Suppose a null hypothesis is that the population mean is greater than or equal to 100. Suppose further that a random sample of 48 items is taken and the population standard deviation is 14. For each of the following α values, compute the probability of committing a Type II error if the population mean actually is 99.

a. α = .10

b. α = .05

c. α = .01

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