Question: It is desired to test H0:µ = 50 against Ha: µ less then 50 using a= .10. The population is question is uniformly distributed with standard deviation 20. A random sample of size 64 will be drawn from the population.

a) find β for each of the following values of the population mean: 49, 47, 45, 43, and 41

b) plot each value of β you obtained in part a against its associated population mean. Show β on the vertical axis and µ on the horizontal axis. Draw a curve through the five points on your graph.

c) Using your graph of part b to find the approximate probability that the hypothesis test will lead to a Type II error when µ = 48

d) Covert each of the values you calculated in part a to the power of the test at the specified value of µ. Plot the power on the vertical axis against µ on the horizontal axis. Compare the graph of part b to the power curve of this part.

e) Examine the graphs of parts b and d. Explain what they reveal about the relationships among the distance between the true mean and the null hypothesized mean µ0 , the value of β , and the power.