It is desired to test H0 : μ = 60 against Ha : μ = 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 μ 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 : μ = 55?

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