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.

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

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

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Definitions:

Hot Drinks

Hot drinks refer to beverages served warm, such as coffee, tea, and hot chocolate, often consumed for their comforting effects or stimulant properties.

Temperature

A measure of the warmth or coldness of an environment or substance, typically expressed in degrees Celsius or Fahrenheit.

Increased

To become or to make something larger or more in number, size, value, or extent.

Hot Drinks

Beverages that are typically served warm, such as coffee, tea, hot chocolate, and certain herbal infusions.