A consumer products company is formulating a new shampoo and is interested in foam height (in millimeters). Foam height is approximately normally distributed and has a standard deviation of 20 millimeters. The company wishes to Ho: μ = 175 millimeters versus H1: μ = 175 millimeters, using the results of n = 10 samples.
(a) Find the type I error probability if the critical region is x > 185.
(b) What is the probability of type II error if the true mean foam height is 195 millimeters?