Question 1

To test for the stopping distances of 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

The answer of To test for the stopping distances of...

Question 2

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 answer of An advertising company is interested in determining...

Question 3

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 4

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.

Accepted Answer

In a two-factor ANOVA design with replications, there are indeed three hypotheses to be tested: the main effect of factor A, the main effect of factor B, and the interaction between factors A and B.

Question 5

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.

Accepted Answer

Even if there is no interaction between factor A and factor B, either factor A or factor B can still be considered statistically significant if they have a significant main effect.

Question 6

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 7

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 any blocking effect is typically denoted by F and is calculated by comparing the variability among the blocks to the variability within the blocks. If the F-statistic is large and the associated p-value is small, then there is evidence of a blocking effect. Since the given ANOVA table includes a value for the F-statistic, we can conclude that a test for blocking effect was performed and the test statistic was found to be F = 4.38. Therefore, the statement "the test statistic for determining if there is any blocking effect is F = 4.38" is true.

Question 8

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

Accepted Answer

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

Question 9

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.

Accepted Answer

The answer of A study recently conducted by a marketing...

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 indicates that there is a significant difference in sales based on store size, suggesting that blocking on store size was effective in controlling for this variable.

Question 11

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

This is true because having at least two measurements at each level of each factor allows for a comparison of the means between the levels and the calculation of variability within and between the groups. Without multiple measurements, it would not be possible to determine if any observed differences were due to chance or if there were significant interactions between factors.

Question 12

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

In a two-factor ANOVA, the minimum number of replications required in any cell is two to allow for calculation of variance and significance. However, all cells must have the same number of replications to ensure balanced design and accurate interpretation of the results.

Question 13

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.

Accepted Answer

The answer of A study recently conducted by a marketing...

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 answer of Six food critics each visited and rated...

Question 15

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.

Accepted Answer

The critical value of F for testing whether there is any difference among the four restaurants with six critics and three visits each is indeed approximately 2.8 at the 0.05 level of significance.

Question 16

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 is a technique used to control for the effects of extraneous variables or nuisance factors that could affect the outcome of an experiment. In this case, the store size could potentially affect the sales of the soft drinks, so the ad company decided to block on store size. By doing so, they ensure that each shelf level is equally represented across different store sizes, allowing them to make valid comparisons between shelf levels. Given that the data reflect the sales for one week at each combination of shelf level and store size, and assuming that the experiment is properly designed and executed, the managers should conclude that they were justified in blocking on store size when testing for differences in mean sales. A significance level of 0.05 is commonly used to determine whether the observed differences are statistically significant or simply due to chance.

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 correct method for analyzing this data is two-factor ANOVA.

Accepted Answer

Two-factor ANOVA is the correct method for analyzing this data as it involves two factors - the restaurant and the critic, and the scores recorded by each critic for each visit to each restaurant.

Question 18

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

Accepted Answer

In a two-factor ANOVA design, the assumption of equal variances (homogeneity of variances) is required regardless of whether there is an interaction effect present. This assumption pertains to the variances within each of the groups formed by the combinations of factors, not to the interaction between factors.

Question 19

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 ANOVA 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 of these numbers.

Question 20

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

Accepted Answer

Interaction in a two-factor ANOVA design refers to a situation where the effect of one factor on the dependent variable depends on the level of the other factor, not just when the two factors have different means.

Quiz 12: Analysis of Variance