A

A

Note how the confidence interval is related to the test statistic. They are linked by the rejection point(s).

- The confidence interval is:
- Recall that the test statistic is:

The likelihood that the z-value will be less than the test statistic is what is being tested. Setting up this inequality, and rearranging, the test is:

Confidence intervals can be used to test hypotheses. Note that the right side of the equation is the left endpoint of the confidence interval. Essentially, if the confidence interval contains the value of the unknown population parameter as hypothesized under H

The reason for the above determination is as follows:

- If the hypothesized value does not fall in the confidence interval, then there is a very small chance that the value can be a true value for the unknown parameter, so H
_{0}is almost certainly wrong and will be rejected. - If the hypothesized value does fall in the confidence interval, then there is a very good chance that the value can be a true value for the unknown parameter, so H
_{0}is definitely possible and will not be rejected.

This comparison can be used only for two-sided tests, not one-sided tests, because confidence intervals cannot be linked with one-sided tests.