Question: a) A market research analyst must estimate the potential average market share for a new product. The product was sold in 16 test markets resulting in an average market share of 30 percent and a sample standard deviation of 3.2 percent. Determine a 95% confidence interval estimate for the actual population mean market share.

b) A quality analyst wishes to estimate the average waiting time for patients at a hospital clinic. She collects data on 49 patients and finds that the average waiting time for this sample is 50 minutes. It is also known that the population standard deviation is 21 minutes. Determine a 99% confidence interval for estimating the population mean waiting time.