What do large p-values indicate about the null hypothesis?

Large p-values indicate that the data do not provide strong evidence against the null hypothesis. In statistical hypothesis testing, a p-value represents the probability of observing the data or something more extreme if the null hypothesis is true. Therefore, when the p-value is large, it suggests that the observed data is consistent with the null hypothesis, leading to the conclusion that there is not enough statistical evidence to reject it.

This understanding emphasizes that large p-values do not confirm the null hypothesis as true but rather imply that there is insufficient evidence to say that it is false, thereby aligning with the choice indicating strong evidence for it. Because of this nuance in interpretation, large p-values are often viewed as supporting the null hypothesis.