Deck 12: Analysis of Variance

Question 1

The one-way ANOVA test involves assuming that the population variances are equal.

Answer 1

True

Question 2

In a one-way analysis of variance design,there is a single factor of interest but there may be multiple levels of the factor.

Answer 2

True

Question 3

In a completely randomized analysis of variance design,the observations from each factor are selected in an independent and random fashion.

Answer 3

True

Question 4

Prior to performing a one-way analysis of variance test,the analysts were interested in determining whether the population variances were equal.The design had one factor with 3 levels and a balanced design with sample size equal to 6.Among others,the following summary statistics were computed: = 50, = 80, = 40.Based on these statistics,the calculated F-value for performing a Hartley's F-test for equality of population variances is F = 2.00.

Question 5

In conducing one-way analysis of variance,the population distributions are assumed normally distributed.

Question 6

Recently,a company tested three different machine types to see if there was a difference in the mean thickness of products produced by the three.A random sample of ten products was selected from the output from each machine.Given this information,the proper design to test whether the means are equal is a one-way ANOVA balanced design.

Question 7

The within sample variation is the dispersion that exists because the sample means for the various factor levels are not all equal.

Question 8

Prior to performing a one-way analysis of variance test,the analysts were interested in determining whether the population variances were equal.The design had one factor with 3 levels and a balanced design with sample size equal to 6.Among others,the following summary statistics were computed: = 50, = 80, = 40.Based on this information,the Hartley F_max critical value is 10.8 if the significance level for the test is 0.05.

Question 9

The term one-way analysis of variance refers to the fact that in conducting the test,there is only one way to set up the null and alternative hypotheses.

Question 10

A study was recently conducted to see whether the mean starting salaries for graduates of engineering,business,healthcare,and computer information systems majors differ.A random sample of 8 graduates was selected from each major.The following chart shows some of the results of the ANOVA computations; however,some of the output is missing.If it had been included,the calculated test statistic would be F = 8.33.
Anova: Single Factor
SUMMARY ANOVA

Question 11

In conducting one-way analysis of variance,the sample size for each group must be equal.

Question 12

Under the basic logic of one-way analysis of variance,if the within variation is large relative to the between variation,it is an indication that the population means are likely to be different.

Question 13

A study was recently conducted to see whether the mean starting salaries for graduates of engineering,business,healthcare,and computer information systems majors differ.A random sample of 8 graduates was selected from each major.The following shows the results of the ANOVA computations.However,the degrees of freedom column has been omitted.The correct number of degrees of freedom for the within variation is 28.
Anova: Single Factor
SUMMARY ANOVA

Question 14

In a one-way analysis of variance design,the total variation in the data across the various factor levels can be partitioned into two parts,the within sample variation and the between sample variation.

Question 15

In conducting a one-way analysis of variance,if the null hypothesis is true then the variance between groups (MSB)should be approximately equal to the variance within groups (MSW).

Question 16

A study was recently conducted to see whether the mean starting salaries for graduates of engineering,business,healthcare,and computer information systems majors differ.A random sample of 8 graduates was selected from each major.Based upon this information,the appropriate null hypothesis to be tested is : - - - = 0.

Question 17

A study was recently conducted to see whether the mean starting salaries for graduates of engineering,business,healthcare,and computer information systems majors differ.A random sample of 8 graduates was selected from each major.If the test is to be conducted using an alpha = 0.05 level,the critical value will be F = 3.838.

Question 18

In a one-way analysis of variance test,the following null and alternative hypotheses are appropriate:

Question 19

In one-way analysis of variance,the within-sample variation is not affected by whether the null hypothesis is true on not.

Question 20

In a recent one-way ANOVA test,SSW was equal to 15,900 and the SSB was equal to 3,100.Therefore,SST is equal to 12,800.

Question 21

A national car rental agency is interested in determining whether the mean days that customers rent cars is the same between three of its major cities.The following data reflect the number of days people rented a car for a sample of people in each of three cities.Assuming that a one-way analysis of variance is to be performed,the value of the test statistic is approximately F = 3.4.

Question 22

Analysis of variance can only be done for fixed effects.

Question 23

The experiment-wide error rate will be higher than the 0.05 significance level if the multiple comparison tests for the mean difference between any two populations use the 0.05 level.

Question 24

The Tukey-Kramer method for multiple comparisons can only be used when the analysis of variance design is balanced.

Question 25

A national car rental agency is interested in determining whether the mean days that customers rent cars is the same between three of its major cities.The following data reflect the number of days people rented a car for a sample of people in each of three cities.Given this information,the correct null and alternative hypotheses are: : = = : not all are equal.

Question 26

A study was recently conducted to see whether the mean starting salaries for graduates of engineering,business,healthcare,and computer information systems majors differ.A random sample of 8 graduates was selected from each major.The following chart shows some of the results of the ANOVA computations; however,some of the output is missing.Given what is available,the proper conclusion to reach based on the sample data is that the population means could be equal using a 0.05 level of significance.
Anova: Single Factor
SUMMARY ANOVA

Question 27

A chain of fast food restaurants wants to compare the average service times at four different restaurants.They want to conduct a hypothesis test to determine if all four means are the same or not.If n = 10 observations are taken at each of the four restaurants,then the degrees of freedom are D₁ = 39 and D₂ = 3.

Question 28

A randomized complete block analysis of variance allows the analyst to control for sources of variation that might adversely affect the analysis by using the concept of paired samples.

Question 29

The Tukey-Kramer method is used to test the assumption made in analysis of variance that the population variances are equal.

Question 30

Three brands of running shoes are each tested by 10 different runners.The amount of wear on the sole of the shoes is then measured.The objective is to determine if there is any difference among the three brands of shoes based on how long the soles last.This means that there is one factor with 10 levels and 3 blocks.

Question 31

If the null hypothesis that all population means are equal is rejected by the analysis of variance F-test,the alternative hypothesis that all population means differ is concluded to be true.

Question 32

A fixed effects analysis of variance differs from a random-effects analysis of variance in the way in which the sums of squares are computed.

Question 33

As a step in establishing its rates,an automobile insurance company is interested in determining whether there is a difference in the mean highway speeds that drivers of different age groups drive.To help answer this question,it has selected a random sample of drivers in three age categories: under 21,21-50,and over 50.The engineers then recorded the drivers' speeds at a designated point on a highway in the state.The subjects were unaware that their speed was being recorded.The following one-way ANOVA output was generated from the sample data.Based on this output,the engineers can conclude that the assumption of equal variances is satisfied since the calculated F-value is less than the critical F from Hartley's table at α = .05.
Anova: Single Factor
SUMMARY ANOVA

Question 34

The Tukey-Kramer method for multiple comparison is used after the analysis of variance F-test has lead us to reject the null hypothesis that all population means are equal.

Question 35

As a step in establishing its rates,an automobile insurance company is interested in determining whether there is a difference in the mean highway speeds that drivers of different age groups drive.To help answer this question,it has selected a random sample of drivers in three age categories: under 21,21-50,and over 50.The engineers then recorded the drivers' speeds at a designated point on a highway in the state.The subjects were unaware that their speed was being recorded.The following one-way ANOVA output was generated from the sample data.Based upon this output,if the significance level is 0.05,the engineers should conclude that the mean speeds may all be equal since the p-value is less than alpha.
Anova: Single Factor
SUMMARY ANOVA

Question 36

As a step in establishing its rates,an automobile insurance company is interested in determining whether there is a difference in the mean highway speeds that drivers of different age groups drive.To help answer this question,it has selected a random sample of drivers in three age categories: under 21,21-50,and over 50.The engineers then recorded the drivers' speeds at a designated point on a highway in the state.The subjects were unaware that their speed was being recorded.The following one-way ANOVA output was generated from the sample data.Before actually testing the central hypothesis involving the mean speeds,if a hypothesis test is conducted to determine whether the population variances are equal using a significance level equal to 0.05,the critical value is approximately F = 2.95.
Anova: Single Factor
SUMMARY ANOVA

Question 37

A national car rental agency is interested in determining whether the mean days that customers rent cars is the same between three of its major cities.The following data reflect the number of days people rented a car for a sample of people in each of three cities.Assuming that a one-way analysis of variance is to be performed,the total sum of squares is computed to be approximately 120.9.

Question 38

Three brands of running shoes are each tested by 10 different runners.The amount of wear on the sole of the shoes is then measured.The objective is to determine if there is any difference among the three brands of shoes based on how long the soles last.The null hypothesis is:
H_o : μ₁ = μ₂ = μ₃.

Question 39

A chain of fast food restaurants wants to compare the average service times at three different restaurants.It wants to conduct a hypothesis test to determine if all three means are the same or not,at the 0.05 level of significance.If n = 7 observations are taken at each of the three restaurants,the critical value is F = 3.555.

Question 40

As a step in establishing its rates,an automobile insurance company is interested in determining whether there is a difference in the mean highway speeds that drivers of different age groups drive.To help answer this question,it has selected a random sample of drivers in three age categories: under 21,21-50,and over 50.The engineers then recorded the drivers' speeds at a designated point on a highway in the state.The subjects were unaware that their speed was being recorded.The following one-way ANOVA output was generated from the sample data.Based upon this output,it is possible that a Type II statistical error has been committed if the null hypothesis is tested at the alpha equal 0.05 level.
Anova: Single Factor
SUMMARY ANOVA

Question 41

If the primary null hypothesis has been rejected for a randomized complete block ANOVA designed test,the next step is to conduct a Tukey-Kramer post-comparison test to determine which shelf levels have different mean sales.

Question 42

A company has established an experiment with its production process in which three temperature settings are used and five elapsed times are used for each setting.The company then produces one product under each and measures the resulting strength of the product.The managers are mainly interested in determining whether the mean strength is the same at all temperature settings,but they know that controlling for process time is important.The following data were observed from the experiment: Based on these data and experimental design,the primary null hypothesis to be tested is : = = .

Question 43

The number of cells in a two-factor analysis of variance design is equal to the number of levels of factor A plus the number of levels of factor B.

Question 44

Based on the partially completed ANOVA table below,the critical value needed for testing whether there is any blocking effect is F = 8.812.

Question 45

To test for the stopping distances of the four brake systems,10 of the same make and model of car are selected randomly and then are assigned randomly to each of four brake systems.This is a randomized complete block design.

Question 46

In a two-factor ANOVA,the minimum number of replications required in any cell is two,but all cells must have the same number of replications.

Question 47

Three brands of running shoes are each tested by 10 different runners.The amount of wear on the sole of the shoes is then measured.The objective is to determine if there is any difference among the three brands of shoes based on how long the soles last.The degrees of freedom for testing whether there is any blocking effect D₁ = 9 and D₂ = 18.

Question 48

In a two-factor ANOVA,the total sum of squares can be partitioned into four parts; the variation due to factor A,the variation due to factor B,the variation due to blocking,and the error variation.

Question 49

A company has established an experiment with its production process in which three temperature settings are used and five elapsed times are used for each setting.The company then produces one product under each and measures the resulting strength of the product.The managers are mainly interested in determining whether the mean strength is the same at all temperature settings,but they know that controlling for process time is important.The following data were observed from the experiment: Based on these data and experimental design,for a significance level of 0.05,the managers should conclude that they were justified in blocking on the basis of processing time.

Question 50

An advertising company is interested in determining if there is a difference in the mean sales that will be generated for a soft drink company based on which shelf the soft drinks are located.There are four possible shelf levels.The ad company wants to control for store size.The following data reflect the sales for one week at each combination of shelf level and store size. Based on the experimental design,the calculated F-test statistic value for testing whether blocking on store size was effective is approximately 16.3.

Question 51

Three brands of running shoes are each tested by 10 different runners.The amount of wear on the sole of the shoes is then measured.The objective is to determine if there is any difference among the three brands of shoes based on how long the soles last.The degrees of freedom for testing whether the brands of shoes differ are D₁ = 9 and D₂ = 2.

Question 52

An advertising company is interested in determining if there is a difference in the mean sales that will be generated for a soft drink company based on which shelf the soft drinks are located.There are four possible shelf levels.The ad company wants to control for store size.The following data reflect the sales for one week at each combination of shelf level and store size. Based on the experimental design,the managers should conclude that they were justified in blocking on store size if they test using a 0.05 level of significance.

Question 53

Six food critics each visited and rated four different restaurants.Each critic visited each restaurant on three separate occasions and recorded a score for each visit.The correct method for analyzing this data is two-factor ANOVA.

Question 54

Six food critics each visited and rated four different restaurants.Each critic visited each restaurant on three separate occasions and recorded a score for each visit.The number of degrees of freedom in the interaction row of the ANOVA table is 15.

Question 55

An advertising company is interested in determining if there is a difference in the mean sales that will be generated for a soft drink company based on which shelf the soft drinks are located.There are four possible shelf levels.The ad company wants to control for store size.The following data reflect the sales for one week at each combination of shelf level and store size. Based on the experimental design,the number of treatments is two.

Question 56

Given the partially completed ANOVA table below,the test statistic for determining if there is any blocking effect is F = 4.38.

Question 57

Six food critics each visited and rated four different restaurants.Each critic visited each restaurant on three separate occasions and recorded a score for each visit.The total number of degrees of freedom is 71.

Question 58

In order to analyze any potential interactions between factors in an analysis of variance study,it is necessary to have at least two measurements at each level of each factor.

Question 59

Based on the partially completed ANOVA table below,we know that 3 samples are being compared using 9 blocks.

Question 60

A company has established an experiment with its production process in which three temperature settings are used and five elapsed times are used for each setting.The company then produces one product under each and measures the resulting strength of the product.This experimental design is called a randomized complete block design.

Question 61

A study recently conducted by a marketing firm analyzed three different advertising designs and four different income levels of potential customers.At each combination of factor A and factor B,5 customers are observed and the number of products produced are recorded.The total number of degrees of freedom associated with this two-factor ANOVA design is 59.

Question 62

A study recently conducted by a marketing firm analyzed three different advertising designs and four different income levels of potential customers.At each combination of factor A and factor B,5 customers are observed and the number of products produced are recorded.The degrees of freedom for the MSE in this two-factor ANOVA design is 48.

Question 63

A study recently conducted by a marketing firm analyzed three different advertising designs (factor A)and four different income levels (factor B)of potential customers.At each combination of factor A and factor B,5 customers are observed and the number of products produced is recorded.Interaction between the two factors would exist if low income customers have higher mean buying when design 1 is used,but higher income customers have higher mean buying when designs 2 and 3 are used.

Question 64

The general idea is that interaction between two factors means that the effect due to one of the factors is not uniform across all levels of the other factor.

Question 65

A hotel chain has four hotels in Oregon.The general manager is interested in determining whether the mean length of stay is the same or different for the four hotels.She selects a random sample of n = 20 guests at each hotel and determines the number of nights they stayed.Assuming that she plans to test this using an alpha level equal to 0.05,which of the following is the appropriate alternative hypothesis?

A) : = = =
B) : ≠ ≠ ≠
C)Not all population means are equal.
D) = = =

Question 66

Interaction is the term that is used in a two-factor ANOVA design when the two factors have different means.

Question 67

The State Transportation Department is thinking of changing its speed limit signs.It is considering two new options in addition to the existing sign design.At question is whether the three sign designs will produce the same mean speed.To test this,the department has conducted a limited test in which a stretch of roadway was selected.With the original signs up,a random sample of 30 cars was selected and the speeds were measured.Then,on different days,the two new designs were installed,30 cars each day were sampled,and their speeds were recorded.Suppose that the following summary statistics were computed based on the data: The appropriate test to conduct to determine if the population means are equal is:

A)Hartley's F-max test.
B)one-way analysis of variance
C)three sample t-test.
D)randomized complete block analysis of variance.

Question 68

In a two-factor ANOVA study,if the two factors do not interact,then neither factor A nor factor B can be considered statistically significant.

Question 69

A hotel chain has four hotels in Oregon.The general manager is interested in determining whether the mean length of stay is the same or different for the four hotels.She selects a random sample of n = 20 guests at each hotel and determines the number of nights they stayed.Assuming that she plans to test this using an alpha level equal to 0.05,which of the following is the correct critical value?

A)F = 3.04
B)F = 2.76
C)t = 1.9917
D)F = 2.56

Question 70

In a two-factor ANOVA with replication in which all hypotheses are to be tested using an alpha = .05 level,if the p-value for interaction is .03467,the decision maker should conclude that no interaction is present.

Question 71

In a two-factor ANOVA design,the variances of the populations are assumed to be equal unless there is interaction present.

Question 72

The State Transportation Department is thinking of changing its speed limit signs.It is considering two new options in addition to the existing sign design.At question is whether the three sign designs will produce the same mean speed.To test this,the department has conducted a limited test in which a stretch of roadway was selected.With the original signs up,a random sample of 30 cars was selected and the speeds were measured.Then,on different days,the two new designs were installed,30 cars each day were sampled,and their speeds were recorded.Suppose that the following summary statistics were computed based on the data: Based on these sample results and significance level equal to 0.05,what is the critical value for this hypothesis test?

A)F = approximately 3.15
B)F = approximately 4.90
C)F = approximately 29.47
D)F = approximately 2.70

Question 73

The State Transportation Department is thinking of changing its speed limit signs.It is considering two new options in addition to the existing sign design.At question is whether the three sign designs will produce the same mean speed.To test this,the department has conducted a limited test in which a stretch of roadway was selected.With the original signs up,a random sample of 30 cars was selected and the speeds were measured.Then,on different days,the two new designs were installed,30 cars each day were sampled,and their speeds were recorded.Suppose that the following summary statistics were computed based on the data: Based on these sample results and significance level equal to 0.05,the sum of squares between is:

A)approximately 3,586.
B)approximately 2,430.
C)approximately 1,215.
D)None of the above.

Question 74

In a two-factor ANOVA design with replication,if the null hypothesis pertaining to interaction between factors A and B is rejected,then it is recommended that the hypothesis tests for factor A and factor B individually should not be conducted because the conclusions might be misleading.

Question 75

In a two-factor ANOVA design with replication,the null hypothesis for testing whether interaction exists is that no interaction exists.The alternative hypothesis is that interaction does exist.

Question 76

In a two-factor ANOVA design with replications,there are three hypotheses to be tested; test for factor A,test for factor B,and test for interaction between factors A and B.

Question 77

Six food critics each visited and rated four different restaurants.Each critic visited each restaurant on three separate occasions and recorded a score for each visit.The critical value for testing whether there is any difference among the four restaurants,using the 0.05 level of significance is approximately F = 2.8.

Question 78

Six food critics each visited and rated four different restaurants.Each critic visited each restaurant on three separate occasions and recorded a score for each visit.Assume that results show that there is an interaction.This would mean that,for example,which restaurant is rated the highest depends on which critic does the rating.

Question 79

Which of the following is an assumption for the one-way analysis of variance experimental design?

A)All populations are normally distributed.
B)The populations have equal variances.
C)The observations are independent.
D)All of the above.

Question 80

In conducting a one-way analysis of variance where the test statistic is less than the critical value,which of the following is correct?

A)Conclude that the means are not all the same and that that the Tukey-Kramer procedure should be conducted
B)Conclude that the means are not all the same and that that the Tukey-Kramer procedure is not needed
C)Conclude that all means are the same and that the Tukey-Kramer procedure should be conducted
D)Conclude that all means are the same and there is no need to conduct the Tukey-Kramer procedure