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

Summary statistics yield $S S _ { x x } = 21,752 , S S _ { x y } = 236.5 , S S _ { y y } = 22 , \bar { x } = 332$, and $\bar { y } = 22.5$. Find a $95 \%$ prediction interval for the length of life of a horse that had a gestation period of 300 days. Use $s = 2$ as an estimate of $\sigma$ and use $y = 18.89 + .01087 x$

Question

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

Summary statistics yield $S S _ { x x } = 21,752 , S S _ { x y } = 236.5 , S S _ { y y } = 22 , \bar { x } = 332$, and $\bar { y } = 22.5$. Find a $95 \%$ prediction interval for the length of life of a horse that had a gestation period of 300 days. Use $s = 2$ as an estimate of $\sigma$ and use $y = 18.89 + .01087 x$

Quizplus · Accepted Answer

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

Summary statistics yield $S S _ { x x } = 21,752 , S S _ { x y } = 236.5 , S S _ { y y } = 22 , \bar { x } = 332$, and $\bar { y } = 22.5$. Find a $95 \%$ prediction interval for the length of life of a horse that had a gestation period of 300 days. Use $s = 2$ as an estimate of $\sigma$ and use $y = 18.89 + .01087 x$

A Breeder of Thoroughbred Horses Wishes to Model the Relationship