Provide an Appropriate Response $95 \%$ Prediction Interval About the Value Of

Short Answer

Provide an appropriate response.
-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. Construct a $95 \%$ prediction interval about the value of $y$ when $x = 300$ days.
$\begin{array}{cccccc}\text { Horse } & \begin{array}{c}\text { Gestation } \\\text { period }\end{array} & \begin{array}{c}\text { Life } \\\text { Length } \\\text { x (days) }\end{array} & \text { Horse } & \begin{array}{c}\text { Gestation } \\\text { period }\end{array} & \begin{array}{c}\text { Life } \\\text { Length }\end{array} \\1 & 416 & 24 & 5 & 356 & 22 \\2 & 279 & 25.5 & 6 & 403 & 23.5 \\3 & 298 & 20 & 7 & 265 & 21 \\4 & 307 & 21.5 & & &\end{array}$