Confidence Intervals as Hypothesis Tests

Using the confidence interval to perform a hypothesis test only works with a two-tailed test.

• If the hypothesized value of the parameter lies within the confidence interval with a 1-alpha level of confidence, then the decision at an alpha level of significance is to fail to reject the null hypothesis.
• If the hypothesized value of the parameter lies outside the confidence interval with a 1-alpha level of confidence, then the decision at an alpha level of significance is to reject the null hypothesis.

Sounds simple enough, right? It is.

However, it has a couple of problems.

• It only works with two-tail hypothesis tests.
• It requires that you compute the confidence interval first. This involves taking a z-score or t-score and converting it into an x-score, which is more difficult than standardizing an x-score.