It is desired to test H0: m = 60 against Ha: m 6 60, using a = .10. The population in question is uniformly distributed with standard deviation 22.5. A random sample of size 81 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 55.

c. If m were really equal to 55, 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 = 55?