5. (15 points) Let X1, ..., Xn i.i.d. ~ N(0, 1). Consider testing Ho : 0 = 0 versus H: 0 = 1. Consider a critical region of the form c = C -{: > to}. xi > ta where to is the critical value (which may depend on n). (a) Find the value of to such that the test has a given significance level a. (b) Find the power under H, i.e., (1). (c) Fix a significance level 0 < a < 0.5. For each n, consider the critical region C = Cn where the critical value t = tan is given by (a). Show that (1) 1 as n .