Deck 12: Analysis of Variance

Question 1

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 1

a ratio of two variances

Question 2

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

Answer 2

False

Question 3

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

Answer 3

False

Question 4

A large department store examined a sample of 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 5

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

Question 6

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

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

Question 7

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 8

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 9

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

Question 10

The F-distribution's curve is positively skewed.

Question 11

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

Question 12

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

Question 13

Which statement is correct about the F-distribution?

A)It cannot be negative.
B)It cannot be positive.
C)It is the same as the t-distribution.
D)It is the same as the z-distribution.

Question 14

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

Question 15

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

Question 16

To employ Analysis of Variance (ANOVA),the populations being studied must be approximately normally distributed.

Question 17

For the hypothesis test,H₀: σ₁²= σ₂²,with n₁ = 10 and n₂ = 10,the F-test statistic is 2.56. At the 0.02 level of significance,we would reject the null hypothesis.

Question 18

Analysis of variance is used to ________.

A)compare nominal data
B)compute a test
C)compare population proportions
D)simultaneously compare several population means

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

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 22

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 23

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 24

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 25

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 26

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 27

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 28

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 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 degrees of freedom for the error source of variation?

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

Question 30

In ANOVA,the null hypothesis is ________.

A)H₀: σ₁² = σ₂² = σ₃²
B)H₀: σ₁² ≠ σ₂² ≠ σ₃²
C)H₀: μ₁² = μ₂² = μ₃²
D)H₀: μ₁² ≠ μ₂² ≠ μ₃²

Question 31

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

A)The p-value is greater 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 32

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 33

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 34

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 35

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) and are significantly different
D)the treatment means are all equal

Question 36

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 37

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 38

A preliminary study of hourly wages paid to unskilled employees in three metropolitan areas was conducted. Seven employees were included from Area A,nine from Area B,and twelve from Area C. The test statistic was computed to be 4.91. What can we conclude at the 0.05 level?

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.
D)None of these is correct.

Question 39

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 40

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 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 are the degrees of freedom for the denominator of the F ratio?

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

Question 42

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 43

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 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 10% 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 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 alternate hypothesis?

A)H₁ : σ₁² = σ₂²
B)H₁ : σ₁² ≠ σ₂²
C)H₁ : μ₁ = μ₂
D)H₁ : μ₁ ≠ μ₂

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 0.02 level of significance?

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

Question 47

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 48

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 * 13.9

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: What are the degrees of freedom for the numerator of the F ratio?

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

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 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 not enough evidence of a 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 51

Given the following ANOVA table for three treatments each with six observations: What is the decision regarding the null hypothesis at the 5% significance level?

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

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 ± 2.056 * 6.52
B)2.0 ± 3.182 * 6.52
C)2.0 ± 2.052 * 42.46
D)2.0 ± 3.182 * 42.46

Question 53

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 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: What is the null hypothesis?

A)H₀ : σ₁² = σ₂²
B)H₀ : σ₁² ≠ σ₂²
C)H₀ : μ₁ = μ₂
D)H₀ : μ₁ ≠ μ₂

Question 55

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 56

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 57

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 2% 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 58

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 0.1 level of significance?

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

Question 59

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 60

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 61

The following 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 62

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 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 interaction degrees of freedom?

A)10
B)2
C)4
D)8

Question 65

If there are five levels of Factor A and seven 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 66

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 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

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 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

Question 69

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 70

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 71

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 72

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

Question 73

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

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

Question 74

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 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 total degrees of freedom?

A)44
B)14
C)30
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 are ________.

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

Question 77

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

Question 78

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 79

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 intervals 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 80

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