Q

The standard process for making a polymer has mean yield no greater than 35%. A chemical engineer has developed a modied process. He runs the process on 10 batches and measures the yield (in %) for each batch. The sample mean and sample standard deviation for these ten measurements are 36.93% and 1.?413'u, respectively. Assume that yield is normal(p., o\") where the standard deviation o = 3% is known. (a) Use a normal prior for u. Take the mean to be 3D and the standard deviation to be 10. Find the posterior distribution. (13) The engineer wants to know if the modied process increases the mean yield. Set this up as a hypothesis test stating clearly the null and alternative hypotheses. (e) Use a Bayesian approach to test the hypothesis