Chapter 16, Problem 28RP

Losses to Robbery. Refer to Problem 24.

1.                                            a.      At the 5% significance level, do the data provide sufficient evidence to conclude that a difference in mean losses exists among the three types of robberies? Use the Kruskal-Wallis procedure to perform the required hypothesis test.
2.                                            b.      The hypothesis test in part (a) was done in Problem 26 by using the one-way ANOVA procedure. The assumptions in that exercise are that, for the three types of robberies, losses are normally distributed and have equal standard deviations. Presuming that to be true, why is performing a Kruskal-Wallis test to compare the means permissible? In this case, is use of the one-way ANOVA test or the Kruskal-Wallis test better? Explain your answers.
3.                                             c.      Compare your hypothesis-testing results with the Kruskal-Wallis test to those of the one-way ANOVA test.

24. Losses to Robbery. The Federal Bureau of Investigation conducts surveys to obtain information on the value of losses from various types of robberies. Results of the surveys are published in Population-at-Risk Rates and Selected Crime Indicators. Independent simple random samples of reports for three types of robberies — highway, gas station, and convenience store — gave the following data, in dollars, on value of losses.

Highway	Gas station	Convenience store
952	1298	844
996	1195	921
839	1174	880
1088	1113	706
1024	953	602
	1280	614

1.                                            a.      What does MSTR measure?
2.                                            b.      What does MSE measure?
3.                                             c.      Suppose that you want to perform a one-way ANOVA to compare the mean losses among the three types of robberies. What conditions are necessary? How crucial are those conditions?