An automobile club that pays for emergency road services (ERS) requested by its members wishes to estimate the proportions of the different types of ERS requests. Upon examining a sample of 2927 ERS calls, it 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) Estimate the true proportion of ERS calls that involved serious mechanical problems requiring towing and determine its 95% margin of error.
(b) Calculate a 98% confidence interval for the true proportion of ERS calls that related to starting problems.