Construct a Confidence Interval About the Slope of the Least $90 \%$

question 50

Short Answer

Construct a Confidence Interval about the Slope of the Least -squares Regression Model
-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 $90 \%$ confidence interval about the slope of the true least-squares regression line.
$\begin{array} { c c c c c c } \text { Horse } & \text { Gestation } & \text { Life } & \text { Horse } & \text { Gestation } & \text { Life } \\ & \begin{array} { c } \text { period } \\ x \text { (days) } \end{array} & \begin{array} { c } \text { Length } \\ \text { y (years) } \end{array} & & \text { period } & \text { Length } \\ 1 & 416 & 24 & 5 & \text { x (days) } & \text { y (years) } \\ 2 & 279 & 25.5 & 6 & 403 & 22 \\ 3 & 298 & 20 & 7 & 265 & 21 \\ 4 & 307 & 21.5 & & & \end{array}$

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Definitions:

High Tide

The state of the tide when at its highest level, typically influenced by the gravitational pull of the moon and sun.

Low Tide

The state of the tide when the water level is at its lowest point, exposing areas of the seafloor near coastlines.

Circular Motion

The movement of an object along the circumference of a circle or rotation about an axis, characterized by a constant change in direction and velocity.

Wave Propagate

The process by which wave motion (sound, light, or water waves) travels through a medium from one point to another.