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

question 35

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

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Definitions:

Weakness

A lack of physical strength, or the state of being less strong or powerful in a physical or emotional sense.

Frailty

A condition often associated with aging, characterized by decreased strength, endurance, and reduced physiological function, making an individual more vulnerable to falls, disability, and disease.

Elderly

A term referring to individuals who are significantly beyond the middle age, often considered to be 65 years and older.

Secure Attachments

A type of attachment characterized by feelings of safety and security in relationships, often resulting from consistent and caring responses from caregivers in early childhood.