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2020-12-24

In there a relationship between confidence intervals and two-tailed hypothesis tests? The answer is yes. Let c be the level of confidence used to construct a confidence interval from sample data. Let * be the level of significance for a two-tailed hypothesis test. The following statement applies to hypothesis tests of the mean: For a two-tailed hypothesis test with level of significance a and null hypothesis ${H}_{0}:mu=k$ we reject Ho whenever k falls outside the $c=1—\alpha$ confidence interval for mu based on the sample data. When A falls within the $c=1—\alpha$ confidence interval. we do reject ${H}_{0}$. For a one-tailed hypothesis test with level of significance Ho : mu = k and null hypothesiswe reject Ho whenever A falls outsidethe $c=1—2\alpha$ confidence interval for p based on the sample data. When A falls within the $c=1—2\alpha$ confidence interval, we do not reject ${H}_{0}$. A corresponding relationship between confidence intervals and two-tailed hypothesis tests is also valid for other parameters, such as $p,{\mu }_{1}—{\mu }_{2},$ and ${p}_{1},-{p}_{2}$. (b) Consider the hypotheses ${H}_{0}:{p}_{1}—{p}_{2}=O$ and ${H}_{1}:{p}_{1}—{p}_{2}=$ Suppose a 98% confidence interval for ${p}_{1}—{p}_{2}$ contains only positive numbers. Should you reject the null hypothesis when alpha = 0.05? Why or why not?

Raheem Donnelly

The-ntiligpediestes ${H}_{0}:{p}_{1}-{p}_{2}=90$
The alternative hypothesis:
${H}_{0}:{p}_{1}-{p}_{2}>0$
Here, from above hypothesis ${p}_{1}—{p}_{2}=0$ and we know that for a one-tailed hypothesis test with level of significance a, we reject ${H}_{0}$ whenever the difference of proportions falls outside the $c=1-\alpha$ confidence interval for p based on the sample data. If a 98% confidence interval for ${p}_{1}—{p}_{2}$ contains only positive numbers then we should reject because the confidence interval does not contain 0. We know that 99% confidence interval is greater than 98% confidence interval and 99% confidence intervalmight contain 0. So, we don’t have enough evidence to reject null hypothesis level of significance.

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