Chapter 12.1, Problem 13E

To determine

To construct: and interpret a 99% confidence interval for the slope of the population regression line.

Answer to Problem 13E

There are 99% confident that the slope of the true regression line is true between 8.677984 and 15.110016.

Explanation of Solution

Given:

This is the output of the computer for a regression analysis of the data

  

  $\begin{array}{l}n=23\\ b=11.894\\ S{E}_b=1.136\end{array}$

Formula used:

The boundaries of the confidence interval

  $\begin{array}{l}b-t^{\ast }\times S{E}_b\\ b+t^{\ast }\times S{E}_b\end{array}$

Calculation:

The degrees of freedom

  $df-n-2=23-2=21$

The critical t-value could be found in the table B , $df=21$ and in the column of $c=99\%$ :

  $t^{\ast }=2.831$

The boundaries of the confidence interval are

  $\begin{array}{l}b-t^{\ast }\times S{E}_b=11.894-2.831\times 1.136=8.677984\\ b+t^{\ast }\times S{E}_b=11.894+2.831\times 1.136=15.110016\end{array}$

There are 99% confident that the slope of the true regression line is true between 8.677984 and 15.110016.