Consider a hypothesis test with null H_0 and alternative H_1 regarding an unknown parameter \theta. You observe a sample X_1, \ldots , X_ n \stackrel{iid}{\sim } P_{\theta } and compute the p-value.

Question

Consider a hypothesis test with null H_0 and alternative H_1 regarding an unknown parameter \theta. You observe a sample X_1, \ldots , X_ n \stackrel{iid}{\sim } P_{\theta } and compute the p-value.

What is a correct interpretation of the p-value?

The smaller a p-value is, the more evidence that is suggested against H_0.

The larger a p-value is, the more evidence that is suggested against H_0.

Answer 1

The smaller a p-value is, the more evidence there is against the null hypothesis (H_0). The p-value represents the probability of observing a test statistic as extreme, or more extreme, than the one observed, under the assumption that the null hypothesis is true. Therefore, a smaller p-value indicates stronger evidence against the null hypothesis.

Answer 2

The correct interpretation of the p-value is that the smaller the p-value is, the more evidence it suggests against the null hypothesis (H_0). This means that if the p-value is very small, it indicates that the observed data is unlikely to occur under the assumption of the null hypothesis, and provides evidence in favor of the alternative hypothesis (H_1). Conversely, a larger p-value suggests weaker evidence against the null hypothesis, indicating that the observed data is reasonably likely to occur under the assumption of the null hypothesis.