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.
a. For each of the following α values, compute the probability of committing a Type II error if the population mean is actually 99.
i. α = 0.10
ii. α = 0.05
iii. α = 0.01
b. Based on the answers to part (a), what happens to the value of β as α gets smaller?