101 It is desired to test H0: m = 50 against Ha: m 6 50, using a = .10. The population in question is uniformly distributed with standard deviation 20. A random sample of size 64 will be drawn from the population.

a. Describe the (approximate) sampling distribution of x under the assumption that H0 is true.

b. Describe the (approximate) sampling distribution of x under the assumption that the population mean is 45.

c. If m were really equal to 45, what is the probability that the hypothesis test would lead the investigator to commit a Type II error?

d. What is the power of this test for detecting the alternative Ha: m = 45?