You have an SRS of size n = 16 from a Normal distribution with standard deviation = 1. You wish to test
H_0 :μ = 0
H_a :μ > 0
You decide to reject H_0 if x bar > 0 and to accept H_0 otherwise.
a. Find the probability of a Type I error. That is, find the probability that the test rejects H_0 when in fact μ = 0.
b. Find the probability of a Type II error when μ = 0.2. This is the probability that the test accepts H_0 when in fact μ = 0.2.
c. Find the probability of a Type II error when μ = 0.5.