Question

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. Here is some regression output for these data:

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

a. $20.230\pm 1.695$

b. $20.230\pm 3.83$

c. $20.230\pm 3.91$

d. $20.230\pm 20.22$

e. $26.7565\pm 3.83$

Short answer

The correct answer is option (c)

Step-by-step solution

Given information

The given data is

Explanation

Park rangers are curious about the weight of the bears that live in their area. The question specifies the output of this data. As a result, it is stated,

$$\begin{gathered} c=0.95 \\ n=10 \end{gathered}$$

The slope estimate is supplied in the output's row "Neck girth" and column "Coef" as follows:

$b=20.230$

The standard error of the slope is calculated as follows in the row "Neck Girth" and column "SE Coef" of the output:

$S{E}_b=1.695$

By degrees of freedom, the critical $t-$value can be identified in the student's T distribution table as,

$$\begin{gathered} df=n-2 \\ =10-2 \\ =8 \end{gathered}$$

Then $t-$values are as follows:

$t^{*}=2.306$

The confidence interval is calculated as follows:

$b\pm t^{*}\times S{E}_b$

$$\begin{gathered} =20.230\pm 2.306\times 1.695 \\ =20.230\pm 3.91 \end{gathered}$$

Option (c) is correct.