What does a smaller p-value indicate in hypothesis testing?

In hypothesis testing, a smaller p-value indicates that the observed data is less likely under the assumption that the null hypothesis is true, leading to stronger evidence against the null hypothesis. When the p-value is small, typically less than a predetermined threshold (often 0.05), it suggests that the data observed would be very unlikely if the null hypothesis were actually correct.

This does not mean that the original hypothesis (or alternative hypothesis) is definitively true, but rather that there is significant evidence to support it. The interpretation is that a smaller p-value reflects a stronger chance that the evidence obtained from the sample supports the alternative hypothesis, leading researchers to consider rejecting the null hypothesis in favor of the alternative.

The other choices do not accurately capture this relationship. A stronger chance that the null hypothesis is true, a weaker chance that the alternative hypothesis is true, and the assertion of no proof regarding either hypothesis do not align with the implications of observing a smaller p-value in the context of statistical analysis.