An automobile club pays for emergency road services (ERS) requested by its members. The current policy rate the automobile club pays is based on the thought that 20% of services requested will be serious mechanical problems requiring towing. However, the insurance company claims that the auto club has a higher rate of serious mechanical problems requiring towing services. Upon examining a sample of 2927 ERS calls from the club members, the club finds that 1499 calls related to starting problems, 849 calls involved serious mechanical failures requiring towing, 498 calls involved flat tires or lockouts, and 81 calls were for other reasons. a. Perform a hypothesis test at the 5% level to test the insurers claim. Make sure you check/comment on all assumptions needed, and explicitly write down the null and alternative hypotheses. Explic- itly write down the distribution of the test statistic ASSUMING the null hypothesis is true.
b. Construct a 98% confidence interval for the rate of all ERS calls from club members that involved flat tires or lockouts (after checking that necessary assumptions are well met).