11.3 The standard process for making a polymer has mean yield 35%. A chemical engineer has developed a modified process. He runs the process on 10 batches and measures the yield (in percent) for each batch. They are:

38.7 40.4 37.2 36.6 35.9 34.7 37.6 35.1 37.5 35.6 Assume that yield is normal (p, u2) where the standard deviation u = 3 is known.

(a) Use a normal (30, lo2) prior for p. Find the posterior distribution.

(b) The engineer wants to know if the modified process increases the mean yield. Set this up as a hypothesis test stating clearly the null and alternative hypotheses.

(c) Perform the test at the 5% level of significance.