Chapter 10.3, Problem 21BB

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:

ŷ − E < $\bar{y}$ < ŷ + E

where

$E\text{ = }{t}_{\alpha /2}\cdot s_e\sqrt{\frac{1}{n}+\frac{n{(x_0-\bar{x})}^2}{n({\displaystyle \sum x^2})-{({\displaystyle \sum x})}^2}}$

The critical value t_α/2 is found with n − 2 degrees of freedom. Using the 23 pairs of chocolate/Nobel data from Table 10-1 on page 469 in the Chapter Problem, find a 95%, confidence interval estimate of the mean Nobel rate given that the chocolate consumption is 10 kg per capita.