Chapter 10.4, Problem 22BB

Confidence Interval for Mean Predicted Value Example 1 in this section illustrated the procedure for finding a prediction interval for an individual value of y. When using a specific value x₀ for predicting the mean of all values of y, the confidence interval is as follows:

$\hat{y}-E<\bar{y}<\hat{y}+E$

where

$E=t_{\alpha /2}\cdot s_l\sqrt{\frac{1}{n}+\frac{n{(x_0-\bar{x})}^2}{n(\sum x^2)-{(\sum x)}^2}}$

The critical value t_α/2, is found with n − 2 degrees of freedom. Using the 40 pairs of shoe print lengths (x) and heights (y) from Data Set 2 in Appendix B, find a 95% confidence interval estimate of the mean height given that the shoe print length is 29.0 cm.