Conduct Inference on the Slope
-A Breeder of Thoroughbred Horses $\alpha = 0.05$

Conduct Inference on the Slope
-A breeder of thoroughbred horses wishes to model the relationship between the gestation period and the length of life of a horse. The breeder believes that the two variables may follow a linear trend. The information in the table was supplied to the breeder from various thoroughbred stables across the state. Test the claim, at the $\alpha = 0.05$ level of significance, that a linear relation exists between the gestation period and the length of life of a horse.
$\begin{array} { c c c c c c } \text { Horse } & \text { Gestation } & \text { Life } & \text { Horse } & \text { Gestation } & \text { Life } \\ & \text { period } & \text { Length } & & \text { period } & \text { Length } \\ & x \text { (days) } & y \text { (years) } & & \text { x (days) } & \text { y (years) } \\ 1 & 416 & 24 & 5 & 356 & 22 \\ 2 & 279 & 25.5 & 6 & 403 & 23.5 \\ 3 & 298 & 20 & 7 & 265 & 21 \\ 4 & 307 & 21.5 & & & \end{array}$