Chapter 12, Problem AP4.28CPT

To determine

To find out which of the following represents a $95\%$ confidence interval for the slope of the population least square regression line relating the weight of a bear and its neck girth.

Answer to Problem AP4.28CPT

Option (c) is the correct option.

Explanation of Solution

Park rangers are interested in estimating the weight of the bears that inhabit their state. The output of this data is given in the question. Thus, it is given,

  $\begin{array}{l}c=0.95\\ n=10\end{array}$

The estimate of the slope is given in the row “Neck girth” and the column “Coef” of the output as:

  $b=20.230$

The estimate of the standard error of the slope is given in the row “Neck Girth” and in the column “SE Coef” of the output as:

  $S{E}_b=1.695$

The critical t-value can be found in the student’s T distribution table by degrees of freedom as,

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

Then t-values is as:

  $t^{*}=2.306$

The confidence interval is as:

  $\begin{array}{l}b\pm t^{*}\times S{E}_b\\ =20.230\pm 2.306\times 1.695\\ =20.230\pm 3.91\end{array}$

Thus, the option (c) is the correct option.