Suppose a null hypothesis is that the population mean is greater than or equal to 40. Suppose further that a random sample of 52 items is taken and the population standard deviation is 8. For each of the following α values, compute the probability of committing a Type II error if the population mean is actually 39.

(a) α = 0.10

(b) α = 0.05

(c) α = 0.01

(d) Based on the answers to parts (a), (b) and (c), what happens to the value of β as α gets smaller?