Exam 12: Analysis of Variance

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.

Suppose that you have just performed an experiment using the randomized complete block analysis of variance design and the output from Excel is shown as follows.The primary null hypothesis to be tested involves whether the means of the three groups are equal. Using a significance level of 0.05,what conclusions should be made about the three groups? Which groups have different means? Discuss.

Recently,a department store chain was interested in determining if there was a difference in the mean number of customers who enter the three stores in Seattle.The analysts set up a study in which the number of people entering the stores was counted depending on whether the day of the week was Saturday,Sunday,or a weekday.The following data were collected: Given this format,what is the null hypothesis for testing whether blocking is effective?

A two-factor analysis of variance is conducted to test the effect that price and advertising have on sales of a particular brand of bottled water.Each week a combination of particular levels of price and advertising are used and the sales amount is recorded.The computer results are shown below. Based on the results above and a 0.05 level of significance,which of the following is correct?

A major consumer group recently undertook a study to determine whether automobile customers would rate the quality of cars differently that were manufactured in the U.S.,Europe,or Japan.To conduct this test,a sample of 20 individuals was asked to look at mid-range model cars made in each of the three countries.The individuals in the sample were then asked to provide a rating for each car on a scale of 1 to 1000.The following computer output resulted,and the tests were conducted using a significance level equal to 0.05. Anova: Two-Factor Without Replication ANOVA Based upon the data,which of the following statements is true?

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.

What is meant by the term balanced design in an analysis of variance application?

Analysis of variance can only be done for fixed effects.

A test is conducted to compare three difference income tax software packages to determine whether there is any difference in the average time it takes to prepare income tax returns using the three different software packages.Ten different people's income tax returns are done by each of the three software packages and the time is recorded for each.Assuming that results show that blocking was effective,this means that:

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.

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

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.

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.

Explain what is meant by partitioning the sum of squares in a one-way analysis of variance application.

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

Which type of ANOVA can include interaction?

Recently,a department store chain was interested in determining if there was a difference in the mean number of customers who enter the three stores in Seattle.The analysts set up a study in which the number of people entering the stores was counted depending on whether the day of the week was Saturday,Sunday,or a weekday.The following data were collected: Given this format,which of the following is true?

Prior to conducting a one-way analysis of variance test,it is a good idea to test to see whether the population variances are equal.One method for doing this is to use:

A two-factor analysis of variance is conducted to test the effect the price and advertising have on sales of a particular brand of bottled water.Each week a combination of particular levels of price and advertising are used and the sales level is recorded.The computer results are shown below. How many replications were used in this study?

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.