Question 1

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.

Accepted Answer

The answer of If the primary null hypothesis has been...

Question 2

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  :  =  =  .

Accepted Answer

The primary null hypothesis is stated as the equality of means for all temperature settings.

Question 3

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.

Accepted Answer

The number of cells in a two-factor analysis of variance design is equal to the product of the number of levels of factor A and the number of levels of factor B, not the sum.

Question 4

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

Accepted Answer

The answer of Based on the partially completed ANOVA table...

Question 5

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.

Accepted Answer

A randomized complete block design involves blocking to control for variability, but in this scenario, there is no mention of blocking; it is a completely randomized design.

Question 6

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.

Accepted Answer

The statement is true. In a two-factor ANOVA, it is necessary to have a minimum of two replications in each cell to obtain valid estimates of the experimental error and to perform hypothesis testing. Additionally, all cells must have the same number of replications to ensure that the analysis is balanced.

Question 7

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.

Accepted Answer

The degrees of freedom for testing blocking effect depend on the number of levels for each block and the number of blocks. In this case, there are two blocks (runners and shoe brands) and each block has two levels (10 runners per brand and 3 brands). Therefore, the degrees of freedom for testing blocking effect should be (2-1)*(2-1)*10 = 10-2 = 8. The values given in the question (D₁ = 9 and D₂ = 18) are incorrect and cannot be used for hypothesis testing.

Question 8

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.

Accepted Answer

In a two-factor ANOVA, the total sum of squares is partitioned into three parts: the variation due to factor A, the variation due to factor B, the interaction between factors A and B, and the error variation. There is no separate partition for "blocking" in the standard two-factor ANOVA model.

Question 9

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.

Accepted Answer

The answer of A company has established an experiment with...

Question 10

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.

Accepted Answer

The calculated F-test statistic value for testing whether blocking on store size was effective is given and it is greater than the critical F-value. Therefore, there is evidence to suggest that blocking on store size was effective in controlling for store size and reducing the variability in the data, making the comparison of sales across shelf levels more reliable. Hence, the answer is true.

Question 11

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.

Accepted Answer

The degrees of freedom given do not seem to be valid for the hypothesis test described. In general, the degrees of freedom for testing the difference among k means (where k is the number of groups or brands of shoes) based on n total observations (where n is the total number of runners across all groups) is df_between = k - 1 and df_within = n - k. In this case, we are not given the sample sizes for each brand of shoe, so we cannot calculate the total sample size n or the df_within. The given degrees of freedom may relate to some other aspect of the statistical analysis, but they do not seem to be relevant to the hypothesis test described.

Question 12

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.

Accepted Answer

Blocking on store size helps to control for potential confounding variables and increase the precision of the estimates. By doing so, the managers can be more confident in their conclusions regarding the effect of shelf location on sales. A level of significance of 0.05 suggests that the managers are willing to accept a 5% chance of making a Type I error (false positive), which is a commonly used threshold in statistical analysis.

Question 13

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.

Accepted Answer

Two-factor ANOVA is appropriate for analyzing data when there are two independent variables and one dependent variable. In this case, the two independent variables are the restaurant and the visit, while the dependent variable is the score given by the critic. Therefore, two-factor ANOVA is the correct method for analyzing this data.

Question 14

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.

Accepted Answer

The formula for calculating the degrees of freedom for the interaction row in a two-way ANOVA is (number of groups in factor A -1) x (number of groups in factor B - 1). In this case, there are 6 critics rating 4 restaurants, so there are 6 groups in factor A and 4 groups in factor B. Therefore, (6-1) x (4-1) = 15 degrees of freedom for the interaction row.

Question 15

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.

Accepted Answer

The number of treatments is actually four, as there are four different shelf levels being tested. The fact that store size is being controlled for does not change the number of treatments.

Question 16

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

Accepted Answer

The test statistic for determining if there is a blocking effect is the F-statistic in the ANOVA table. Since the F-value is given as 4.38, it means that the hypothesis test for blocking effect is being conducted and the calculated F-value is compared to the critical F-value to make a decision. Therefore, the statement is true.

Question 17

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.

Accepted Answer

The total number of observations is $6 \text{ critics} \times 4 \text{ restaurants} \times 3 \text{ visits} = 72$. Since the degrees of freedom are calculated as the total number of observations minus 1, we have $72 - 1 = 71$ degrees of freedom.

Question 18

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.

Accepted Answer

Having at least two measurements at each level of each factor allows for comparison of the means and calculation of the variance between the groups. Without multiple measurements, it would not be possible to assess potential interactions between factors.

Question 19

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

Accepted Answer

The ANOVA table does not provide information about the number of blocks used for the experiment. Therefore, we cannot determine whether 3 samples are being compared using 9 blocks based on this information alone.

Question 20

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.

Accepted Answer