The marketers of shampoo products know that customers like their product to have a lot of foam. A manufacturer of shampoo claims that the foam height of his product exceeds 200 millimeters. It is known from prior experience that the standard deviation of foam height is 8 millimeters. For each of the following sample sizes, and a fixed a = 0.05, find the power of the test if the true mean is 204 millimeters.
(a) n = 20
(b) n = 50
(c) n = 100
(d) Does the power of the test increase or decrease as the sample size increases? Explain your answer.