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

Question

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

GPT 3.5 · Answer

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.

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.