Exam 12: 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.

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

A major consumer group recently undertook a study to determine whether automobile customers would rate the quality of cars differently whether they 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 Based upon the data,which of the following statements is true?

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.

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

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.

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 H₀ : μ₁ - μ₂ - μ₃ - μ₄ = 0

Considering the following printout from a two-factor ANOVA design,how many levels of factor A (Sample)were there in this study?

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.

A car company is interested in testing to see whether the mean miles that a car engine will last without changing oil is the same or different depending on which brand of oil is used.The engineers also wish to control for the type of transmission (manual or automatic)that is used.To conduct this test,the car company obtains enough engines so that all four oil brands can be tested in a design that involves no replication.Based on this information,how many engines will be needed to conduct the test?

A start-up cell phone applications company is interested in determining whether house-hold incomes are different for subscribers to three different service providers.A random sample of 25 subscribers to each of the three service providers was taken,and the annual household income for each subscriber was recorded.The partially completed ANOVA table for the analysis is shown here: Based on the sample results,can the start-up firm conclude that there is a difference in household incomes for subscribers to the three service providers? You may assume normal distributions and equal variances.Conduct your test at the alpha= 0.10 level of significance.Be sure to state a critical F-statistic,a decision rule,and a conclusion.

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

In conjunction with the housing foreclosure crisis of 2009,many economists expressed increasing concern about the level of credit card debt and efforts of banks to raise interest rates on these cards.The banks claimed the increases were justified.A Senate subcommittee decided to determine if the average credit card balance depends on the type of credit card used.Under consideration are Visa,MasterCard,Discover,and American Express.The sample sizes to be used for each level are 25,25,26,and 23,respectively. State the number of degrees of freedom available for determining the within-samples variation.

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.

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.

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: H₀ : μ₁ = μ₂ = μ₃.

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

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.

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

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.