Assume That Under the Null Hypothesis $\bar { Y }$ Has an Expected Value of 500 and a Standard Deviation

Assume that under the null hypothesis, $\bar { Y }$ has an expected value of 500 and a standard deviation of 20. Under the alternative hypothesis, the expected value is 550 . Sketch the probability density function for the null and the alternative hypothesis in the same figure. Pick a critical value such that the $p$ -value is approximately 5\%. Mark the areas, which show the size and the power of the test. What happens to the power of the test if the alternative hypothesis moves closer to the null hypothesis, i.e., $\mu _ { Y } = 540,530,520$ , etc.? 25