MATH STATS

Let X ~ N(0,4) where 0 real; thus E(X) = 0 and var(X) = 4. Assume a random sample of size n will be taken from the population. Test : Ho : 0 = 2 vs. HA : 0 = 5, at significance level a, by constructing a most powerful test at that given significance level, and justifying your work. Compute the power of your test. Without having to prove it, tell at what rate your power would tend to 100%, as n tends to infinity