What does the p-value indicate in hypothesis testing?

The p-value is a critical component in hypothesis testing, serving as a statistical measure that helps to determine the significance of the results obtained from a sample. Specifically, the p-value indicates the probability of obtaining a sample mean that is as extreme, or even more extreme, than what has been observed in the sample data, under the assumption that the null hypothesis is true.

This statistical concept allows researchers to assess whether their results provide enough evidence to reject the null hypothesis. A small p-value suggests that the observed data is unlikely to occur if the null hypothesis is indeed correct, thereby indicating potential support for the alternative hypothesis.

The context around the incorrect options highlights important distinctions in hypothesis testing. While the probability of a Type 1 error refers to the likelihood of incorrectly rejecting a true null hypothesis, this is not what the p-value directly measures. The p-value does not indicate the probability that the null hypothesis itself is true; rather, it assesses the sample data against the null hypothesis. Lastly, while the term "error rate" can relate to statistical tests, it does not define the p-value directly; instead, it refers to the overall mistake rate of a test rather than a singular measurement related to p-value outcomes. Therefore, the definition of the p-value