Exam 11: Multiple Comparisons and Analysis of Variance

The waiting time (in minutes) was measured for a random sample of patients with non-life threatening injuries in emergency rooms at four local hospitals who arrived between 2:00 and 3:00pm on a particular Saturday. Check the output to see whether the same-variance condition for ANOVA holds. Show your work. Is ANOVA appropriate? Source DF Adj SS Adj MS F-Value P-Value Factor 3 504.8 168.28 4.97 0.006 Error 31 1048.7 33.83 Total 34 1553.5 Analysis of Variance Means Factor N Mean StDev A 9 13.11 3.41 B 7 14.29 1.60 C 9 16.33 8.08 D 10 22.60 6.82

Suppose a researcher collected data to compare whether cats of different size categories differed in mean number of hours slept per day. Cats were categorized as small, medium, or large. The calculated F-statistic was 220.41. Given this test statistic, can we conclude that there is relatively more variation between groups or within groups? Based on the test statistic, is it likely that an association exists between cat size and mean number of hours that a cat sleeps per day? Explain.

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

Suppose you wish to compare the means of m groups pair-by-pair. Choose the statement that is true about the Bonferroni Correction. Choose (d) if none of the statements is true.

Choose the appropriate test for the following situation: You wish to test whether an association exists between type of vehicle purchased and vehicle color.

Suppose that you wish to compare the mean home values from three different regions. The Bonferroni-corrected intervals for all three comparisons are shown in the table. Assume an overall confidence level of 95%, that is, an individual confidence level of 98.33%. Choose the statement that is true about the differences among the three means. If none of the statements is true, then choose (d). North East - North Central ($52,485, $78,875) North East - Far West (-$8,724, $14,547) Far West - North Central ($50,093, $75,443)

Choose the appropriate test for the following situation: You wish to test whether the mean number of boxes of a new cereal sold in several different markets around the country is different for three different package types.

Choose the statement that is true about the level of significance when performing several hypothesis tests at the same time. Choose (d) if all statements are true.

Suppose that you wish to compare the mean starting salaries of students from three different majors. The Bonferroni- corrected intervals for all three comparisons are shown in the table. Assume an overall confidence level of 95%, that is, an individual confidence level of 98.33%. Choose the statement that is true about the differences among the three means. If all of the statements are true, then choose (d). Business - Education ($8,425, $16,825) Business - Computer Science (-$514, $4,682) Computer Science - Education ($8,324, $12,759)

The figure below shows the F-distribution with 5 and 12 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? F(5,12) Distribution 0 1.5390.25 F-values

In a car bumper test, three types of sub-compact cars were deliberately crashed into a barrier at 5 mph with the resulting damage (in dollars) recorded. Eight test cars of each type were crashed. Test results indicated that post-hoc procedures were

In a bumper test, three types of sub-compact cars were deliberately crashed into a barrier at 5 mph with the resulting damage (in dollars) recorded. Eight test cars of each type were crashed. Test results indicated that post-hoc procedures were warranted. The TUKEY HSD approach was used with the following results: Using an overall significance level of 5%, is there evidence that one type of car had less bumper damage than the others? Which car appears to have the least bumper damage?

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

In the context of the ANOVA test, do the phrases "variation due to treatment", "explained variation", and "variation due to factors", describe variation within groups or variation between groups?

Choose the statement that is true about the F-statistic. Choose (d) if all statements are true.

Suppose you have observations from six different regions within your state and you wish to perform hypothesis tests to compare the mean home value across groups. There will be a total of 15 pairwise comparisons. Using the Bonferroni Correction, what significance level should you use for each hypothesis test if you want an overall significance of 0.05? Round to the nearest thousandth.

Suppose that you wish to determine whether the mean starting salaries of students from seven different majors differ. If you compared groups two-at-a-time, what significance level should you use for each hypothesis test if you want an overall significance level of 0.10? Round your answer to the nearest thousandth.

Use the following information to answer questions (17) - (19). 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 questions (17) - (19). One-way ANOVA Variance between groups = 2063.33 Variance within gr p-value = 0.000239 oups = 296.25 -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.

Which of the following statements about the p-value of an ANOVA test is not true?

Suppose that you wish to determine whether the mean starting salaries of students from seven different majors differ. How many comparisons (comparing two groups at a time) can be made with seven groups?