A study is designed to test the hypotheses H0: μ ≥ 26 versus Ha: μ ≥ 26. A random sample of 50 units was selected from a specified population, and the measurements were summarized to y = 25.9 and s = 7.6.
a. With α = .05, is there substantial evidence that the population mean is less than 26?
b. Calculate the probability of making a Type II error if the actual value of the population mean is at most 24.
c. If the sample size is doubled to 100, what is the probability of making a Type II error if the actual value of the population mean is at most 24?