Chapter 9.3, Problem 58E

a.

To determine

Find the confidence interval for the mean response.

Find the prediction interval for the response

Answer to Problem 58E

The confidence interval for the mean response is A: (10 to 14).

The prediction interval for the response is B: (4 to 20).

Explanation of Solution

The prediction interval is always wider when compared to the confidence interval. Based on the situation, interval B (4 to 20) is wider when compared to Interval A (10 to 14).

Thus, the confidence interval for the mean response is A (10 to 14) and the prediction interval for the response is B (4 to 20).

b.

To determine

Find the predicted value of the response variable for this value of the explanatory variable.

Answer to Problem 58E

The predicted value of the response variable for this value of the explanatory variable is 12.

Explanation of Solution

The predicted value of the response variable for this value of the explanatory variable is as follows.

$\begin{array}{c}\text{Predicted}\text{value}=\frac{10+14}{2}\\ =\frac{24}{2}\\ =12\end{array}$

Thus, the predicted value of the response variable for this value of the explanatory variable is 12.