Question: For problem, give a highest-posterior-density credible set of probability 0.80 for the population mean.
Problem: GM is designing a new car, the Chevrolet Volt, which is expected to get 100 mpg on the highway.12 In trying to estimate how much people would be willing to pay for the new car, the company assesses a normal distribution for the average maximum price with mean $29,000 and standard deviation $6,000. A random sample of 30 potential buyers yields an average maximum price of $26,500 and standard deviation $3,800. Give a 95% highest-posterior-density credible set for the average maximum price a consumer would pay.