To test H0: m = 50 versus H1: m 6 50, a simple random sample of size n = 24 is obtained from a population that is known to be normally distributed, and the sample standard deviation is found to be 6.

(a) A researcher decides to test the hypothesis at the a = 0.05 level of significance. Determine the sample mean that separates the rejection region from the nonrejection region. Follow the same approach as that laid out on page 514, but use Student's t-distribution to find the critical value.]

(b) Suppose the true population mean is m = 48.9. Use technology to find the area under the t-

distribution to the right of the sample mean found in part (a) assuming m = 48.9. [Hint: This can

be accomplished by performing a one-sample t-test.] This represents the probability of making a

Type II error, b. What is the power of the test?