Exam 12: Analysis of Variance

In order for a one-way analysis of variance to be considered a balanced design,which of the following must hold?

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 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.

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.

Which of the following describes a treatment in a randomized complete block analysis of variance?

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.

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.

What are the assumptions for a one-way analysis of variance design?

Under what circumstances would you use a randomized complete block analysis of variance design instead of a one-way analysis of variance?

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

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.

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.

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.

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.The computer results are shown below. Assuming that the hypothesis tests are conducted using a significance level equal to 0.05,the Fisher's LSD value for multiple comparisons is:

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

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.Given this format and testing using an alpha level equal to 0.05,the critical value associated with the primary hypothesis test is:

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.

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. Based on the results above,which of the following is correct?

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.

In a one-way analysis of variance test in which the levels of the factor being analyzed are randomly selected from a large set of possible factors,the design is referred to as: