Chapter 11.5, Problem 8Q

In a study of heart disease $\left(79\right)$, the weight (in pounds) and the blood cholesterol (in mg/dl) of fourteen men without a history of coronary incidents were recorded. At the $\alpha =0.05$ level, can we conclude from these data that the two variables are independent?

Subject	Weight, $x$	Cholesterol, $y$
1	168	135
2	175	403
3	173	294
4	158	312
5	154	311
6	214	222
7	176	302
8	262	269
9	181	311
10	143	286
11	140	403
12	187	244
13	163	353
14	164	252

The data in the table give the following sums:

$\begin{array}{l}{\displaystyle \underset{i=1}{\overset{14}{\sum }}{x}_i=2,458}{\displaystyle \underset{i=1}{\overset{14}{\sum }}{y}_i}=4,097\\ {\displaystyle \underset{i=1}{\overset{14}{\sum }}{x}_i^2}=444,118{\displaystyle \underset{i=1}{\overset{14}{\sum }}{y}_i^2=1,262,559}\\ {\displaystyle \underset{i=1}{\overset{14}{\sum }}{x}_i{y}_i=710,499}\end{array}$