p-value
The p-value is P(test statistic as extreme as observed | H₀ is true). For a two-sided test with test statistic z, p-value = 2 × P(Z ≥ |z|). For one-sided tests, the p-value is P(Z ≥ z) or P(Z ≤ z) depending on direction. The p-value is compared to the significance level α to make a decision.
Real World
When Pfizer analysed COVID-19 vaccine trial data, a p-value well below 0.05 indicated the observed efficacy would be extraordinarily unlikely if the vaccine had no effect — strong evidence against H₀.
Exam Focus
Never write 'the p-value is the probability H₀ is true'; always compare p-value directly to α and state a conclusion in context.
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