What does a p-value indicate in hypothesis testing?

• A. Probability that the null hypothesis is true
• B. The probability of making a Type I error
• C. Probability of observing the data (or more extreme) if the null hypothesis is true
• D. The confidence level of the test

Answer: (C)

The p-value measures how compatible the observed data are with the assumption that the null hypothesis is true. It is the probability, under the null, of obtaining data at least as extreme as what was observed (for the test statistic you’re using). A small p-value means the observed pattern would be unlikely if the null were true, providing evidence against the null; a large p-value means the data are reasonably consistent with the null.

This is not the probability that the null hypothesis is true, nor the probability of making a Type I error (that chance is set by your chosen significance level, not by the data). It also isn’t the test’s confidence level, which relates to long-run frequency of intervals rather than the specific observed data.