Exam 11: Multiple Comparisons and Analysis of Variance

Use the following information for the question. Researchers conducted a study that examined marital status and work hours. A hypothesis test was conducted to test the claim that people with different marital statuses have a different mean number of work hours. Participants were categorized as married, single, or divorced. Assume that all conditions for the ANOVA test have been met. The TI-84 output for the test is shown below. One-way ANOVA =7.010859729 p=007083712 Factor =2 =860.777778 =430.388889 -State the null and alternative hypothesis.

Identify the test statistic used for the ANOVA procedure and how it is calculated.

Choose the statement that best describes the F-statistic for the ANOVA test.

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 $= 17.82025$ $\mathrm { p } = .3255653716$ -Compute the F-statistic. Show your work. Round to the nearest hundredth.

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?

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 Mean StDev =7.5111227-5 17-24 20 9.5 7.02 Factor 25-32 12 14.7 5.82 =2 33-40 21 6.5 9.21 =1957.90476 =978.952381 Error =21 =1331.42857 =63.4013605 =7.96249713

An ANOVA test was conducted to see whether running shoe sole type (Type A, Type B, or type C) had an effect on shoe wear over a six month period. Test results warranted post-hoc procedures. The Tukey HSD approach was used with the following results: Group Comparison 98.33\% Confidence Interval Type A - Type B (-14.02,11.23) Type C - Type B (-9.25,-1.25) Type C - Type A (-10.11,-3.21) Is there evidence that one type of running shoe sole wears better than the others? Which type of running shoe sole appears to wear the best? Explain.

Use the following information for the questions. A group of home gardeners want to test whether the type of soil used to grow carrots has an effect on the number of carrots harvested. Gardeners randomly assigned carrot plants to be grown in soil with no fertilizer, commercial plant food, and homemade compost. All other growing conditions were kept the same. Fifty plants were assigned to each group. At the end of the growing season the number of carrots harvested was counted. Use the output below to answer the question. Assume that all other conditions for the ANOVA test have been met. One-way ANOVA =1.110676532 p=0.3434138248 Factor =2 =19888.2933 =9944.14663 -State the null and alternative hypothesis.

What is the test statistic used for the ANOVA procedure? Explain how it is calculated.

Use the following information for the questions. A group of home gardeners want to test whether the type of soil used to grow carrots has an effect on the number of carrots harvested. Gardeners randomly assigned carrot plants to be grown in soil with no fertilizer, commercial plant food, and homemade compost. All other growing conditions were kept the same. Fifty plants were assigned to each group. At the end of the growing season the number of carrots harvested was counted. Use the output below to answer the question. Assume that all other conditions for the ANOVA test have been met. One-way ANOVA =1.110676532 p=0.3434138248 Factor =2 =19888.2933 =9944.14663 -Using the test results provided, test the hypothesis that soil treatment affects the number of carrots harvested. Use a significance level of 5%. State the correct decision regarding the null hypothesis and write a sentence summarizing the conclusion.

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 $= 17.82025$ $\mathrm { p } = .3255653716$ -Assume that all ANOVA test conditions have been satisfied. State the correct decision regarding the null hypothesis for the claim that jersey color affects race finish times. Write a sentence summarizing your conclusion.

Use the following information for the question. Researchers conducted a study that examined marital status and stress levels. A hypothesis test was conducted to test the claim that people with different marital statuses have a different mean stress level. The TI-84 output for the test is shown below. One-way ANOVA $\mathrm { F } = 5.21104034$ $P = .0105994136$ Factor $\mathrm { df } = 3$ $\mathrm { SS } = 76.7$ $\mathrm { MS } = 25.5666667$ -State the null and alternative hypothesis.

What is the meaning the overall significance level of a test? Explain what happens to the overall significance level when multiple comparisons are made, that is, when multiple hypothesis tests are conducted in an effort to compare the means of several groups.

Choose the appropriate test for the following situation: You wish to test whether the mean number of words recalled from short term memory is different for males and females.

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

Use the following information for the questions. A group of home gardeners want to test whether the type of soil used to grow carrots has an effect on the number of carrots harvested. Gardeners randomly assigned carrot plants to be grown in soil with no fertilizer, commercial plant food, and homemade compost. All other growing conditions were kept the same. Fifty plants were assigned to each group. At the end of the growing season the number of carrots harvested was counted. Use the output below to answer the question. Assume that all other conditions for the ANOVA test have been met. One-way ANOVA =1.110676532 p=0.3434138248 Factor =2 =19888.2933 =9944.14663 -Interpret the boxplots given. Compare medians, interquartile ranges, and shapes, and mention any potential outliers.

A television studio did a poll to determine whether women in different age groups watched different amounts of comedy programming. Check the TI-84 output to see whether the same-variance condition for ANOVA holds. Show your work. Is ANOVA appropriate? One-way ANOVA =1.739515653 Cat Mean StDev =.2092138468 17-24 25 3.42 1.28 Factor 25-32 15 4.50 3.45 =2 33-40 21 2.17 0.75 =16.3611111 =8.18055556 Error =15 =70.5416667 =4.70277778 =2.16858889

Choose the statement that best describes the purpose of ANOVA.

What is the value of the test statistic? Round to the nearest hundredth if necessary.

Compute the F-statistic. Round to the nearest hundredth.