Relationship between a hypothesis test and confidence interval

Suppose that you are conducting a hypothesis test. Recall that the decision to reject the null hypothesis (H0) or fail to reject it can be based on the p-value and your chosen level of significance (a-level). If the p-value is less than or equal to a, you reject H0; if it is greater than a, you fail to reject H0.

Your decision can also be based on the confidence interval (or bound) constructed using the same a-level. For example, the decision for a test at the 0.05 level of significance can be based on the 95% confidence interval:

·    If the reference value specified in H0 lies outside the interval (that is, is less than the lower bound or greater than the upper bound), you can reject H0.

·    If the reference value specified in H0 lies within the interval (that is, is not less than the lower bound or greater than the upper bound), you fail to reject H0.