Suppose you are interested in conducting the statistical test of H0: = 200 against Ha:

Question:

Suppose you are interested in conducting the statistical test of H0: μ = 200 against Ha: μ > 200, and you have decided to use the following decision rule: Reject H0 if the sample mean of a random sample of 100 items is more than 215. Assume that the standard deviation of the population is 80.
a. Express the decision rule in terms of z.
b. Find α, the probability of making a Type I error, by using this decision rule. Standard deviation = 10, and alternative < with the normal distribution. Set the null mean to 55 and run the applet several times without clearing. Record the proportion of Type II errors that occurred at the .01 level. Clear the applet and repeat for null means of 54, 53, 52, and 51. What can you conclude about the probability of a Type II error as the null mean gets closer to the actual mean?
Can you offer a reasonable explanation for this behavior?