Suppose that a light-bulb manufacturing plant produces bulbs with a mean life of 2000 hours and a standard deviation of 200 hours. An inventor claims to have developed an improved process that produces bulbs with a longer mean life and the same standard deviation. The plant manager randomly selects 100 bulbs produced by the process. She says that she will believe the inventor's claim if the sample mean life of the bulbs is greater than 2100 hours; otherwise, she will conclude that the new process is no better than the old process. Let µ denote the mean of the new process. Consider the null and alternative hypothesis H0: µ = 2000 vs. H1. µ > 2000.
(a) What is the size of the plant manager's testing procedure?
(b) Suppose the new process is in fact better and has a mean bulb life of 2150 hours. What is the power of the plant manager's testing procedure?
(c) What testing procedure should the plant manager use if she wants the size of her test to be 5%?