it is desired to test H0 : p, = 50 against Ha : ,u

It is desired to test 110 : 50 against Ila : < 50, using a 0.10. 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 under the assumption that Ho is true. (b) Describe the (approximate) sampling distribution of under the assumption that the population mean is 45. (c) If 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 : 45?