47 Let denote the proportion of schizophrenics who respond positively to a particular treat- ment A test is conducted of 15 against H: >.5. based on a sample of size 25. using a = .05.

a) Find the region of sample proportion values for which He is injected. for a large-sample z lest

b) Suppose that, unknown to the researcher, the true value of is 60. Find the probabil- ity that a Type II error occurs.

c) Explain why the probability of Type II error increases toward .95 as the true value of moves down toward 5. (Assuinen and a stay fixed.]