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You toss a fair coin n times and conduct a test of H0 : θ =...

You toss a fair coin n times and conduct a test of H0 : θ = 0.5 vs. H1 : θ ̸= 0.5, where θ denotes the probability of a head, allowing a Type I error rate of 0.05. If you repeat this whole process 20 times, what is the probability that at least one of the 20 tests will be statistically significant? Show your work.

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Answer #1

Here

H0 : = 0.5

H1 : 0.5

where θ denotes the probability of a head.

Type I error rate = 0.05

Here the sample size = 20 times

P(Atleast one of the 20 tests wiil be statistically significant) =1 - P(No tests will be statistically significant)

P(No tests will be statistically significant) = 20C0 (0.05)0 (0.95)20 = 0.3585

P(Atleast one of the 20 tests wiil be statistically significant) = 1 - 0.3585 = 0.6415

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