Deck 12: Analysis of Variance

Question 1

When a blocking effect is included in an ANOVA, the analysis is more likely to detect differences in the treatment means.

Answer 1

True

Question 2

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

Answer 2

B

Question 3

Interaction between two factors occurs when the effect of one factor on the response variable is the same for any value of another factor.

Answer 3

False

Question 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.

Question 5

In an ANOVA table, k represents the total number of sample observations and n represents the total number of treatments.

Question 6

To employ ANOVA, the populations being studied must be approximately normally distributed.

Question 7

The F distribution's curve is positively skewed.

Question 8

If the computed value of F is 0.99 and the F critical value is 3.89, we would not reject the null hypothesis.

Question 9

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.

Question 10

Analysis of variance is used to _____________.

A) Compare nominal data
B) Compute a t test
C) Compare population proportions
D) Simultaneously compare several population means

Question 11

In a two-way ANOVA with interaction, there are two factor effects and an interaction effect.

Question 12

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

Question 13

For an ANOVA test, rejecting the null hypothesis does not identify which treatment means differ significantly.

Question 14

When a blocking effect is included in an ANOVA, the result is a larger error sum of squares.

Question 15

What distribution does the F distribution approach as the sample size increases?

A) Binomial
B) Normal
C) Poisson
D) Exponential

Question 16

If we want to determine which treatment means differ, we compute a confidence interval for the difference between each pair of means.

Question 17

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

Question 18

One characteristic of the F distribution is that the computed F can only range between -1 and +1.

Question 19

The alternative hypothesis used in ANOVA is H₁: All population means are equal.

Question 20

To employ ANOVA, the populations should have approximately equal standard deviations.

Question 21

Suppose 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, economy, premium, and super premium. The test car made three trial runs on the test track using each of the four grades. The miles per gallon were recorded for each grade. 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 are the same?

A) 1.96
B) 4.07
C) 2.33
D) 12.00

Question 22

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)

Question 23

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 was 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.

Question 24

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

Question 25

If an ANOVA test is conducted and the null hypothesis is rejected, what does this indicate?

A) The p-value is less than α.
B) The population means are equal.
C) At least one pair of population means is different.
D) All population means are different.

Question 26

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 next. In an ANOVA table, what are the degrees of freedom for the error source of variation?

A) 3
B) 10
C) 27
D) 30

Question 27

When the null hypothesis for an ANOVA analysis comparing four treatment means is rejected, _________________.

A) Two comparisons of treatment means can be made
B) Four comparisons of treatment means can be made
C) Six comparisons of treatment means can be made
D) Eight comparisons of treatment means can be made

Question 28

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 next. In an ANOVA table, what are the degrees of freedom for the treatment source of variation?

A) 2
B) 3
C) 10
D) 27

Question 29

When testing for differences between treatment means, a confidence interval is computed with __________________.

A) the mean square error
B) the standard deviation
C) the sum of squared errors
D) the standard error of the mean

Question 30

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

A) 2
B) 3
C) 11
C) The cost of maintaining each truck was recordeD. The company used ANOVA to test if the mean maintenance costs of the trucks from each manufacturer were equal. To apply the F test, how many degrees of freedom must be in the denominator?
D) 14

Question 31

In ANOVA, the null hypothesis is:

A)
B)
C)
D)

Question 32

The null hypothesis for an ANOVA analysis comparing four treatment means is rejected. The four sample means are = 10, = 12, = 15, = 18. The sample size for each treatment is the same. If ( - ) is significantly different from zero, then ___________.

A)
B)
C)
D) The treatment means are all equal

Question 33

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 next. 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

Question 34

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

A) The mean hourly wages of unskilled employees of all areas are equal.
B) The mean hourly wages in at least two metropolitan areas are different.
C) More degrees of freedom are needed.
C) The test statistic was computed to be 4.91. What can we conclude at the 0.05 level?
D) None of these is correct.

Question 35

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

Question 36

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

Question 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 next. 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

Question 38

In ANOVA analyses, 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

Question 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 next. In an ANOVA table, what are the total degrees of freedom?

A) 27
B) 28
C) 29
D) 30

Question 40

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

Question 41

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 those with an 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

Question 42

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

Question 43

Given the following ANOVA 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.

Question 44

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.

Question 45

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 null hypothesis?

A)
B)
C)
D)

Question 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 the alternate hypothesis?

A)
B)
C)
D)

Question 47

A random sample of 40 companies with assets over $10 million was surveyed and asked to indicate their industry and annual computer technology expense. 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, which of 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

Question 48

Given the following ANOVA table for three treatments each with six observations: What are the degrees of freedom for the treatment and error sources of variation?

A) 3 and 18
B) 2 and 17
C) 3 and 15
D) 2 and 15

Question 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: The calculated F ratio is ______.

A) 3.484
B) 1.867
C) 3.18
D) 5.35

Question 50

A random sample of 40 companies with assets over $10 million was surveyed and asked to indicate their industry and annual computer technology expense. 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

Question 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 0.01 level of significance?

A) 5.85
B) 5.35
C) 6.51
D) 4.03

Question 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: 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.

Question 53

Given the following ANOVA 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

Question 54

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 degrees or more, which of the following 95% confidence interval can be constructed?

A) 2.0 ± 2.052 * 6.52
B) 2.0 ± 3.182 * 6.52
C) 2.0 ± 2.052 * 42.46
D) 2.0 ± 3.182 * 42.46

Question 55

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

Question 56

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

Question 57

Given the following ANOVA table for three treatments each with six observations: What is the treatment mean square?

A) 71.2
B) 71.4
C) 558
D) 534

Question 58

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 degrees 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

Question 59

A random sample of 40 companies with assets over $10 million was surveyed and asked to indicate their industry and annual computer technology expense. 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 -5.85 to 14.85 for the difference. This result indicates that _______________.

A) there is no significant difference between the two industry technology expenses
B) the interval contains a difference of 20.7
C) companies in the food service industry spend significantly more than companies in the tax service industry
D) companies in the food service industry spend significantly less than companies in the tax service industry

Question 60

Given the following ANOVA 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

Question 61

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 a.m. class

Question 62

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

Question 63

The following partial ANOVA table was derived from data having four treatments and a total of 16 observations. The mean square between treatments (MST) is _______.

A) 85.33
B) 22.40
C) 48.00
D) 64.00

Question 64

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

Question 65

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

Question 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 treatment variable?

A) Day
B) Class time
C) Tuesday
D) 8:00 a.m. class

Question 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 are the block and treatment degrees of freedom?

A) 5 and 3
B) 5 and 5
C) 4 and 2
D) 3 and 15

Question 68

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

Question 69

The annual dividend rates for a random sample of 16 companies in three different industries, utilities, banking, and insurance were recorded. The ANOVA comparing the mean annual dividend rate among three industries rejected the null hypothesis that the dividend rates were equal. 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

Question 70

Below is the information for a completely randomized experimental design involving four treatments, where 12 observations were recorded for each treatment for a total of 48 observations. SST = 210 (Sum of Squares Between Groups)
SS Total = 840 (Sum of Squares Total)
The computed value of F, or the test statistic, is ______.

A) 0.25
B) 12.0
C) 4.88
D) 8.0

Question 71

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

Question 72

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

Question 73

In an ANOVA problem involving three treatments and 12 observations per treatment, SSE = 297. The MSE for this scenario is _____.

A) 99
B) 33
C) 19.8
D) 9

Question 74

The annual dividend rates for a random sample of 16 companies in three different industries, utilities, banking, and insurance were recorded. The ANOVA comparing the mean annual dividend rate among three industries rejected the null hypothesis that the dividend rates were equal. 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 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 the banking industry
D) the annual dividend rate in the banking industry is significantly less than the annual dividend rate in the utilities industry

Question 75

A two-way ANOVA with interaction has how many sources of variation?

A) 5
B) 4
C) 3
D) 2

Question 76

An ANOVA procedure is applied to data obtained from four distinct populations. The samples, each comprised of 15 observations, were taken from the four populations. The degrees of freedom for the numerator and denominator for the critical value of F are:

A) 4 and 60, respectively.
B) 4 and 21, respectively.
C) 3 and 59, respectively.
D) 3 and 56, respectively.

Question 77

ANOVA is a statistical approach used to determine whether or not _________.

A) the means of two or more samples are equal
B) the means of two samples are equal
C) the means of two or more populations are equal
D) the means of more than two samples are equal

Question 78

The annual dividend rates for a random sample of 16 companies in three different industries, utilities, banking, and insurance were recorded. The ANOVA comparing the mean annual dividend rate among three industries rejected the null hypothesis that the dividend rates were equal. 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, which of 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

Question 79

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

Question 80

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