Consider the null hypothesis 56. The population standard deviation is guessed to be 2.16. Type II error probabilities are to be calculated at

Consider the null hypothesis μ ≥ 56. The population standard deviation is guessed to be 2.16. Type II error probabilities are to be calculated at μ = 55.

a. Draw a β versus α chart with sample sizes 30, 40, 50, and 60.

b. The test is conducted with a random sample of size 50 with α = 5%. Draw the power curve. What is the power when μ = 55.5?

c. Draw an OC curve with n = 50 and 60; α = 5%. Is there a lot to gain by going from n = 50 to n = 60?