The Gibralter Insurance Co. is reevaluating the premiums 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. They are currently examining an imported mid-size four-door sedan and wish 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 between 2 percent and 4 percent of the vehicles insured. A random sample with replacement of 400 insured vehicles of the type in question resulted in a claims percentage of 7 percent.

(a) Design a UMPU level \(\alpha\) test of the null hypothesis \(H_{0}\) : \(\mu \in[2,4]\) versus \(H_{a}: \mu otin[2,4]\). You can base your test on the asymptotic normal distribution of the test statistic.

(b) Test the null hypothesis using a size 05 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?