For Neyman-Pearson hypothesis testing, we need to balance the trade-off between alpha, the probability of a type I error and power, i.e., 1-beta, where beta is the probability of a type II error. Compute alpha, beta, and the power for the cases given below, where we specify the null and alternative distributions and the accompanying critical region. All distributions are guassian with some specificed mean and standard deviation , i.e., N( ,). Let T be the test statistic.

a) H_0: N( 0,1), H_1: N(3,1), critical region: T>2.

b) H_0: N(-1,1), H_1: N(3,1), critical region |T|>1