In hypothesis testing, what does it mean when the p-value is less than the significance level?

In hypothesis testing, the p-value is a critical statistic that helps determine whether to reject or fail to reject the null hypothesis. When the p-value is less than the predetermined significance level (often denoted as alpha, commonly set at 0.05), it indicates that the probability of observing the test results, or something more extreme, under the null hypothesis is very low.

This low probability suggests that the evidence against the null hypothesis is strong enough to warrant its rejection. Therefore, under these circumstances, it is appropriate to reject the null hypothesis in favor of the alternative hypothesis. This rejection implies that the data observed are statistically significant, indicating that an effect or difference likely exists.

The interpretation of the p-value being less than the significance level is foundational in inferential statistics, as it guides researchers in making data-driven decisions about hypotheses based on empirical evidence.