Question

If the assumptions for a nonpooled \(t-\)interval are satisfied, the formula for a \((1-\alpha)\) level lower confidence bound for the difference, \(\mu_{1}-\mu{2}\), between two population means is

\((\bar{x_{1}}-\bar{x_{2}})-t_{\alpha}\cdot \sqrt{(s_{1}^{2}/n_{1})+(s_{2}^{2}/n_{2})}\)

For a right tailed hypothesis test at the significance level \(\alpha\), the null hypothesis \(H_{0}:\mu_{1}=\mu_{2}\) will be rejected in favor of the alternative hypothesis \(H_{a}:\mu_{1}>\mu_{2}\) if and only if the \((1-\alpha)\) level lower confidence bound for \(\mu_{1}-\mu_{2}\) is greater than or equal to \(0\). In each case, illustrate the preceding relationship by obtaining the appropriate lower confidence bound and comparing the result to the conclusion of the hypothesis test in the specified exercise.

a. Exercise \(10.82\)

b. Exercise \(10.85\)

Short answer

Part a. It can be concluded that test results are statistically significant at \(1%\) level of significant.

Part b. It can be concluded that test results are statistically significant at \(1%\) level of significant.

Step-by-step solution

Part a. Step 1. Explanation

Consider the data,

It can be concluded that test results are statistically significant at \(1%\) level of significant.

Part b. Step 1. Explanation

Consider the data,

It can be concluded that test results are statistically significant at \(1%\) level of significant.