What does a p-value indicate in hypothesis testing?

A p-value indicates the probability of obtaining results at least as extreme as those observed in the data, assuming that the null hypothesis is true. In hypothesis testing, the null hypothesis typically represents a statement of no effect or no difference, and the p-value helps assess whether the observed data provide sufficient evidence to reject this hypothesis.

When you calculate a p-value, you essentially evaluate how compatible the observed data are with the null hypothesis. A smaller p-value suggests that the observed data would be very unlikely under the null hypothesis, leading researchers to consider rejecting the null in favor of the alternative hypothesis. This insight is central to making informed decisions in statistical analysis, forming the basis for determining whether the results are statistically significant.

In this context, the other options do not accurately reflect the role of a p-value. The first choice, while discussing observations under the alternative hypothesis, does not capture the essence of what a p-value signifies in relation to the null hypothesis. The third option speaks to the likelihood of a Type I error, which is directly related to the significance level rather than the interpretation of p-values. Lastly, the fourth option describes the significance level, which is a predetermined threshold for deciding whether to reject the null hypothesis, rather than the outcome of conducting the test