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A Breeder of Thoroughbred Horses Wishes to Model the Relationship

Question 110

Essay

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.

 Horse Gestation Life  Horse  Gestation  Life  period  Length  period  Length x (days) y (years) x (days) y (years) 141624535622227925.5640323.5329820726521430721.5\begin{array}{lllll}\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) } && x \text { (days) } &y \text { (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}

Summary statistics yield SSxx=21,752,SSxy=236.5,SSyy=22,xˉ=332S S _ { x x } = 21,752 , S S _ { x y } = 236.5 , S S _ { y y } = 22 , \bar { x } = 332 , and yˉ=22.5\bar { y } = 22.5 . Test to determine if a linear relationship exists between the gestation period and the length of life of a horse. Use α=.05\alpha = .05 and use s=1.97s = 1.97 as an estimate of σ\sigma .

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