Using the confidence interval when conducting a two-tail test for the population mean m , we do not reject the null hypothesis if the hypothesized value for m falls between the lower and upper confidence limits.

Question

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If the hypothesized value for $m$ falls within the confidence interval, it means that the observed data is consistent with the null hypothesis, so we do not have enough evidence to reject the null hypothesis.

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