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If a 95% confidence interval for is calculated to be (21.4 , 27.9) , what would be the result of a hypothesis test at a 5% significance level performed on the set of hypotheses?

H0: mean = 27
Ha: mean different 27

User Zalis
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Based on the given 95% confidence interval of (21.4, 27.9), we can see that it does not include the hypothesized mean of 27 within its range. This means that the data used to calculate the confidence interval provides evidence against the null hypothesis (H0: mean = 27) and suggests that the true population mean is likely to be different from 27.

Since the confidence interval does not include the hypothesized mean of 27, we can reject the null hypothesis at the 5% significance level. In other words, we have enough evidence to conclude that the true population mean is different from 27 based on the given confidence interval.

This result is consistent with the alternative hypothesis (Ha: mean different from 27), which states that the true population mean is not equal to 27. Thus, we can reject the null hypothesis in favor of the alternative hypothesis at the 5% significance level based on the given confidence interval.
User Imanpal Singh
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