What does a p-value represent in the context of hypothesis testing?

In hypothesis testing, the p-value serves as a critical metric for decision-making regarding the null hypothesis. Specifically, it represents the probability of obtaining the observed results, or something more extreme, assuming that the null hypothesis is true. This means that if the p-value is low (typically below a predetermined significance level, such as 0.05), it suggests that the observed data is unlikely under the null hypothesis, which may lead to its rejection in favor of the alternative hypothesis.

This interpretation is fundamental to understanding how statistical significance is determined. A small p-value indicates strong evidence against the null hypothesis, prompting researchers to consider that there may be a significant effect or relationship present. On the other hand, a larger p-value suggests that the observed data fits within the range that would be expected if the null hypothesis were true, which does not provide strong evidence to reject it.

The other choices represent concepts that either misinterpret the role of the p-value or address different statistical aspects. For example, stating that it indicates the likelihood that the null hypothesis is true misunderstands that the p-value does not provide evidence regarding the true state of the null hypothesis; rather, it assesses the data in relation to that hypothesis. The options that mention measuring differences or quantifying confidence