Deck 12: Analysis of Variance

Question 1

For the hypothesis test, ,with n₁ = 4 and n₂ = 4,the F-test statistic is 50.01.At the 0.01 level of significance,we would reject the null hypothesis.

Answer 1

True

Question 2

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

Answer 2

True

Question 3

The alternate hypothesis for ANOVA states that not all the means are equal.

Answer 3

True

Question 4

The shape of the F distribution is determined by the degrees of freedom for the F-statistic,one for the numerator and one for the denominator.

Question 5

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

Question 6

For the hypothesis test, ,with n₁ = 9 and n₂ = 9,the F-test statistic is 4.53.At the 0.05 level of significance,we would reject the null hypothesis.

Question 7

The test statistic used in ANOVA is Student's t.

Question 8

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

Question 9

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 10

There is one,unique F distribution for a F-statistic with 29 degrees of freedom in the numerator and 28 degrees of freedom in the denominator.

Question 11

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

Question 12

The F distribution's curve is positively skewed.

Question 13

Like Student's t distribution,a change in the degrees of freedom causes a change in the shape of the F distribution.

Question 14

If the computed value of F is 4.01 and the critical value is 2.67,we would conclude that all the population means are equal.

Question 15

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

Question 16

For the hypothesis test, ,with n₁ = 7 and n₂ = 7,the F-test statistic is 2.56.At the 0.05 level of significance,we would reject the null hypothesis.

Question 17

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

Question 18

One characteristic of the F distribution is that F cannot be negative.

Question 19

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

Question 20

The alternate hypothesis used in ANOVA is .

Question 21

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.

Question 22

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 23

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 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

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.

Question 26

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 27

If the endpoints of a confidence interval for the difference between a pair of treatment means are both positive numbers,then we reject the null hypothesis that there is no difference in the pair of treatment means.

Question 28

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 29

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,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 30

Analysis of variance is used to

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

Question 31

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

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 below. What is the sum of squares for the treatment?

A)67.80
B)58.07
C)149.34
D)23.47

Question 33

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 34

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

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

Question 35

If a confidence interval for the difference between a pair of treatment means includes 0,then we fail to reject the null hypothesis that there is no difference in the pair of treatment means.

Question 36

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

A)4 comparisons of treatment means can be made.
B)8 comparisons of treatment means can be made.
C)12 comparisons of treatment means can be made.
D)16 comparisons of treatment means can be made.

Question 37

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 38

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

Question 39

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 40

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

Question 41

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

Question 42

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 is the critical value of F at the 5% level of significance?

A)19.45
B)3.00
C)3.35
D)3.39

Question 43

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 is the calculated F?

A)0.086
B)1.168
C)11.56
D)13.50

Question 44

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 is the sum of squares of the error?

A)67.80
B)58.07
C)149.34
D)23.47

Question 45

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

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 0.01 level of significance?

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

Question 47

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

Question 48

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 is the mean square for error?

A)2.511
B)2.151
C)33.9
D)29.035

Question 49

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

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

A)8
B)9
C)10
D)18
E)20

Question 51

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 is the critical value of F at the 1% level of significance?

A)99.46
B)5.49
C)5.39
D)4.61

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

A)20
B)18
C)10
D)9
E)8

Question 53

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 is the decision?

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 54

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

Question 55

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

Question 56

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

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: What is H₁?

A)Option A
B)Option B
C)Option C
D)Option D

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 H₀?

A)Option A
B)Option B
C)Option C
D)Option D

Question 59

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

Question 60

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 is the mean square for treatments?

A)2.511
B)2.151
C)33.9
D)29.035

Question 61

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 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.

Question 62

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.

Question 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 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 64

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 65

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 for companies in the utilities and insurance industries,the following 95% confidence interval can be constructed:

A)5.78 $\pm$ 2.160 * 2.40
B)5.78 $\pm$ 2.120 * 2.40
C)5.78 $\pm$ 2.160 * 1.11
D)5.78 $\pm$ 2.120 * 1.11

Question 66

The F distribution is a ______________ distribution.

Question 67

What are the minimum and maximum of values of an F distribution? _______ and _______

Question 68

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.

Question 69

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 variance is different.
B)Fail to reject the null hypothesis and conclude no significant difference in the variance.
C)Reject the null hypothesis and conclude the variance is the same.
D)Fail to reject the null hypothesis and conclude the variance is the same.

Question 70

All values in a F distribution must be ______________.

Question 71

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 $\pm$ 2.052 * 6.51
B)2.0 $\pm$ 3.182 * 6.51
C)2.0 $\pm$ 2.052 * 42.46
D)2.0 $\pm$ 3.182 * 42.46

Question 72

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 73

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.

Question 74

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 $\pm$ 2.026 * 5.78
B)13.5 $\pm$ 2.021 * 5.78
C)13.5 $\pm$ 2.026 * 13.96
D)13.5 $\pm$ 2.021 * 13.96

Question 75

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 variance is different.
B)Fail to reject the null hypothesis and conclude the variance is different.
C)Reject the null hypothesis and conclude the variance is the same.
D)Fail to reject the null hypothesis and conclude the variance is the same.

Question 76

What is the shape of the F distribution? ______________________

Question 77

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 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 78

What test statistic is used to compare two variances? ________________

Question 79

The F-distribution is useful when testing a requirement of two-sample tests of hypothesis.What is the assumption? ________________

Question 80

ANOVA requires that the populations should be _______,_______,and ______.