Exam 11: Multiple Comparisons and Analysis of Variance

Use the following information to answer the question. Researchers want to test whether the color of a cyclist's jersey has an effect on race finish times. Four jersey colors were used for the study--red, green, blue, and yellow. Thirty cyclists were randomly assigned to each group. Use the output below to answer the question. One-way ANOVA Variation between groups $= 21.8848611$ Variation within groups $= 17.82025$ $\mathrm { p } = .3255653716$ -Do the ANOVA test results warrant a post-hoc procedure? Explain why or why not.

Choose the statement that best describes the purpose of ANOVA.

State the null and alternative hypothesis.

Choose the appropriate test for the following situation: You wish to test whether an association exists between the type of vehicle purchased and how many children the buyer has.

A movie studio did a poll to determine whether women in different age groups watched different amounts of horror movies. Check the computer output to see whether the same-variance condition For ANOVA holds. Is ANOVA appropriate? One-way ANOVA =15.44055794 Cat Mean StDev =7.5111227-5 17-24 20 9.5 6.02 Factor 25-32 12 14.7 4.82 =2 33-40 21 6.5 10.21 =1957.90476 =978.952381 Error =21 =1331.42857 =63.4013605 =7.96249713

Use the following information for the question. A group of home gardeners want to test whether the type of soil used to grow heirloom tomatoes has an effect on the number of tomatoes harvested. Gardeners randomly assigned tomato plants to be grown in soil with no fertilizer, commercial plant food, and homemade compost. All other growing conditions were kept the same. Forty plants were assigned to each group. At the end of the growing season the number of tomatoes harvested was counted. Assume that all other conditions for the ANOVA test have been met. One-way ANOVA =12.57818941 P=2.5637132E-4 Factor $\mathrm { df } = 2$ $\mathrm { SS } = 710.349206$ $\mathrm { MS } = 355.174603$ -State the null and alternative hypothesis.

The figure below shows the F-distribution with 5 and 10 degrees of freedom to test the hypothesis that age groups and reading speed are associated. The shaded area represents the p-value. Assume that all conditions for ANOVA have been met. Should the null hypothesis that the age group population means are equal be rejected? What conclusion can be drawn about the association between age group and reading speed?

Suppose you have observations from six different school districts within your state and you wish to do hypothesis tests to compare the mean home value across school districts. How many comparisons can be done with six groups?

Use the following information to answer the question. Researchers want to test whether the color of a vehicle ticketed for speeding has an effect on the amount of the ticket. Four vehicle colors were used for the study--red, white, black, and silver. Thirty vehicles were randomly assigned to each group. Use the output below to answer the question. One-way ANOVA Variation between groups $= 462.5$ Variation within groups $= 388.54$ $\mathrm { p } = .3547790947$ -Choose the correct conclusion for the hypothesis that vehicle color affects the amount of a speeding ticket. Assume all ANOVA test conditions have been satisfied.

Suppose you have observations from six different regions within your state and you wish to do hypothesis tests to compare the mean income across groups. Using the Bonferroni Correction, what Significance level should you use for each hypothesis test if you want an overall significance of 0)10? Round to the nearest thousandth.

Use the following information to answer the question. Researchers want to test whether the color of a vehicle ticketed for speeding has an effect on the amount of the ticket. Four vehicle colors were used for the study--red, white, black, and silver. Thirty vehicles were randomly assigned to each group. Use the output below to answer the question. One-way ANOVA Variation between groups $= 462.5$ Variation within groups $= 388.54$ $\mathrm { p } = .3547790947$ -Do the ANOVA test results warrant a Post-hoc procedure?

Choose the appropriate test for the following situation: You wish to test whether an association exists between the type of vehicle a driver owns and the cost of speeding tickets.

Use the following information to answer the question. Researchers want to test whether the color of a vehicle ticketed for speeding has an effect on the amount of the ticket. Four vehicle colors were used for the study--red, white, black, and silver. Thirty vehicles were randomly assigned to each group. Use the output below to answer the question. One-way ANOVA Variation between groups $= 2063.33$ Variation within groups $= 196.25$ $\mathrm { p } = 4.5985705 \mathrm { E } - 4$ -Do the ANOVA test results warrant a Post-hoc procedure?

In the context of the ANOVA test, which of the following phrases is equivalent to the phrase "variation between groups?"

Suppose you have observations from five different regions within your state and you wish to do hypothesis tests to compare the mean home value across groups. How many comparisons can be Done with six groups?

Suppose you have observations from six different school districts within your state and you wish to do hypothesis tests to compare the mean home value across groups. Using the Bonferroni Correction, what significance level should you use for each hypothesis test if you want an overall significance of 0.10? Round to the nearest thousandth.

Which of the following is not one of the conditions that must be checked in order for the calculated F-statistic to follow the F-distribution.

Suppose a researcher collected data to compare whether dogs of different size categories differed in mean cost to a pet owner. Dogs were categorized as small, medium, or large. Cost was calculated as The average annual amount spent on food, veterinary visits, and medications. The calculated F-statistic was 421.58. Given this test statistic, which of the following is the most reasonable Conclusion?

Choose the statement that is not true about multiple comparisons and ANOVA. Choose (d) if all the statements are true.

Describe two of the four conditions that must be checked in order for the calculated F-statistic to follow the F-distribution.