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Exam 12: Analysis of Variance

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Question 61

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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.Before actually testing the central hypothesis involving the mean speeds,if a hypothesis test is conducted to determine whether the population variances are equal using a significance level equal to 0.05,the critical value is approximately F = 2.95. Anova: Single Factor SUMMARY ANOVA

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Question 62

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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.

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Question 63

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Considering the following printout for a two-factor ANOVA study,which of the following is the number of replications used?

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.

In one-way analysis of variance,the within-sample variation is not affected by whether the null hypothesis is true on not.

A large orchard owner in the state of Washington is interested in determining whether the mean number of bushels of peaches per acre is the same or different depending on the type of tree that is used.He also thinks that production may be affected by the type of fertilizer that is used.To test,he has set up a test in which a one-acre plot of peach trees with a combination each of 5 varieties and 3 fertilizer types are studied.The following data reflect the number of bushels of peaches on each acre plot. Assuming that the hypothesis tests will be conducted using an alpha equal 0.05 level,which of the following is true?

A golf ball manufacturer has three dimple patterns it is interested in analyzing to see whether one results in longer driving distances.However,it also wishes to control for the material the ball is made from since it believes that the material might affect driving distance.Four materials can be used.The following data represent the results of tests in which each combination of dimple pattern and cover material were used and the length of the ball hit by a robot has been recorded.The test will be conducted using an alpha = 0.05 level. Given these data,what is the value of Fisher's Least Significant Difference critical value?

A real estate broker is interested in determining whether there is a difference in the mean number of days a home stays on the market before selling based on which area of the city it is located in.However,she is also concerned that the price of the house may be an issue in determining how long it takes to sell a house,so she wants to control for this.To carry out the test,she plans to randomly select one house from each part of the city in each price range.The following data show the number of days for the sample of houses selected. Using a significance level equal to 0.05,determine whether the broker was justified in controlling for house prices.Be sure to indicate what type of statistical test should be used and why.

Prior to performing a one-way analysis of variance test,the analysts were interested in determining whether the population variances were equal.The design had one factor with 3 levels and a balanced design with sample size equal to 6.Among others,the following summary statistics were computed: = 50, = 80, = 40.Based on this information,the Hartley F_max critical value is 10.8 if the significance level for the test is 0.05.

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.Which of the following is true?

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 and testing using an alpha level equal to 0.05,which of the following statements is true?

Assume you are conducting a one-way analysis of variance using a 0.05 level of significance and have found that the p-value = 0.02.Which of the follow is correct regarding what you can conclude?

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.

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 SUMMARY ANOVA

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: H_o : μ₁ = μ₂ = μ₃.

A hotel chain has four hotels in Oregon.The general manager is interested in determining whether the mean length of stay is the same or different for the four hotels.She selects a random sample of n = 20 guests at each hotel and determines the number of nights they stayed.Assuming that she plans to test this using an alpha level equal to 0.05,which of the following is the correct critical value?

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.

An Internet service provider is interested in testing to see if there is a difference in the mean weekly connect time for users who come into the service through a dial-up line,DSL,or cable Internet.To test this,the ISP has selected random samples from each category of user and recorded the connect time during a week period.The following data were collected: Assuming that the test is to be conducted at a 0.01 level of significance,what would the critical value be for this test?

An Internet service provider is interested in testing to see if there is a difference in the mean weekly connect time for users who come into the service through a dial-up line,DSL,or cable Internet.To test this,the ISP has selected random samples from each category of user and recorded the connect time during a week period.The following data were collected: Which of the following would be the correct alternative hypotheses for the test to be conducted?

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.