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Suppose we are about to carry out 95 independent hypothesis tests. We intend to carry out each test at a significance level of 0.05. Suppose

Suppose we are about to carry out 95 independent hypothesis tests. We intend to carry out each test at a significance level of 0.05. Suppose that the assumptions of each test are true, and, unknown to us, the null hypothesis is true in all 95 situations.

What is the probability that we make a Type I error in exactly 5 of the 95 tests?

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