Park rangers are interested in estimating the weight of the bears that inhabit their state. The rangers have data

on weight (in pounds) and neck girth (distance around the neck in inches) for 10 randomly selected bears. Some

regression output for these data is shown below.

Which of the following represents a 95% confidence interval for the true slope of the least-squares regression line relating the weight of a bear and its neck girth?

$$\begin{gathered} \left(a\right)241.710\pm 38.57 \\ \left(b\right)241.70\pm 88.94 \\ \left(c\right)20.230\pm 1.695 \\ \left(d\right)20.230\pm 3.83 \\ \left(e\right)20.230\pm 3.91 \end{gathered}$$

We are given that Park rangers are interested in estimating the weight of the bears that inhabit their state. The rangers have data on weight (in pounds) and neck girth (distance around the neck in inches) for 10 randomly selected bears and graph is given above and we need to find the true slope of the least-squares regression line relating the weight of a bear and its neck girth of $95\%$confidence level.

We are given that confidence level $c=95\%=0.95andn=10$

Estimation of the slope is given in the row "Neck girth"and column "Coef"of the given computer output is

$b=20.230$

Estimation of the standard error of the slope is given in the row "Neck girth"and the column "SE Coef"of the given Computer output is

$S{E}_b=1.695$

The critical t value can be found in the student's T distribution table in the appendix in the row of localid="1651647744705" $df=n-2\Rightarrow df=8$and column $\frac{1-c}{2}=0.025$

$t^{*}=2.306$

The boundaries of confidence interval then become:

$$\begin{gathered} {\beta }^1\pm t^{*}\times S{E}_b \\ 20.239\pm 1.695\times 2.306 \\ 20.239\pm 3.91 \end{gathered}$$

So option (c) is correct.