Which statement about p-values is correct?

• A. The probability of observing the data as extreme as the observed, assuming the null is true.
• B. The probability that the null hypothesis is true.
• C. The probability that the alternative hypothesis is true.
• D. The strength of the evidence against the null.

Answer: (D)

A p-value is the probability, under the null hypothesis, of obtaining data as extreme as or more extreme than what was observed. This captures how unusual the observed result would be if the null were true, with smaller values indicating more surprising data under H0.

It is not the probability that the null hypothesis is true, nor the probability that the alternative is true. Those are Bayesian ideas about the truth of hypotheses, not what a p-value measures. Describing the p-value as the “strength of the evidence against the null” is common but imprecise, because the p-value is a sampling-procedure quantity that depends on sample size and the specific test, not a direct measure of how strong the evidence is.