Problem 2. 16 independent normal observations were collected from a population with unknown mean ,u and known variance 02 = 4. We want to test H0:,u=0 vs Hazn70 (a) (2 points) Write down the GLRT rejection region for the problem. (b) (5 points) Consider an alternative test that rejects H0 if |E| > 1. Compute the level of signicance (Here :E is the sample mean of x's). (c) (11 points) Compute the power of test from part (a) and part (b) for the alternative u = 1.5. Which test seems better w.r.t. the power at ,u = 1.5