could you help giving me explanations on this problem ? Thank you.

Let X be a normal random variable with unknown mean / and known variance o? = 1. . The null hypothesis is that #o = 2; . The alternative hypothesis is that #1 = 3. Let X1, . . . Xn be n = 20 independent samples of X, and let Z be Z := (-1)iX, = -X1 + 2X2 - 3X3 + 4X, - ... + (-1)"nXn i=1 Consider another critical region C" given by C := (X1 , . . . , Xn) | X Z Hot 20.05 Vn the type I error for this test is a = 0.05. Compute the type II error for this test