See the attached file.
It is desired to test H0: u=50 against H1: u<50 using alpha=0.1. The population in question is uniformly distributed with standard deviation 20. A random sample of size 64 will be drawn from the population.
a) Find beta for each of the following values of the population mean: 49, 47, 45, 43 and 41
b) Plot each value of beta you obtained in part against its associated population mean. Show beta on the vertical axis and u on the horizontal axis. Draw a curve through the five points on your graph.
c) Use your graph from part (b) to find the approximate probability that the hypothesis test will lead to a type II error when u=48.
d) Using the values obtained in part (a) plot the power curve.
e) examine the two graphs in parts (b) and (d). Explain what they reveal about the relationship among distance between the true mean and the null hypothesis mean, the value beta, and the power.
This solution goes through various statistical concepts including means, null hypothesis, beta values and power.