Using a confidence interval to decide whether to reject the null hypothesis

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

Your decision can also be based on the confidence interval (or bound) calculated using the same α. 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.
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