A group of psychologists once measured 77 variables on a sample of schizophrenic

Question

A group of psychologists once measured 77 variables on a sample of schizophrenic people and a sample of people who were not schizophrenic. 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 variables between people who are and people who are not schizophrenic, so that all 77 null hypotheses are true. What is the probability that one specific test shows a difference significant at the 5% level?

Explanation / Answer

we are given that the probability that 1 test shows a significant difference at the 5% level = 2/77
p=2/77
n=77 , which is the total number of tests conducted
x =how many out of 77 shows significance

P(x=4) = (2/77)^4 =

0.0000004552

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