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 40.0 37.2 36.6 35.9 34.7 37. 35.1 37.5 35.6 Assume that yield is normal (µ, σ2) where the standard deviation σ = 3 is known.

(a) Use a normal (30, 102) prior for µ. 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.