Lecture 14 testing hypotheses about proportions ii. P-value: probability of observing something as extreme as our sample if the null was true. If p-value is small enough , we can reject the null hypothesis: this lecture: Relationship between con dence intervals and hypothesis testing. Common ones: 0. 1, 0. 05 or 0. 01. Very often: 0. 05: if the p-value is smaller than , we reject h0, if the p-value is greater than or equal to , we fail to reject h0. H0: how to phrase the conclusion: we reject/fail to reject the null hypothesis at the signi cance level. , notice that it may still be useful to report p-values, since they are more informative. We would fail to reject the null hypothesis if p-value 0. 101, but reject if p-value 0. 099. 3 di erence between statistical and economic signi cance: statistical signi cance: statistically di erent from the hypothesized value of the parameter. 4 critical values: the values are probabilities.