The null hypothesis 30 is to be tested. The population standard deviation is guessed to

The null hypothesis μ ≤ 30 is to be tested. The population standard deviation is guessed to be 0.52. Type II error probabilities are to be calculated at μ = 30.3.

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 30 with an α of 5%. Draw the power curve. What is the power when μ = 30.2?

c. Draw an OC curve with n = 30 and 60; α = 5%. If type II error is to be almost zero when μ = 30.3, is it better to go for n = 60?