Chapter PVI, Problem 34RE

(a)

To determine

To find out what is the margin of error for this estimate.

Answer to Problem 34RE

The margin of error is $373.5$ .

Explanation of Solution

It is given in the question that every statement about a confidence interval contains two parts: the level of confidence and the interval. The confidence interval is $(\$1644,\$2391)$ with $\alpha =0.05$ . Thus, the margin of error is half the width of the confidence interval as:

  $\begin{array}{l}E=\frac{2391-1644}{2}\\ =\frac{747}{2}\\ =373.5\end{array}$

Thus, the margin of error is $373.5$ .

(b)

To determine

To carefully explain what the interval means.

Explanation of Solution

It is given in the question that every statement about a confidence interval contains two parts: the level of confidence and the interval. The confidence interval is $(\$1644,\$2391)$ with $\alpha =0.05$ . So, we can interpret that we are $95\%$ confident that the mean loss claimed by clients after home burglaries between $\$1644\text{ and \$2391}$ .

(c)

To determine

To carefully explain what the $95\%$ confidence level means.

Explanation of Solution

It is given in the question that every statement about a confidence interval contains two parts: the level of confidence and the interval. The confidence interval is $(\$1644,\$2391)$ with $\alpha =0.05$ . So, we can interpret that we are $95\%$ confident that the mean loss claimed by clients after home burglaries between $\$1644\text{ and \$2391}$ . Thus, “ $95\%$ confident” means that $95\%$ of all possible samples have a $95\%$ confidence interval that contains the true value of the population mean.