The Gibralter Insurance Co. is reevaluating the pre miums it charges on car insurance and is analyzing classifications of cars into high risk, average risk, and low risk on the basis of frequency of accidents. It is cur rently examining an imported mid-size four-door sedan and wishes to examine whether its frequency of claims history is significantly different than a range of values considered to be consistent with the expected frequency of claims of the average risk class, the range being be tween 2 percent and 4 percent of the vehicles insured. A random sample with replacement of 400 insured ve hicles of the type in question resulted in a claims per centage of 7 percent.
a. Design a UMPU level-a test of the null hypothesis Ho : µ, E [2, 4] versus Ha : µ, ¢ [2, 4]. You can base your test on the asymptotic normal distribution of the test statistic.
b. Test the null hypothesis using a size .OS UMPU test. Does the outcome contradict classifying the vehicle in the average risk class? Why or why not?
c. Supposing you rejected the hypothesis, what would be your conclusion? Is further statistical analysis warranted?