Chapter 12.1, Problem 14E

To determine

To construct: and interpret the 90% confidence interval for the slope of the population regression line.

Answer to Problem 14E

There are 90% confident that the slope of the regression line is between 0.69915114 and 0.98168886.

Explanation of Solution

Given:

  

  $\begin{array}{l}n=18\\ b=0.84042\\ S{E}_b=0.08091\end{array}$

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 is

  $df-n-2=18-2=16$

The critical t-value could be found in the table B, $df=16$ and in the column of $c=90\%$ :

  $t^{\ast }=1.746$

The boundaries of the confidence interval are

  $\begin{array}{l}b-t^{\ast }\times S{E}_b=0.84042-1.746\times 0.08091=0.69915114\\ b+t^{\ast }\times S{E}_b=0.84042+1.746\times 0.08091=0.98168886\end{array}$

There are 90% confident that the slope of the regression line is between 0.69915114 and 0.98168886.