Chapter 24, Problem 4E

(a)

To determine

To explain what does “the endpoints of this confidence interval are negative” indicate.

Explanation of Solution

It is given that in June, consumer reports examined top loading and front loading washing machines testing samples of several different brands of each type. Among the machines rated good to excellent, the $98\%$ confidence interval for the difference in mean cycle time ${\mu }_{\text{Top}}-{\mu }_{\text{Front}}$ is $(-40,-22)$ . Thus, the endpoints of this confidence interval are negative indicates that the difference ${\mu }_{\text{Top}}-{\mu }_{\text{Front}}$ is negative and thus the mean cycle time of top-loading washing machine is higher than the mean cycle time of front-loading washing machine.

(b)

To determine

To explain what does the fact that the confidence interval does not contain zero indicate.

Explanation of Solution

It is given that in June, consumer reports examined top loading and front loading washing machines testing samples of several different brands of each type. Among the machines rated good to excellent, the $98\%$ confidence interval for the difference in mean cycle time ${\mu }_{\text{Top}}-{\mu }_{\text{Front}}$ is $(-40,-22)$ . Thus, the fact that the confidence interval does not contain zero indicate that since the confidence interval does not contain zero, this indicates that the difference ${\mu }_{\text{Top}}-{\mu }_{\text{Front}}$ is nonzero and thus the mean cycle time of top-loading machines is significantly different from the mean cycle time for front-loading washing machines.

(c)

To determine

To explain what does the corresponding alpha level.

Answer to Problem 4E

The corresponding alpha levelis $0.02$ .

Explanation of Solution

It is given that in June, consumer reports examined top loading and front loading washing machines testing samples of several different brands of each type. Among the machines rated good to excellent, the $98\%$ confidence interval for the difference in mean cycle time ${\mu }_{\text{Top}}-{\mu }_{\text{Front}}$ is $(-40,-22)$ . It is given if we use this confidence interval to test the hypothesis that ${\mu }_{\text{Top}}-{\mu }_{\text{Front}}=0$ . As given confidence level $98\%$ then the corresponding alpha level of the two sided test is one decreased by the confidence interval as:

  $\begin{array}{l}\alpha =1-98\%\\ =1-0.98\\ =0.02\end{array}$