way ANOVA with interaction and describe the results.
Topic: Two-way ANOVA with interaction
15. Interaction between two factors occurs when the effect of one factor on the response
variable is the same for any value of another factor.
FALSE
AACSB: Communication Abilities
Bloom's: Comprehension
Difficulty: Hard
Learning Objective: 12-08 Perform a two-way ANOVA with interaction and describe the results.
Topic: Two-way ANOVA with interaction
Multiple Choice Questions
16. An F statistic is:
A. a ratio of two means.
B. a ratio of two variances.
C. the difference between three means.
D. a population parameter.
AACSB: Communication Abilities
Bloom's: Knowledge
Difficulty: Easy
Learning Objective: 12-01 List the characteristics of the F distribution and locate values in an F table.
Topic: F-distribution
12-47
Chapter 12 - Analysis of Variance
17. What distribution does the F distribution approach as the sample size increases?
A. Binomial
B. Normal
C. Poisson
D. Exponential
AACSB: Communication Abilities
Bloom's: Comprehension
Difficulty: Medium
Learning Objective: 12-01 List the characteristics of the F distribution and locate values in an F table.
Topic: F-distribution
18. Which statement is correct about the F distribution?
A. Cannot be negative
B. Cannot be positive
C. Is the same as the t distribution
D. Is the same as the z distribution
AACSB: Communication Abilities
Bloom's: Knowledge
Difficulty: Medium
Learning Objective: 12-01 List the characteristics of the F distribution and locate values in an F table.
Topic: F-distribution
19. Analysis of variance is used to
A. compare nominal data.
B. compute t test.
C. compare population proportions.
D. simultaneously compare several population means.
AACSB: Communication Abilities
Bloom's: Comprehension
Difficulty: Medium
Learning Objective: 12-03 Describe the ANOVA approach for testing differences in sample means.
Topic: ANOVA Concepts
12-48
Chapter 12 - Analysis of Variance
20. A large department store examined a sample of the 18 credit card sales and recorded the
amounts charged for each of three types of credit cards: MasterCard, Visa and Discover. Six
MasterCard sales, seven Visa and five Discover sales were recorded. The store used an
ANOVA to test if the mean sales for each credit card were equal. What are the degrees of
freedom for the F statistic?
A. 18 in the numerator, 3 in the denominator
B. 3 in the numerator, 18 in the denominator
C. 2 in the numerator, 15 in the denominator
D. 6 in the numerator, 15 in the denominator
AACSB: Analytic Skills
Bloom's: Application
Difficulty: Medium
Learning Objective: 12-05 Conduct a test of hypothesis among three or more treatment means and describe the results.
Topic: The ANOVA test
21. Suppose that an automobile manufacturer designed a radically new lightweight engine and
wants to recommend the grade of gasoline that will have the best fuel economy. The four
grades are: regular, below regular, premium, and super premium. The test car made three trial
runs on the test track using each of the four grades and the miles per gallon recorded. At the
0.05 level, what is the critical value of F used to test the hypothesis that the miles per gallon
for each fuel is the same?
A. 1.96
B. 4.07
C. 2.33
D. 12.00
AACSB: Analytic Skills
Bloom's: Application
Difficulty: Medium
Learning Objective: 12-05 Conduct a test of hypothesis among three or more treatment means and describe the results.
Topic: The ANOVA test
12-49
Chapter 12 - Analysis of Variance
22. Three different fertilizers were applied to a field of celery. In computing F, how many
degrees of freedom are there in the numerator?
A. 0
B. 1
C. 2
D. 3
AACSB: Analytic Skills
Bloom's: Application
Difficulty: Medium
Learning Objective: 12-05 Conduct a test of hypothesis among three or more treatment means and describe the results.
Topic: The ANOVA test
23. Suppose a package delivery company purchased 14 trucks at the same time. Five trucks
were purchased from manufacturer A, four from manufacturer B, and five from manufacturer
C. The cost of maintaining each truck was recorded. The company used ANOVA to test if the
mean maintenance cost of the trucks from each manufacturer were equal. To apply the F test,
how many degrees of freedom must be in the denominator?
A. 2
B. 3
C. 11
D. 14
AACSB: Analytic Skills
Bloom's: Application
Difficulty: Medium
Learning Objective: 12-05 Conduct a test of hypothesis among three or more treatment means and describe the results.
Topic: The ANOVA test
12-50
Chapter 12 - Analysis of Variance
24. An experiment to determine the most effective way to teach safety principles applied four
different teaching methods. Some employees were given programmed instruction booklets
and worked through the course at their own pace. Other employees attended lectures. A third
group watched a television presentation, and a fourth group was divided into small discussion
groups. A high of 10 was possible. A sample of five tests was selected from each group. The
test grade results were:
At the 0.01 level, what is the critical value?
A. 1.00
B. 1.96
C. 3.24
D. 5.29
AACSB: Analytic Skills
Bloom's: Application
Difficulty: Medium
Learning Objective: 12-05 Conduct a test of hypothesis among three or more treatment means and describe the results.
Topic: The ANOVA test
12-51
Chapter 12 - Analysis of Variance
25. In ANOVA, an F statistic is used to test a null hypothesis such as:
A. Option A
B. Option B
C. Option C
D. Option D
AACSB: Communication Abilities
Bloom's: Comprehension
Difficulty: Easy
Learning Objective: 12-05 Conduct a test of hypothesis among three or more treatment means and describe the results.
Topic: The ANOVA test
26. An electronics company wants to compare the quality of their cell phones to the cell
phones from three competitors. They sample 10 phones from each company and count the
number of defects for each phone. If ANOVA were used to compare the average number of
defects, then the treatments would be defined as:
A. The number of cell phones sampled.
B. The average number of defects.
C. The total number of phones.
D. The four companies.
AACSB: Communication Abilities
Bloom's: Comprehension
Difficulty: Easy
Learning Objective: 12-04 Organize data into appropriate ANOVA tables for analysis.
Topic: ANOVA Hypotheses
12-52
Chapter 12 - Analysis of Variance
27. Several employees have submitted different methods of assembling a subassembly.
Sample data for each method are:
How many treatments are there?
A. 3
B. 4
C. 12
D. 0
AACSB: Communication Abilities
Bloom's: Comprehension
Difficulty: Medium
Learning Objective: 12-04 Organize data into appropriate ANOVA tables for analysis.
Topic: ANOVA Hypotheses
28. If an ANOVA test is conducted and the null hypothesis is rejected, what does this
indicate?
A. Too many degrees of freedom
B. No difference between the population means
C. A difference between at least one pair of population means
D. All population means are different
AACSB: Communication Abilities
Bloom's: Comprehension
Difficulty: Medium
Learning Objective: 12-05 Conduct a test of hypothesis among three or more treatment means and describe the results.
Topic: The ANOVA test
12-53
Chapter 12 - Analysis of Variance
29. A preliminary study of hourly wages paid to unskilled employees in three metropolitan
areas was conducted. Seven employees were included from Area A, 9 from Area B, and 12
from Area C. The test statistic was computed to be 4.91. What can we conclude at the 0.05
level?
A. Mean hourly wages of unskilled employees of all areas are equal
B. Mean hourly wages in at least 2 metropolitan areas are different
C. More degrees of freedom are needed
D. None of these is correct
AACSB: Analytic Skills
Bloom's: Application
Difficulty: Medium
Learning Objective: 12-05 Conduct a test of hypothesis among three or more treatment means and describe the results.
Topic: The ANOVA test
30. In ANOVA analysis, when the null hypothesis is rejected, we can test for differences
between treatment means by
A. constructing confidence intervals.
B. adding another treatment.
C. doing an additional ANOVA.
D. doing a t test.
AACSB: Communication Abilities
Bloom's: Comprehension
Difficulty: Medium
Learning Objective: 12-06 Develop confidence intervals for the differences between treatment means and interpret the results.
Topic: Inferences about pairs of treatment means
31. When the null hypothesis for an ANOVA analysis comparing four treatment means, is
rejected,
A. 2 comparisons of treatment means can be made.
B. 4 comparisons of treatment means can be made.
C. 6 comparisons of treatment means can be made.
D. 8 comparisons of treatment means can be made.
AACSB: Communication Abilities
Bloom's: Comprehension
Difficulty: Medium
Learning Objective: 12-06 Develop confidence intervals for the differences between treatment means and interpret the results.
Topic: Inferences about pairs of treatment means
12-54
Chapter 12 - Analysis of Variance
32. The null hypothesis for an ANOVA analysis comparing four treatment means is rejected.
The four sample means are:
1= 10,
2=12,
3= 15,
4=18. The sample size for each
treatment is the same. If ( 1) is significantly different from zero, then
2
A. 1 is significantly less than 2, 3, and 4.
B. 2 is significantly less than 3 and 4.
C. 3 and 4 are significantly different.
D. 1, 2, 3, and 4 are all equal.
AACSB: Communication Abilities
Bloom's: Comprehension
Difficulty: Medium
Learning Objective: 12-06 Develop confidence intervals for the differences between treatment means and interpret the results.
Topic: Inferences about pairs of treatment means
33. When testing for differences between treatment means, the t statistic is based on:
A. The treatment degrees of freedom.
B. The total degrees of freedom.
C. The error degrees of freedom.
D. The ratio of treatment and error degrees of freedom.
AACSB: Communication Abilities
Bloom's: Comprehension
Difficulty: Medium
Learning Objective: 12-06 Develop confidence intervals for the differences between treatment means and interpret the results.
Topic: about Inferences pairs of treatment means
34. When testing for differences between treatment means, a confidence interval is based on
A. the mean square error.
B. the standard deviation.
C. the sum of squared errors.
D. the standard error of the mean.
AACSB: Communication Abilities
Bloom's: Comprehension
Difficulty: Medium
Learning Objective: 12-06 Develop confidence intervals for the differences between treatment means and interpret the results.
Topic: Inferences about pairs of treatment means
12-55
Chapter 12 - Analysis of Variance
35. When testing for differences between treatment means, the degrees of freedom for the t
statistic are:
A. k
B. (n - 1)
C. (n - k)
D. (1/n1 + 1/n2)
AACSB: Communication Abilities
Bloom's: Comprehension
Difficulty: Medium
Learning Objective: 12-06 Develop confidence intervals for the differences between treatment means and interpret the results.
Topic: Inferences about pairs of treatment means
36. A manufacturer of automobile transmissions uses two different processes. Management
ordered a study of the production costs to see if there is a difference among the two processes.
A summary of the findings is shown below.
What is the critical value of F at the 5% level of significance?
A. 19.45
B. 3.00
C. 4.41
D. 4.38
AACSB: Analytic Skills
Bloom's: Application
Difficulty: Hard
Learning Objective: 12-05 Conduct a test of hypothesis among three or more treatment means and describe the results.
Topic: The ANOVA test
12-56
Chapter 12 - Analysis of Variance
37. A manufacturer of automobile transmissions uses two different processes. Management
ordered a study of the production costs to see if there is a difference between the two
processes. A summary of the findings is shown below.
What is the critical value of F at the 1% level of significance?
A. 9.46
B. 8.29
C. 8.18
D. 4.61
AACSB: Analytic Skills
Bloom's: Application
Difficulty: Hard
Learning Objective: 12-05 Conduct a test of hypothesis among three or more treatment means and describe the results.
Topic: The ANOVA test
38. A manufacturer of automobile transmissions uses three different processes. Management
ordered a study of the production costs to see if there is a difference among the three
processes. A summary of the findings is shown below.
What are the degrees of freedom for the treatment sum of squares?
A. 2
B. 3
C. 10
D. 27
AACSB: Analytic Skills
Bloom's: Application
Difficulty: Medium
Learning Objective: 12-05 Conduct a test of hypothesis among three or more treatment means and describe the results.
Topic: The ANOVA test
12-57
Chapter 12 - Analysis of Variance
39. A manufacturer of automobile transmissions uses three different processes. Management
ordered a study of the production costs to see if there is a difference among the three
processes. A summary of the findings is shown below.
What are the degrees of freedom for the error sum of squares?
A. 3
B. 10
C. 27
D. 30
AACSB: Analytic Skills
Bloom's: Application
Difficulty: Medium
Learning Objective: 12-05 Conduct a test of hypothesis among three or more treatment means and describe the results.
Topic: The ANOVA test
40. A manufacturer of automobile transmissions uses three different processes. Management
ordered a study of the production costs to see if there is a difference among the three
processes. A summary of the findings is shown below.
What are the total degrees of freedom?
A. 27
B. 28
C. 29
D. 30
AACSB: Analytic Skills
Bloom's: Application
Difficulty: Medium
Learning Objective: 12-05 Conduct a test of hypothesis among three or more treatment means and describe the results.
Topic: The ANOVA test
12-58
Chapter 12 - Analysis of Variance
41. Given the following Analysis of Variance table for three treatments each with six
observations.
What are the degrees of freedom for the treatment and error sum of squares?
A. 3 and 18
B. 2 and 17
C. 3 and 15
D. 2 and 15
AACSB: Analytic Skills
Bloom's: Application
Difficulty: Medium
Learning Objective: 12-05 Conduct a test of hypothesis among three or more treatment means and describe the results.
Topic: The ANOVA test
42. Given the following Analysis of Variance table for three treatments each with six
observations.
What is the critical value of F at the 5% level of significance?
A. 3.29
B. 3.68
C. 3.59
D. 3.20
AACSB: Analytic Skills
Bloom's: Application
Difficulty: Medium
Learning Objective: 12-05 Conduct a test of hypothesis among three or more treatment means and describe the results.
Topic: The ANOVA test
12-59
Chapter 12 - Analysis of Variance
43. Given the following Analysis of Variance table for three treatments each with six
observations.
What is the mean square for treatments?
A. 71.2
B. 71.4
C. 558
D. 534
AACSB: Analytic Skills
Bloom's: Application
Difficulty: Hard
Learning Objective: 12-05 Conduct a test of hypothesis among three or more treatment means and describe the results.
Topic: The ANOVA test
44. Given the following Analysis of Variance table for three treatments each with six
observations.
What is the computed value of F?
A. 7.48
B. 7.84
C. 8.84
D. 8.48
AACSB: Analytic Skills
Bloom's: Application
Difficulty: Hard
Learning Objective: 12-05 Conduct a test of hypothesis among three or more treatment means and describe the results.
Topic: The ANOVA test
12-60
Chapter 12 - Analysis of Variance
45. Given the following Analysis of Variance table for three treatments each with six
observations.
What is the decision regarding the null hypothesis?
A. Reject H0 - there is a difference in treatment means
B. Fail to reject H0 - there is a difference in treatment means
C. Reject H0 - there is a difference in errors
D. Fail to reject H0 - there is a difference in errors
AACSB: Reflective Thinking
Bloom's: Analysis
Difficulty: Hard
Learning Objective: 12-05 Conduct a test of hypothesis among three or more treatment means and describe the results.
Topic: The ANOVA test
46. Two accounting professors decided to compare the variance of their grading procedures.
To accomplish this, they each graded the same 10 exams with the following results:
What is H0?
A. Option A
B. Option B
C. Option C
D. Option D
AACSB: Communication Abilities
Bloom's: Knowledge
Difficulty: Medium
Learning Objective: 12-02 Perform a test of hypothesis to determine whether the variances of two populations are equal.
Topic: Comparing two population variances
12-61
Chapter 12 - Analysis of Variance
47. Two accounting professors decided to compare the variance of their grading procedures.
To accomplish this, they each graded the same 10 exams with the following results:
What is H1?
A. Option A
B. Option B
C. Option C
D. Option D
AACSB: Communication Abilities
Bloom's: Knowledge
Difficulty: Medium
Learning Objective: 12-02 Perform a test of hypothesis to determine whether the variances of two populations are equal.
Topic: Comparing two population variances
48. Two accounting professors decided to compare the variance of their grading procedures.
To accomplish this, they each graded the same 10 exams with the following results:
What are the degrees of freedom for the numerator of the F ratio?
A. 8
B. 9
C. 10
D. 18
AACSB: Analytic Skills
Bloom's: Application
Difficulty: Medium
Learning Objective: 12-02 Perform a test of hypothesis to determine whether the variances of two populations are equal.
Topic: Comparing two population variances
12-62
Chapter 12 - Analysis of Variance
49. Two accounting professors decided to compare the variance of their grading procedures.
To accomplish this, they each graded the same 10 exams with the following results:
What are the degrees of freedom for the denominator of the F ratio?
A. 20
B. 18
C. 10
D. 9
AACSB: Analytic Skills
Bloom's: Application
Difficulty: Medium
Learning Objective: 12-02 Perform a test of hypothesis to determine whether the variances of two populations are equal.
Topic: Comparing two population variances
50. Two accounting professors decided to compare the variance of their grading procedures.
To accomplish this, they each graded the same 10 exams with the following results:
What is the critical value of F at the 0.01 level of significance?
A. 5.85
B. 5.35
C. 6.51
D. 4.03
AACSB: Analytic Skills
Bloom's: Application
Difficulty: Medium
Learning Objective: 12-02 Perform a test of hypothesis to determine whether the variances of two populations are equal.
Topic: Comparing two population variances
12-63
Chapter 12 - Analysis of Variance
51. Two accounting professors decided to compare the variance of their grading procedures.
To accomplish this, they each graded the same 10 exams with the following results:
What is the critical value of F at the 0.05 level of significance?
A. 5.85
B. 5.35
C. 3.18
D. 4.03
AACSB: Analytic Skills
Bloom's: Application
Difficulty: Medium
Learning Objective: 12-02 Perform a test of hypothesis to determine whether the variances of two populations are equal.
Topic: Comparing two population variances
52. Two accounting professors decided to compare the variance of their grading procedures.
To accomplish this, they each graded the same 10 exams with the following results:
The calculated F ratio is
A. 3.484
B. 1.867
C. 3.18
D. 5.35
AACSB: Analytic Skills
Bloom's: Application
Difficulty: Hard
Learning Objective: 12-02 Perform a test of hypothesis to determine whether the variances of two populations are equal.
Topic: Comparing two population variances
12-64
Chapter 12 - Analysis of Variance
53. Two accounting professors decided to compare the variance of their grading procedures.
To accomplish this, they each graded the same 10 exams with the following results:
At the 1% level of significance, what is the decision?
A. Reject the null hypothesis and conclude the variances are different.
B. Fail to reject the null hypothesis and conclude the variances are different.
C. Reject the null hypothesis and conclude the variances are the same.
D. Fail to reject the null hypothesis and conclude the variances are the same.
AACSB: Reflective Thinking Skills
Bloom's: Analysis
Difficulty: Hard
Learning Objective: 12-02 Perform a test of hypothesis to determine whether the variances of two populations are equal.
Topic: Comparing two population variances
54. Two accounting professors decided to compare the variance of their grading procedures.
To accomplish this, they each graded the same 10 exams with the following results:
At the 5% level of significance, what is the decision regarding the null hypothesis?
A. Reject the null hypothesis and conclude the variances are different.
B. Fail to reject the null hypothesis and conclude no significant difference in the variances.
C. Reject the null hypothesis and conclude the variances are the same.
D. Fail to reject the null hypothesis and conclude the variances are the same.
AACSB: Reflective Thinking
Bloom's: Analysis
Difficulty: Hard
Learning Objective: 12-02 Perform a test of hypothesis to determine whether the variances of two populations are equal.
Topic: Comparing two population variances
12-65
Chapter 12 - Analysis of Variance
55. A random sample of 30 executives from companies with assets over $1 million was
selected and asked for their annual income and level of education. The ANOVA comparing
the average income among three levels of education rejected the null hypothesis. The Mean
Square Error (MSE) was 243.7. The following table summarized the results:
When comparing the mean annual incomes for executives with Undergraduate and Master's
Degree or more, the following 95% confidence interval can be constructed:
A. 2.0 2.052 * 6.51
B. 2.0 3.182 * 6.51
C. 2.0 2.052 * 42.46
D. 2.0 3.182 * 42.46
AACSB: Analytic Skills
Bloom's: Application
Difficulty: Hard
Learning Objective: 12-06 Develop confidence intervals for the differences between treatment means and interpret the results.
Topic: Inferences about pairs of treatment means
56. A random sample of 30 executives from companies with assets over $1 million was
selected and asked for their annual income and level of education. The ANOVA comparing
the average income among three levels of education rejected the null hypothesis. The Mean
Square Error (MSE) was 243.7. The following table summarized the results:
Based on the comparison between the mean annual incomes for executives with
Undergraduate and Master's Degree or more,
A. A confidence interval shows that the mean annual incomes are not significantly different.
B. The ANOVA results show that the mean annual incomes are significantly different.
C. A confidence interval shows that the mean annual incomes are significantly different.
D. The ANOVA results show that the mean annual incomes are not significantly different.
AACSB: Analytic Skills
Bloom's: Application
Difficulty: Medium
Learning Objective: 12-06 Develop confidence intervals for the differences between treatment means and interpret the results.
Topic: Inferences about pairs of treatment means
12-66
Chapter 12 - Analysis of Variance
57. A random sample of 30 executives from companies with assets over $1 million was
selected and asked for their annual income and level of education. The ANOVA comparing
the average income among three levels of education rejected the null hypothesis. The Mean
Square Error (MSE) was 243.7. The following table summarized the results:
When comparing the mean annual incomes for executives with a High School education or
less and Undergraduate Degree, the 95% confidence interval shows an interval of 11.7 to 42.7
for the difference. This result indicates that
A. There is no significant difference between the two incomes.
B. The interval contains a difference of zero.
C. Executives with an Undergraduate Degree earn significantly more than executives with a
High School education or less.
D. Executives with an Undergraduate Degree earn significantly less than executives with a
High School education or less.
AACSB: Analytic Skills
Bloom's: Application
Difficulty: Hard
Learning Objective: 12-06 Develop confidence intervals for the differences between treatment means and interpret the results.
Topic: Inferences about pairs of treatment means
12-67
Chapter 12 - Analysis of Variance
58. A random sample of 40 companies with assets over $10 million was selected and asked
for their annual computer technology expense and industry. The ANOVA comparing the
average computer technology expense among three industries rejected the null hypothesis.
The Mean Square Error (MSE) was 195. The following table summarized the results:
When comparing the mean annual computer technology expense for companies in the
Education and Tax services industries, the following 95% confidence interval can be
constructed:
A. 13.5 2.026 * 5.78
B. 13.5 2.021 * 5.78
C. 13.5 2.026 * 13.96
D. 13.5 2.021 * 13.96
AACSB: Analytic Skills
Bloom's: Application
Difficulty: Hard
Learning Objective: 12-06 Develop confidence intervals for the differences between treatment means and interpret the results.
Topic: Inferences about pairs of treatment means
12-68
Chapter 12 - Analysis of Variance
59. A random sample of 40 companies with assets over $10 million was selected and asked
for their annual computer technology expense and industry. The ANOVA comparing the
average computer technology expense among three industries rejected the null hypothesis.
The Mean Square Error (MSE) was 195. The following table summarized the results:
Based on the comparison between the mean annual computer technology expense for
companies in the Education and Tax services industries,
A. A confidence interval shows that the mean annual computer technology expenses are not
significantly different.
B. The ANOVA results show that the mean annual computer technology expenses are
significantly different.
C. A confidence interval shows that the mean annual computer technology expenses are
significantly different.
D. The ANOVA results show that the mean annual computer technology expenses are not
significantly different.
AACSB: Analytic Skills
Bloom's: Application
Difficulty: Medium
Learning Objective: 12-06 Develop confidence intervals for the differences between treatment means and interpret the results.
Topic: Inferences about pairs of treatment means
12-69
Chapter 12 - Analysis of Variance
60. A random sample of 40 companies with assets over $10 million was selected and asked
for their annual computer technology expense and industry. The ANOVA comparing the
average computer technology expense among three industries rejected the null hypothesis.
The Mean Square Error (MSE) was 195. The following table summarized the results:
Based on the comparison between the mean annual computer technology expense for
companies in the Tax Service and Food Service industries, the 95% confidence interval shows
an interval of -14.85 to 5.85 for the difference. This result indicates that
A. There is no significant difference between the two expenses.
B. The interval contains a difference of 20.7.
C. Companies in the Tax Service industry spend significantly less than companies in the Food
Service industry.
D. Companies in the Food Service industry spend significantly less than companies in the Tax
Service industry.
AACSB: Analytic Skills
Bloom's: Application
Difficulty: Hard
Learning Objective: 12-06 Develop confidence intervals for the differences between treatment means and interpret the results.
Topic: Inferences about pairs of treatment means
12-70
Chapter 12 - Analysis of Variance
61. A random sample of 16 companies was selected and asked for their annual dividend rate
in three different industries: utilities, banking, and insurance. The ANOVA comparing the
mean annual dividend rate among three industries rejected the null hypothesis. The Mean
Square Error (MSE) was 3.36. The following table summarized the results:
When comparing the mean annual dividend rate for companies in the utilities and insurance
industries, the following 95% confidence interval can be constructed:
A. 5.78 2.160 * 2.40
B. 5.78 2.120 * 2.40
C. 5.78 2.160 * 1.11
D. 5.78 2.120 * 1.11
AACSB: Analytic Skills
Bloom's: Application
Difficulty: Hard
Learning Objective: 12-06 Develop confidence intervals for the differences between treatment means and interpret the results.
Topic: Inferences about pairs of treatment means
12-71
Chapter 12 - Analysis of Variance
62. A random sample of 16 companies was selected and asked for their annual dividend rate
in three different industries: utilities, banking, and insurance. The ANOVA comparing the
mean annual dividend rate among three industries rejected the null hypothesis. The Mean
Square Error (MSE) was 3.36. The following table summarized the results:
Based on the comparison between the mean annual dividend rate for companies in the utilities
and insurance industries,
A. A confidence interval shows that the mean annual dividend rates are not significantly
different.
B. The ANOVA results show that the mean annual dividend rates are significantly different.
C. A confidence interval shows that the mean annual dividend rates are significantly different.
D. The ANOVA results show that the mean annual dividend rates are not significantly
different.
AACSB: Analytic Skills
Bloom's: Application
Difficulty: Medium
Learning Objective: 12-06 Develop confidence intervals for the differences between treatment means and interpret the results.
Topic: Inferences about pairs of treatment means
12-72
Chapter 12 - Analysis of Variance
63. A random sample of 16 companies was selected and asked for their annual dividend rate
in three different industries: utilities, banking, and insurance. The ANOVA comparing the
mean annual dividend rate among three industries rejected the null hypothesis. The Mean
Square Error (MSE) was 3.36. The following table summarized the results:
Based on the comparison between the mean annual dividend rate for companies in the utilities
and banking, the 95% confidence interval shows an interval of 1.28 to 6.28 for the difference.
This result indicates that
A. There is no significant difference between the two rates.
B. The interval contains a difference of 5.00.
C. The annual dividend rate in the utilities industry is significantly less than the annual
dividend rate in banking industry.
D. The annual dividend rate in banking industry is significantly less than the annual dividend
rate in utilities industry.
AACSB: Analytic Skills
Bloom's: Application
Difficulty: Hard
Learning Objective: 12-06 Develop confidence intervals for the differences between treatment means and interpret the results.
Topic: Inferences about pairs of treatment means
64. In a two-way ANOVA, a blocking variable is used to
A. increase the error sum of squares.
B. decrease the error sum of squares.
C. increase the treatment sum of squares.
D. decrease the treatment sum of squares.
AACSB: Communication Abilities
Bloom's: Comprehension
Difficulty: Medium
Learning Objective: 12-07 Carry out a test of hypothesis among treatment means using a blocking variable and understand the results.
Topic: Two-way ANOVA
12-73
Chapter 12 - Analysis of Variance
65. In a two-way ANOVA, the sources of variation are
A. Total variation and error variation.
B. Total variation, treatment variation, and error variation.
C. Total variation, treatment variation, blocking variation and error variation.
D. Treatment variation and blocking variation.
AACSB: Communication Abilities
Bloom's: Comprehension
Difficulty: Medium
Learning Objective: 12-07 Carry out a test of hypothesis among treatment means using a blocking variable and understand the results.
Topic: Two-way ANOVA
66. The college of business was interested in comparing the attendance for three different
class times for a business statistics class. The data follow.
What is the blocking variable?
A. Day.
B. Class time.
C. Tuesday.
D. 8:00 am class.
AACSB: Communication Abilities
Bloom's: Comprehension
Difficulty: Medium
Learning Objective: 12-07 Carry out a test of hypothesis among treatment means using a blocking variable and understand the results.
Topic: Two-way ANOVA
12-74
Chapter 12 - Analysis of Variance
67. The college of business was interested in comparing the attendance for three different
class times for a business statistics class. The data follow.
What is the treatment variable?
A. Day.
B. Class time.
C. Tuesday.
D. 8:00 am class.
AACSB: Communication Abilities
Bloom's: Comprehension
Difficulty: Medium
Learning Objective: 12-07 Carry out a test of hypothesis among treatment means using a blocking variable and understand the results.
Topic: Two-way ANOVA
12-75
Chapter 12 - Analysis of Variance
68. The college of business was interested in comparing the attendance for three different
class times for a business statistics class. The data follow.
What are the block and treatment degrees of freedom?
A. 5 and 3.
B. 5 and 5.
C. 4 and 2.
D. 3 and 15.
AACSB: Communication Abilities
Bloom's: Comprehension
Difficulty: Medium
Learning Objective: 12-07 Carry out a test of hypothesis among treatment means using a blocking variable and understand the results.
Topic: Two-way ANOVA
12-76
Chapter 12 - Analysis of Variance
69. The college of business was interested in comparing the attendance for three different
class times for a business statistics class. The data follow.
What is the critical F statistic for testing the hypothesis of equal treatment means at the 0.05
significance level?
A. 1.96.
B. 6.94.
C. 3.84.
D. 4.46.
AACSB: Communication Abilities
Bloom's: Comprehension
Difficulty: Medium
Learning Objective: 12-07 Carry out a test of hypothesis among treatment means using a blocking variable and understand the results.
Topic: Two-way ANOVA
70. In a two-way ANOVA with interaction, a significant interaction term indicates that
A. the response variable is interactive.
B. a blocking factor is present.
C. both factors are unrelated.
D. both factors have a combined effect on the response variable.
AACSB: Communication Abilities
Bloom's: Comprehension
Difficulty: Medium
Learning Objective: 12-08 Perform a two-way ANOVA with interaction and describe the results.
Topic: Two-way ANOVA with interaction
12-77
Chapter 12 - Analysis of Variance
71. A two-way ANOVA with interaction has how many sources of variation?
A. 5.
B. 4.
C. 3.
D. 2.
AACSB: Communication Abilities
Bloom's: Comprehension
Difficulty: Medium
Learning Objective: 12-08 Perform a two-way ANOVA with interaction and describe the results.
Topic: Two-way ANOVA with interaction
72. If there are 5 levels of Factor A and 7 levels of Factor B for an ANOVA with interaction,
what are the interaction degrees of freedom?
A. 12.
B. 35.
C. 24.
D. 10.
AACSB: Communication Abilities
Bloom's: Comprehension
Difficulty: Medium
Learning Objective: 12-08 Perform a two-way ANOVA with interaction and describe the results.
Topic: Two-way ANOVA with interaction
12-78
Chapter 12 - Analysis of Variance
73. The college of business was interested in comparing the interaction of Academic status
and class time on class attendance. Three different classes were sampled for each cell in the
table. The means for each cell follow.
What are the total degrees of freedom?
A. 44.
B. 14.
C. 4.
D. 2.
AACSB: Communication Abilities
Bloom's: Comprehension
Difficulty: Medium
Learning Objective: 12-08 Perform a two-way ANOVA with interaction and describe the results.
Topic: Two-way ANOVA with interaction
12-79
Chapter 12 - Analysis of Variance
74. The college of business was interested in comparing the interaction of Academic status
and class time on class attendance. Three different classes were sampled for each cell in the
table. The means for each cell follow.
What are the error degrees of freedom?
A. 44.
B. 14.
C. 30.
D. 2.
AACSB: Communication Abilities
Bloom's: Comprehension
Difficulty: Medium
Learning Objective: 12-08 Perform a two-way ANOVA with interaction and describe the results.
Topic: Two-way ANOVA with interaction
12-80
Chapter 12 - Analysis of Variance
75. The college of business was interested in comparing the interaction of Academic status
and class time on class attendance. Three different classes were sampled for each cell in the
table. The means for each cell follow.
What are the interaction degrees of freedom?
A. 10.
B. 2.
C. 4.
D. 8.
AACSB: Communication Abilities
Bloom's: Comprehension
Difficulty: Medium
Learning Objective: 12-08 Perform a two-way ANOVA with interaction and describe the results.
Topic: Two-way ANOVA with interaction
Fill in the Blank Questions
76. The F distribution is a ______________ distribution.
continuous
AACSB: Communication Abilities
Bloom's: Knowledge
Difficulty: Medium
Learning Objective: 12-01 List the characteristics of the F distribution and locate values in an F table.
Topic: F-distribution
12-81
Chapter 12 - Analysis of Variance
77. What is the shape of the F distribution? ______________________
Positively skewed
AACSB: Communication Abilities
Bloom's: Knowledge
Difficulty: Medium
Learning Objective: 12-01 List the characteristics of the F distribution and locate values in an F table.
Topic: F-distribution
78. What are the minimum and maximum of values of an F distribution? _______ and
_______
Zero and positive infinity
AACSB: Communication Abilities
Bloom's: Knowledge
Difficulty: Medium
Learning Objective: 12-01 List the characteristics of the F distribution and locate values in an F table.
Topic: F-distribution
79. All values in an F distribution must be _____________.
positive values
AACSB: Communication Abilities
Bloom's: Knowledge
Difficulty: Medium
Learning Objective: 12-01 List the characteristics of the F distribution and locate values in an F table.
Topic: F-distribution
80. What test statistic is used to compare two variances? ________________
F statistic
AACSB: Communication Abilities
Bloom's: Knowledge
Difficulty: Easy
Learning Objective: 12-02 Perform a test of hypothesis to determine whether the variances of two populations are equal.
Topic: Comparing two population variances
12-82
Chapter 12 - Analysis of Variance
81. The F-distribution is useful when testing a requirement of two-sample tests of hypothesis.
What is the assumption? ________________
The population variances are equal
AACSB: Communication Abilities
Bloom's: Comprehension
Difficulty: Medium
Learning Objective: 12-02 Perform a test of hypothesis to determine whether the variances of two populations are equal.
Topic: Comparing two population variances
82. ANOVA requires that the populations should be ______, ______, and _____.
normal or normally distributed; independent; have equal standard deviations or
variances
AACSB: Communication Abilities
Bloom's: Comprehension
Difficulty: Medium
Learning Objective: 12-03 Describe the ANOVA approach for testing differences in sample means.
Topic: ANOVA Concepts
83. What statistical technique is used to test the equality of three or more population means?
____________________
Analysis of variance (ANOVA)
AACSB: Communication Abilities
Bloom's: Knowledge
Difficulty: Easy
Learning Objective: 12-03 Describe the ANOVA approach for testing differences in sample means.
Topic: ANOVA Concepts
84. What is the least number of sources of variation in ANOVA? _________
Two, treatment and error
AACSB: Communication Abilities
Bloom's: Comprehension
Difficulty: Medium
Learning Objective: 12-03 Describe the ANOVA approach for testing differences in sample means.
Topic: ANOVA Concepts
12-83
Chapter 12 - Analysis of Variance
85. In an one-way ANOVA, what are the degrees of freedom associated with the error sum of
squares? ___________
n-k
AACSB: Communication Abilities
Bloom's: Comprehension
Difficulty: Medium
Learning Objective: 12-05 Conduct a test of hypothesis among three or more treatment means and describe the results.
Topic: The ANOVA test
86. In an one-way ANOVA, how many degrees of freedom are associated with the numerator
of the F ratio? _______
k-1
AACSB: Communication Abilities
Bloom's: Comprehension
Difficulty: Medium
Learning Objective: 12-05 Conduct a test of hypothesis among three or more treatment means and describe the results.
Topic: The ANOVA test
87. What is the sum of squares divided by its corresponding degrees of freedom called?
_________________
Mean square
AACSB: Communication Abilities
Bloom's: Comprehension
Difficulty: Hard
Learning Objective: 12-05 Conduct a test of hypothesis among three or more treatment means and describe the results.
Topic: The ANOVA test
88. Assuming that the larger of two variances is in the numerator of an F statistic, in which
tail of the F distribution is the rejection region for analysis of variance? ________
Upper
AACSB: Communication Abilities
Bloom's: Knowledge
Difficulty: Medium
Learning Objective: 12-05 Conduct a test of hypothesis among three or more treatment means and describe the results.
Topic: The ANOVA test
12-84
Chapter 12 - Analysis of Variance
89. In ANOVA, when we do not reject the null hypothesis, what inference do we make about
the population means? ________________
They are equal
AACSB: Communication Abilities
Bloom's: Comprehension
Difficulty: Medium
Learning Objective: 12-04 Organize data into appropriate ANOVA tables for analysis.
Topic: ANOVA Hypotheses
90. What is the null hypothesis for an ANOVA comparing three population means?
____________________
Ho: 1 = 2 = 3
AACSB: Communication Abilities
Bloom's: Knowledge
Difficulty: Medium
Learning Objective: 12-04 Organize data into appropriate ANOVA tables for analysis.
Topic: ANOVA Hypotheses
91. When H0 is rejected in ANOVA, _______ _______ are constructed to identify pairs of
means that differ.
confidence intervals
AACSB: Communication Abilities
Bloom's: Comprehension
Difficulty: Medium
Learning Objective: 12-06 Develop confidence intervals for the differences between treatment means and interpret the results.
Topic: Inferences about pairs of treatment means
92. In a study of protein breakfast bars, five bars from each of three brands were tested to see
if the mean amount of protein per bar differs among the brands. What are the degrees of
freedom for the numerator? ______
2
AACSB: Communication Abilities
Bloom's: Comprehension
Difficulty: Hard
Learning Objective: 12-05 Conduct a test of hypothesis among three or more treatment means and describe the results.
Topic: The ANOVA test
12-85
Chapter 12 - Analysis of Variance
93. In a study of protein breakfast bars, five bars from each of three brands were tested to see
if the mean amount of protein per bar differs among the brands. What are the degrees of
freedom for the denominator? ______
12
AACSB: Communication Abilities
Bloom's: Comprehension
Difficulty: Hard
Learning Objective: 12-05 Conduct a test of hypothesis among three or more treatment means and describe the results.
Topic: The ANOVA test
94. In a study of protein breakfast bars, five bars from each of three brands were tested to see
if the mean amount of protein per bar differs among the brands. If the sum of squares for the
brands is 0.07, what is the mean square for brands? ______
0.035
AACSB: Analytic Skills
Bloom's: Application
Difficulty: Hard
Learning Objective: 12-05 Conduct a test of hypothesis among three or more treatment means and describe the results.
Topic: The ANOVA test
95. In a study of protein breakfast bars, five bars from each of three brands were tested to see
if the mean amount of protein per bar differs among the brands. If the sum of squares for the
error is 0.09, what is the mean square for the error? ______
0.0075
AACSB: Analytic Skills
Bloom's: Application
Difficulty: Hard
Learning Objective: 12-05 Conduct a test of hypothesis among three or more treatment means and describe the results.
Topic: The ANOVA test
12-86
Chapter 12 - Analysis of Variance
96. In a study of protein breakfast bars, five bars from each of three brands were tested to see
if the mean amount of protein per bar differs among the brands. What is the F critical value
for = 0.05? ______
3.89
AACSB: Communication Abilities
Bloom's: Comprehension
Difficulty: Medium
Learning Objective: 12-04 Organize data into appropriate ANOVA tables for analysis.
Topic: ANOVA Hypotheses
97. In a study of protein breakfast bars, five bars from each of three brands were tested to see
if the mean amount of protein per bar differs among the brands. What is the calculated value
of F, if the brand sum of squares is 0.07 and the error sum of squares is 0.09? ______
4.66
AACSB: Analytic Skills
Bloom's: Application
Difficulty: Hard
Learning Objective: 12-05 Conduct a test of hypothesis among three or more treatment means and describe the results.
Topic: The ANOVA test
98. In a two-way ANOVA table with interaction, what are the error degrees of freedom?
_________
(n - kb)
AACSB: Communication Abilities
Bloom's: Comprehension
Difficulty: Hard
Learning Objective: 12-08 Perform a two-way ANOVA with interaction and describe the results.
Topic: Two-way ANOVA with interaction
99. When a second source of variance is included in the ANOVA analysis without interaction,
that source is called a _________________.
blocking variable
AACSB: Communication Abilities
Bloom's: Comprehension
Difficulty: Medium
Learning Objective: 12-07 Carry out a test of hypothesis among treatment means using a blocking variable and understand the results.
Topic: Two-way ANOVA
12-87
Chapter 12 - Analysis of Variance
100. How many mean square errors are summarized in a two-way ANOVA table?
_________
Three - treatment, block and error
AACSB: Communication Abilities
Bloom's: Comprehension
Difficulty: Medium
Learning Objective: 12-07 Carry out a test of hypothesis among treatment means using a blocking variable and understand the results.
Topic: Two-way ANOVA
Short Answer Questions
101. A company compared the variance of salaries for employees who have been employed
for 5 years or less with employees who have been employed for 10 years or more. They
randomly selected 21 employees with 5 years or less experience and 15 employees with 10
years or more experience. The standard deviation for the group with 5 years or less experience
was $2,225; the standard deviation for the group with 10 years or more experience is $1,875.
What is the F test statistic for the hypothesis test?
1.408
AACSB: Analytic Skills
Bloom's: Application
Difficulty: Easy
Learning Objective: 12-02 Perform a test of hypothesis to determine whether the variances of two populations are equal.
Topic: Comparing two population variances
102. A company compared the variance of salaries for employees who have been employed
for 5 years or less with employees who have been employed for 10 years or more. They
randomly selected 21 employees with 5 years or less experience and 15 employees with 10
years or more experience. The standard deviation for the group with 5 years or less experience
was $2,225; the standard deviation for the group with 10 years or more experience is $1,875.
Using the 0.05 significance level, what is the F critical value for the hypothesis test?
2.39
AACSB: Analytic Skills
Bloom's: Application
Difficulty: Easy
Learning Objective: 12-02 Perform a test of hypothesis to determine whether the variances of two populations are equal.
Topic: Comparing two population variances
12-88
Chapter 12 - Analysis of Variance
103. A company compared the variance of salaries for employees who have been employed
for 5 years or less with employees who have been employed for 10 years or more. They
randomly selected 21 employees with 5 years or less experience and 15 employees with 10
years or more experience. The standard deviation for the group with 5 years or less experience
was $2,225; the standard deviation for the group with 10 years or more experience is $1,875.
Using the 0.05 significance level, what is the decision regarding the null hypothesis?
Fail to reject the null hypothesis that the two population variances are equal.
AACSB: Analytic Skills
Bloom's: Application
Difficulty: Easy
Learning Objective: 12-02 Perform a test of hypothesis to determine whether the variances of two populations are equal.
Topic: Comparing two population variances
104. To test the hypothesis that two population variances are equal, a random sample of size
13 was selected from the first population, and a random sample of size 21 was selected from
the second population. What are the degrees of freedom to test the hypothesis?
12 and 20
AACSB: Analytic Skills
Bloom's: Application
Difficulty: Easy
Learning Objective: 12-02 Perform a test of hypothesis to determine whether the variances of two populations are equal.
Topic: Comparing two population variances
105. To test the hypothesis that two population variances are equal, a random sample of size
13 was selected from the first population, and a random sample of size 21 was selected from
the second population. Given that the sample standard deviation from the first population is
larger than the sample standard deviation from the second population, what is the F-critical
value using 0.01 as the significance level?
3.23
AACSB: Analytic Skills
Bloom's: Application
Difficulty: Easy
Learning Objective: 12-02 Perform a test of hypothesis to determine whether the variances of two populations are equal.
Topic: Comparing two population variances
12-89
Chapter 12 - Analysis of Variance
106. A bottle cap manufacturer with four machines and six operators wants to see if variation
in production is due to the machines and/or the operators. The ANOVA table follows.
What are the degrees of freedom for the machines?
3
AACSB: Analytic Skills
Bloom's: Application
Difficulty: Medium
Learning Objective: 12-07 Carry out a test of hypothesis among treatment means using a blocking variable and understand the results.
Topic: Two-way ANOVA
107. A bottle cap manufacturer with four machines and six operators wants to see if variation
in production is due to the machines and/or the operators. ANOVA table follows.
What are the degrees of freedom for the operators?
5
AACSB: Analytic Skills
Bloom's: Application
Difficulty: Medium
Learning Objective: 12-07 Carry out a test of hypothesis among treatment means using a blocking variable and understand the results.
Topic: Two-way ANOVA
12-90
Chapter 12 - Analysis of Variance
108. A bottle cap manufacturer with four machines and six operators wants to see if variation
in production is due to the machines and/or the operators. ANOVA table follows.
What are the degrees of freedom for the errors?
15
AACSB: Analytic Skills
Bloom's: Application
Difficulty: Hard
Learning Objective: 12-07 Carry out a test of hypothesis among treatment means using a blocking variable and understand the results.
Topic: Two-way ANOVA
109. A bottle cap manufacturer with four machines and six operators wants to see if variation
in production is due to the machines and/or the operators. ANOVA table follows.
What is the critical value of F for the machine treatment effect at the 1% level of
significance? ____
5.42
AACSB: Analytic Skills
Bloom's: Application
Difficulty: Medium
Learning Objective: 12-07 Carry out a test of hypothesis among treatment means using a blocking variable and understand the results.
Topic: Two-way ANOVA
12-91
Chapter 12 - Analysis of Variance
110. A bottle cap manufacturer with four machines and six operators wants to see if variation
in production is due to the machines and/or the operators. ANOVA table follows.
What is the critical value of F for the operator block effect at the 1% level of significance?
4.56
AACSB: Analytic Skills
Bloom's: Application
Difficulty: Medium
Learning Objective: 12-07 Carry out a test of hypothesis among treatment means using a blocking variable and understand the results.
Topic: Two-way ANOVA
111. A bottle cap manufacturer with four machines and six operators wants to see if variation
in production is due to the machines and/or the operators. ANOVA table follows.
What is the mean square for machines?
38
AACSB: Analytic Skills
Bloom's: Application
Difficulty: Medium
Learning Objective: 12-07 Carry out a test of hypothesis among treatment means using a blocking variable and understand the results.
Topic: Two-way ANOVA
12-92
Chapter 12 - Analysis of Variance
112. A bottle cap manufacturer with four machines and six operators wants to see if variation
in production is due to the machines and/or the operators. ANOVA table follows.
What is the mean square for operators?
43
AACSB: Analytic Skills
Bloom's: Application
Difficulty: Medium
Learning Objective: 12-07 Carry out a test of hypothesis among treatment means using a blocking variable and understand the results.
Topic: Two-way ANOVA
113. A bottle cap manufacturer with four machines and six operators wants to see if variation
in production is due to the machines and/or the operators. ANOVA table follows.
What is the mean square for error?
3.6
AACSB: Analytic Skills
Bloom's: Application
Difficulty: Medium
Learning Objective: 12-07 Carry out a test of hypothesis among treatment means using a blocking variable and understand the results.
Topic: Two-way ANOVA
12-93
Chapter 12 - Analysis of Variance
114. A bottle cap manufacturer with four machines and six operators wants to see if variation
in production is due to the machines and/or the operators. ANOVA table follows.
What is the computed value of F for the machines?
10.56
AACSB: Analytic Skills
Bloom's: Application
Difficulty: Medium
Learning Objective: 12-07 Carry out a test of hypothesis among treatment means using a blocking variable and understand the results.
Topic: Two-way ANOVA
115. A bottle cap manufacturer with four machines and six operators wants to see if variation
in production is due to the machines and/or the operators. ANOVA table follows.
What is the computed value of F for the operators? _____
11.94
AACSB: Analytic Skills
Bloom's: Application
Difficulty: Medium
Learning Objective: 12-07 Carry out a test of hypothesis among treatment means using a blocking variable and understand the results.
Topic: Two-way ANOVA
12-94
Chapter 12 - Analysis of Variance
116. A bottle cap manufacturer with four machines and six operators wants to see if variation
in production is due to the machines and/or the operators. ANOVA table follows.
Test the hypothesis that all operators are equally productive. State your decision in terms of
the null hypothesis.
Reject the null hypothesis and conclude that the operators are not equally productive
AACSB: Analytic Skills
Bloom's: Application
Difficulty: Medium
Learning Objective: 12-07 Carry out a test of hypothesis among treatment means using a blocking variable and understand the results.
Topic: Two-way ANOVA
117. An ANOVA showed the following comparison of four treatment means.
Which treatment means are significantly different?
None
AACSB: Reflective Thinking
Bloom's: Analysis
Difficulty: Medium
Learning Objective: 12-06 Develop confidence intervals for the differences between treatment means and interpret the results.
Topic: Inferences about pairs of treatment means
12-95
Chapter 12 - Analysis of Variance
118. An ANOVA comparing the waiting times for four different emergency rooms shows the
following comparison of the four mean waiting times.
Which two pairs of means are significantly different?
The mean waiting time for ER1 is significantly different from mean waiting time for ER2;
The mean waiting time for ER2 is significantly different from mean waiting time for ER4;
AACSB: Reflective Thinking
Bloom's: Analysis
Difficulty: Medium
Learning Objective: 12-06 Develop confidence intervals for the differences between treatment means and interpret the results.
Topic: Inferences about pairs of treatment means
119. A random sample of 20 female executives from companies with assets over $1 million
was selected and asked for their annual income and level of education. The ANOVA
comparing the average income among three levels of education rejected the null hypothesis.
The Mean Square Error (MSE) was 250. The following table summarized the results:
To compare the mean annual incomes of female executives with an undergraduate degree and
female executives with a high school or less education, compute the 95% confidence interval.
[21.46, 64.54]
AACSB: Analytic Skills
Bloom's: Application
Difficulty: Hard
Learning Objective: 12-06 Develop confidence intervals for the differences between treatment means and interpret the results.
Topic: Inferences about pairs of treatment means
12-96
Chapter 12 - Analysis of Variance
120. A random sample of 20 female executives from companies with assets over $1 million
was selected and asked for their annual income and level of education. The ANOVA
comparing the average income among three levels of education rejected the null hypothesis.
The Mean Square Error (MSE) was 250. The following table summarized the results:
To compare the mean annual incomes of female executives with an undergraduate degree and
female executives with a Master's degree or more, compute the 99% confidence interval.
[-18.66, 28.66]
AACSB: Analytic Skills
Bloom's: Application
Difficulty: Hard
Learning Objective: 12-06 Develop confidence intervals for the differences between treatment means and interpret the results.
Topic: Inferences about pairs of treatment means
12-97
Chapter 12 - Analysis of Variance
121. A random sample of 20 female executives from companies with assets over $1 million
was selected and asked for their annual income and level of education. The ANOVA
comparing the average income among three levels of education rejected the null hypothesis.
The Mean Square Error (MSE) was 250. The following table summarized the results:
To compare the mean annual incomes of female executives with a high school education or
less and female executives with a Master's degree or more, compute the 90% confidence
interval.
[31.72, 64.28]
AACSB: Analytic Skills
Bloom's: Application
Difficulty: Hard
Learning Objective: 12-06 Develop confidence intervals for the differences between treatment means and interpret the results.
Topic: Inferences about pairs of treatment means
12-98
Chapter 12 - Analysis of Variance
122. The human resources department of a software company encourages their employees to
participate in a wellness program. They sampled 16 employees, 2 males and 2 females from
four different workout routines and measured their peak heart rate. The ANOVA for the
research follows.
What is the Interaction sum of squares?
60.187
AACSB: Analytic Skills
Bloom's: Analysis
Difficulty: Medium
Learning Objective: 12-08 Perform a two-way ANOVA with interaction and describe the results.
Topic: Two-way ANOVA with interaction
123. The human resources department of a software company encourages their employees to
participate in a wellness program. They sampled 16 employees, 2 males and 2 females from
four different workout routines and measured their peak heart rate. The ANOVA for the
research follows.
What is the Workout mean square?
189.063
AACSB: Analytic Skills
Bloom's: Analysis
Difficulty: Medium
Learning Objective: 12-08 Perform a two-way ANOVA with interaction and describe the results.
Topic: Two-way ANOVA with interaction
12-99
Chapter 12 - Analysis of Variance
124. The human resources department of a software company encourages their employees to
participate in a wellness program. They sampled 16 employees, 2 males and 2 females from
four different workout routines and measured their peak heart rate. The ANOVA for the
research follows.
What is the F-statistic for Gender?
1.94
AACSB: Analytic Skills
Bloom's: Analysis
Difficulty: Medium
Learning Objective: 12-08 Perform a two-way ANOVA with interaction and describe the results.
Topic: Two-way ANOVA with interaction
125. The human resources department of a software company encourages their employees to
participate in a wellness program. They sampled 16 employees, 2 males and 2 females from
four different workout routines and measured their peak heart rate. The ANOVA for the
research follows.
Which source of variation significantly affects peak heart rate?
Workout routine
AACSB: Analytic Skills
Bloom's: Analysis
Difficulty: Medium
Learning Objective: 12-08 Perform a two-way ANOVA with interaction and describe the results.
Topic: Two-way ANOVA with interaction
12-100
Chapter 12 - Analysis of Variance
Essay Questions
126. What is the purpose of using a blocking variable in a two-way ANOVA?
A blocking variable accounts for an additional source of variation. The total sum of squares is
now partitioned into treatment, block and error sum of squares. By including a blocking
variable in an ANOVA, the error sum of squares and the corresponding mean square error
(MSE) is decreased. The ultimate effect is in the calculation of the F-statistic to test the
hypothesis of equal treatment means. Since the MSE has been decreased by the inclusion of a
blocking variable, the hypothesis test of equal treatment means will be more sensitive to
significant differences because the denominator of the F-statistic is smaller.
AACSB: Reflective Thinking
Bloom's: Analysis
Difficulty: Hard
Learning Objective: 12-07 Carry out a test of hypothesis among treatment means using a blocking variable and understand the results.
Topic: Two-way ANOVA
127. When testing a hypothesis regarding the equality of two population means, what is the
analogy to a blocking variable?
The pairing of observations.
AACSB: Reflective Thinking
Bloom's: Analysis
Difficulty: Hard
Learning Objective: 12-07 Carry out a test of hypothesis among treatment means using a blocking variable and understand the results.
Topic: Two-way ANOVA
128. In a two-way ANOVA, when is an interaction source of variance included?
An interaction source of variance is included in an ANOVA if there is reason to believe that
the variance in the response variable is affected by both factors in a two-way ANOVA.
AACSB: Reflective Thinking
Bloom's: Comprehension
Difficulty: Medium
Learning Objective: 12-08 Perform a two-way ANOVA with interaction and describe the results.
Topic: Two-way ANOVA with interaction
12-101
Chapter 12 - Analysis of Variance
129. What is the advantage of using ANOVA to test for differences among treatment means
rather than testing all possible pairs of treatment means?
The advantage of using ANOVA rather than comparing all possible pairs of treatment means
is to avoid the buildup of Type I error. For example, if three independent means were
compared using an alpha of 0.05, there would be three independent tests. The probability of
not making a Type I error is 0.95. The probability of not making a Type I error on the three
independent tests is 0.95*0.95*0.95 or 0.86. Now the cumulative probability of a Type I error
is 0.14 rather than 0.05. ANOVA simultaneously compares all possible means at a stated level
of significance or Type I error rate.
AACSB: Reflective Thinking
Bloom's: Comprehension
Difficulty: Hard
Learning Objective: 12-03 Describe the ANOVA approach for testing differences in sample means.
Topic: ANOVA Concepts
12-102