A Company Keeps Extensive Records on Its New Salespeople on the Premise

A company keeps extensive records on its new salespeople on the premise that sales should increase with experience. A random sample of seven new salespeople produced the data on experience and sales shown in the table.

$\begin{array}{c|c}\text { Months on Job } & \begin{array}{c}\text { Monthly Sales } \\\text { y (\$ thousands) }\end{array} \\\hline 2 & 2.4 \\4 & 7.0 \\8 & 11.3 \\12 & 15.0 \\1 & .8 \\5 & 3.7 \\9 & 12.0\end{array}$

Summary statistics yield $S S _ { x x } = 94.8571 , S S _ { x y } = 124.7571 , S S _ { y y } = 176.5171 , \bar { x } = 5.8571$ , and $\bar { y } = 7.4571$ . Calculate a $90 \%$ confidence interval for $E ( y )$ when $x = 5$ months. Assume $s = 1.577$ and the prediction equation is $\hat { y } = - .25 + 1.315 x$ .