You take a random sample of size 100 from a normal population with unknown mean but known standard deviation 40. You plan to test H(null): mu=85 versus H(alternative): mu > 85. Your procedure will be to observe the sample then reject H(null) is xbar>90.
a.) What is the probability of rejecting the null if in fact mu=95?
b.) What is the Type II error and what is the power of the test if in fact mu=95?