1. (50 points) Suppose Y1, ..., Yn is a random sample of size n = 10 from a normal population with mean 0 and variance o (unknown). (a) Find the most powerful test with significance level 0.05 to test Ho : 02 = 2 vs. Ha : 02 - 1. (b) Under the alternative hypothesis in (a), find , the probability of the type II error. Further, find the power of the test in this situation. (c) Suppose that we observe _1 1 y? = 4. Is there enough evidence to conclude that the random sample is drawn from a standard normal distribution at the significance level a = 0.05? (d) Find a when the rejection region in (a) is RR = { CT , y?