Question

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. Perform a hypothesis test at the 5% level (after checking assumptions) to test the insurers claim.

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.

Answer 1

Here claim is that the auto club has a higher rate of serious mechanical problems requiring towing services. ie p>0.20

So hypothesis is vs

Here sample size of 2927 members out of which 849 calls involved serious mechanical failures requiring towing

So

Also

Hence test statistics is

So P value is P(z>12.16)=0

As P value is less than alpha=0.05, we reject the null hypothesis

Hence we have sufficient evidence to support the claim that the auto club has a higher rate of serious mechanical problems requiring towing services. ie p>0.20