23.20 What distinguishes those who have schizophrenia? Psychologists once measured 77 variables on a sample of people who had schizophrenia and a sample of people who did not have schizophrenia. They compared the two samples using 77 separate significance tests. Two of these tests were significant at the 5% level. Suppose that there is, in fact, no difference in any of the 77 variables between people who do and do not have schizophrenia in the adult population. That is, all 77 null hypotheses are true.
(a) What is the probability that one specific test shows a difference that is significant at the 5% level?
(b) Why is it not surprising that two of the 77 tests were significant at the 5% level?