Suppose that X is normally distributed with mean p and variance 400, and you want to test Ho'.p = 50 against Hi'.p = 0>Q.

If a — .10 and N — 4, find the critical value of M and compute /?. Now suppose that you wanted to test Ho against H\ :p = 80. For the same values of a and N, find the critical value of M and compute (3. In the light of these results, comment on the “classical” convention and how the test is affected by changes in Hi.