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

question 3

Essay

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.
$\begin{array} { c c c c c c } \text { Horse } & \text { Gestation } & \text { Life } & \text { Horse } & \text { Gestation } & \text { Life } \\ & \text { period } & \text { Length } & & \text { period } & \text { Length } \\ & x \text { (days) } & y \text { (years) } & & \text { x (days) } & \text { y (years) } \\ 1 & 416 & 24 & 5 & 356 & 22 \\ 2 & 279 & 25.5 & 6 & 403 & 23.5 \\ 3 & 298 & 20 & 7 & 265 & 21 \\ 4 & 307 & 21.5 & & & \end{array}$

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Definitions:

Direct Fitness

The reproductive success of an individual based on the number of offspring it directly produces and supports to adulthood.

Alarm-Calling

A behavior in which animals emit specific vocalizations to warn conspecifics of potential danger or predators.

Inclusive Fitness

A concept in evolutionary biology that considers an individual's genetic success through its own offspring and by supporting relatives.

Indirect Fitness

The genetic gain achieved by an organism by helping relatives rear their offspring, thereby passing on shared genes.