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

Question

Quizplus · Accepted Answer

The confidence interval represents a range of values for the population mean that are considered plausible based on the sample data. If the hypothesised value for $\mu$ falls within this range (between the LCL and UCL), then we do not have enough evidence to reject the null hypothesis. Only if the hypothesised value falls outside this range (either to the left of the LCL or to the right of the UCL) would we have enough evidence to reject the null hypothesis. Thus, the correct choice is C.

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