Compute p-values and adjust multiplicity

Q: Compute p-values and adjust multiplicity

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Question

You test if a coin is fair after 20 flips and observe 17 heads. (a) Compute the exact two-sided p-value under a Binomial(20, 0.5) model. (b) Approximate the p-value using a normal z-test with and without continuity correction; discuss accuracy. (c) Now you simultaneously test 6 independent features of a product using similar binomial tests at familywise α=0.05; apply Bonferroni and Holm corrections and state your decision rule. (d) Explain precisely why a p-value is not the probability that H0 is true. (e) When should you use z-test vs t-test for a mean difference, and what assumptions must hold?

Compute p-values and adjust multiplicity

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