Reconsider the chemical process yield data from Exercise 8-9. Recall that = 3, yield is normally distributed and that n = 5 observations on yield are 91.6%, 88.75%, 90.8%, 89.95%, and 91.3%. Use a = 0.05.
(a) Is there evidence that the mean yield is not 90%?
(b) What is the P-value for this test?
(c) What sample size would be required to detect a true mean yield of 85% with probability 0.95?
(d) What is the type II error probability if the true mean yield is 92%?
(e) Compare the decision you made in part (c) with the 95% CI on mean yield that you constructed in Exercise 8-7.