Refer to Exercise 7.97. Suppose you want to test H0: = 500 against Ha: >

Question:

Refer to Exercise 7.97.
Suppose you want to test H0: μ = 500 against Ha: μ > 500 using α = .05. The population in question is normally distributed with standard deviation 100. A random sample of size n = 25 will be used.
a. If μ = 575 instead of 550, what is the probability that the hypothesis test will incorrectly fail to reject H0? That is, what is b?
b. If μ = 575, what is the probability that the test will correctly reject the null hypothesis? That is, what is the power of the test?
c. Compare β and the power of the test when μ = 575 with the values you obtained in Exercise 7.97 for μ = 550. Explain the differences.