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 $\mu$ falls between the lower and upper confidence limits.

Question

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When conducting a two-tail test and using the confidence interval approach, the null hypothesis is not rejected if the hypothesized value for the population mean falls between the lower and upper confidence limits. This is because the confidence interval provides a range of plausible values for the population mean, and if the hypothesized value falls within this range, we cannot reject the null hypothesis at the given level of confidence.

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