The hypotheses of H0: μ = 5.5 and Ha: μ < 5.5 were to be tested. An equivalent confidence interval was found to be (5.2, 5.9). Will the hypothesis test result in “rejecting the null hypothesis” or “failing to reject the null hypothesis”?

Answer 1

To determine whether to reject or fail to reject the null hypothesis \( H_0: \mu = 5.5 \) based on the confidence interval (CI) of \( (5.2, 5.9) \), we need to evaluate the relationship between the null hypothesis value and the confidence interval.

1. The null hypothesis \( H_0: \mu = 5.5 \) posits that the population mean \( \mu \) is equal to 5.5.
2. The alternative hypothesis \( H_a: \mu < 5.5 \) indicates we are testing if the true population mean is less than 5.5.
3. The confidence interval \( (5.2, 5.9) \) suggests that we are 95% (or whichever confidence level was used) confident that the true population mean lies between 5.2 and 5.9.

Since the value \( 5.5 \), which is the mean specified in the null hypothesis, is contained within this confidence interval, we do not have sufficient evidence to reject the null hypothesis.

Thus, the conclusion is:

Fail to reject the null hypothesis.