Question

Ideal proportions The students in Mr. Shenk's class measured the arm spans and heights (in inches) of a random sample of 18 students from their large high school. Some computer output from a least-squares regression analysis on these data is shown below. Construct and interpret a 90% confidence interval for the slope of the population regression line. Assume that the conditions for performing inference are met.

Short answer

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

Step-by-step solution

Given Information

Given:

$n=18$

$S{E}_b=0.08091$

Explanation

The degrees of freedom is the sample size decreased by 2 :

$$\begin{gathered} df=n-2 \\ =18-2 \\ =16 \end{gathered}$$

The critical t-value can be found in table B in the row of d f=16 and in the column of c=90% :

$t^{*}=1.746$

The boundaries of the confidence interval then become:

localid="1650689704858" $$\begin{gathered} b-t^{*}\times S{E}_b=0.84042-1.746\times 0.08091 \\ =0.69915114 \end{gathered}$$

localid="1650689713665" $$\begin{gathered} b+t^{*}\times S{E}_b=0.84042+1.746\times 0.08091 \\ =0.98168886 \end{gathered}$$

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