Deck 12: Analysis of Variance

Question 1

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

Answer 1

False

Question 2

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, 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

Answer 2

4.07

Question 3

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

Answer 3

2 in the numerator, 15 in the denominator

Question 4

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

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

Question 5

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

Question 6

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 7

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

Question 8

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

Question 9

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

Question 10

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 11

The F distribution's curve is positively skewed.

Question 12

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 13

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 14

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 15

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

Question 16

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

Question 17

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

Question 18

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 19

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 costs 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

Question 20

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 21

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 22

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 23

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 24

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 25

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 26

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 27

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 two metropolitan areas are different.
C)More degrees of freedom are needed.
D)None of these is correct.

Question 28

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 29

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 30

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 31

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 32

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 33

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 34

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 35

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 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 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 37

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 38

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 39

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) is significantly less than ,
,
.
B) is significantly less than , and
.
C) are significantly different.
D)The treatment means are all equal.

Question 40

In ANOVA, the null hypothesis is:

A)
B)
C)
D)

Question 41

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 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 denominator of the F ratio?

A)20
B)18
C)10
D)9

Question 43

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 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: 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 45

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, 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 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 critical value of F at the 0.05 level of significance?

A)5.85
B)5.35
C)3.18
D)4.03

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: 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 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: The calculated F ratio is ______.

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

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: 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 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 alternate hypothesis?

A)
B)
C)
D)

Question 51

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 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 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 53

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 54

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 55

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 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 numerator of the F ratio?

A)8
B)9
C)10
D)18

Question 57

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, 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 58

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, 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 59

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 60

The F distribution is a ______________ distribution.

Question 61

In a one-way ANOVA, ______ degrees of freedom are associated with the numerator of the F ratio.

Question 62

In a one-way ANOVA, the degrees of freedom associated with the error sum of squares is __________.

Question 63

When H₀: is rejected in ANOVA, we compute ____________ to identify pairs of means that differ.

Question 64

A sum of squares divided by its corresponding degrees of freedom is called a ________________.

Question 65

The statistical technique used to test the equality of three or more population means is ___________________.

Question 66

The minimum and maximum of values of an F statistic are _______ and ______.

Question 67

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. The F critical value for α = 0.05 is _____.

Question 68

In ANOVA, when we do not reject the null hypothesis, ______ inference is made about the population means.

Question 69

An ANOVA has three sources of variation. They are _____, _____, and _____.

Question 70

ANOVA requires that the populations should be ______, ______, and have _____.

Question 71

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. To select a critical F-statistic, the number of degrees of freedom for the numerator is _____.

Question 72

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 error sum of squares is 0.09, the mean square error is _____.

Question 73

The shape of the F distribution is _____________________.

Question 74

Assuming that the larger of two variances is in the numerator of an F-statistic, the rejection region to test a null hypothesis is in the _________ tail of the F distribution.

Question 75

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 brand sum of squares is 0.07 and the error sum of squares is 0.09, the calculated value of F is _____.

Question 76

The test statistic used to compare two variances is the ___________ statistic.

Question 77

All values in an F distribution must be _____________.

Question 78

The F distribution is useful when testing a requirement of two-sample tests of hypothesis. The requirement is _______________.

Question 79

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, the mean square for brands is _____.

Question 80

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. To select a critical F-statistic, the number of degrees of freedom for the denominator is _____.