Using the confidence interval when conducting a two-tail test for the population mean $\mu$ we do not reject the null hypothesis if the hypothesized value for $\mu$ :
A) is to the left of the lower confidence limit.
B) is to the right of the upper confidence limit.
C) falls between the lower and upper confidence limits.
D) falls in the rejection region.

Question

Quizplus · Accepted Answer

If the hypothesized value for $\mu$ falls between the lower and upper confidence limits, then it is within the range of values that we are reasonably confident could represent the true population mean. Therefore, we do not reject the null hypothesis in this case. If the hypothesized value falls outside of this range, either to the left or right of the confidence limits, then we would reject the null hypothesis in favor of the alternative hypothesis. The rejection region refers to the area outside of the confidence interval where we would reject the null hypothesis.

Using the Confidence Interval When Conducting a Two-Tail Test for the Population