Two Hits Among Twenty Nulls
A researcher tests 20 independent hypotheses, all of which are true nulls, each at significance level 0.05 (so each p-value is uniform on [0, 1]). What is the probability that at least two of the tests come out significant? Give your answer rounded to 4 decimal places; 3 decimal places is also accepted.
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Source: Standard multiple-comparisons illustration of chance findings. Statement written for AxiomIQ.