Consider a general one-sided hypothesis test on a populationmean µ with null hypothesis H0 : µ = 0, alternative hypothesis Ha :µ > 0, and Type I Error ? = 0.02. Assume that using a sample ofsize n = 100 units, we observe some positive sample mean x > 0with standard deviation s = 5. (a) Calculate the Type II Error andthe power of the test assuming the following observed sample means:(i) x = 1.5 and (ii) x = 2.0. (b) How does the power of test behaveas the observed sample mean x gets further away from the nullhypothesis mean µ0?
