What does it mean if a p-value is lower than the significance level?

When the p-value is lower than the significance level, it indicates that the observed data provides sufficient statistical evidence to reject the null hypothesis. The p-value represents the probability of obtaining test results at least as extreme as the observed results, assuming that the null hypothesis is true. A lower p-value suggests that such an extreme result is very unlikely under the null hypothesis framework.

Therefore, when the p-value falls below the predetermined significance level (often set at 0.05), it implies that the data is not consistent with the null hypothesis, and we conclude that there is enough evidence to favor the alternative hypothesis. This rejection does not prove the alternative hypothesis is true, but it does strongly suggest that the null hypothesis does not adequately explain the observed data.

In this context, the significance level acts as a threshold; values above this threshold do not provide strong enough evidence to doubt the null hypothesis, while values below it signify that the evidence against the null hypothesis is strong enough to warrant its rejection in favor of the alternative hypothesis.