A consumer products company is formulating a new shampoo and is interested in foam height (in mm). Foam height is approximately normally distributed and has a standard deviation of 20 mm. The company wishes to test H0 : l = 175 mm versus HA : l > 175 mm, using the results of n = 16 samples with a sample mean of ¯x = 185.
(a) Find the value of the boundary of the critical region (that is, find C) if the type I error probability is 0.05.
(b) Using n = 16 and the critical region found in part (a), find the type II error probability if the true mean foam height is 195 mm.