What does a p-value indicate in hypothesis testing?

In hypothesis testing, a p-value serves as a measure of the strength of evidence against the null hypothesis. Specifically, it quantifies the probability of obtaining results at least as extreme as those observed in the sample data, assuming that the null hypothesis is true. A smaller p-value indicates that the observed results would be rare under the null hypothesis, thereby providing stronger evidence to reject it.

This concept is essential because it helps researchers determine whether the observed data is consistent with what would be expected if the null hypothesis were indeed true. In contrast, the other options do not accurately capture the role of the p-value in this context. The sample size relates to the power of a test but does not define what a p-value represents. The probability of not rejecting the null hypothesis is more related to confidence levels and intervals rather than the p-value itself. Similarly, the standard deviation of the sample data describes the variability in the dataset but has no direct relation to the p-value's role in hypothesis testing.