91Ó°ÊÓ

We have to construct and interpret the $95\%$confidence interval for the slope of the true regression line.

We will use the following formula :-

The boundaries of the confidence interval

$$\begin{gathered} b−t^{*}×S{E}_b \\ b+t^{*}×S{E}_b \end{gathered}$$

The slope $b_1$is calculated in the row "Tapping time" and the column "coef" of the following computer output:

$b1=−2.6350$

In the row "tapping time" and the column "SE Coef" of the given computer output, the computed standard deviation of the slope $S{E}_{b_1}$is mentioned:

$S{E}_{b_1}=0.1769$

In the T distribution table, you'll find the crucial.

$df−n−2=40−2=38$

$df=38$,as a result, it would use the nearest smaller degrees of freedom, $df=30$, in the column with $c=95\%$: $ t^{*}=2.042$

The confidence interval's bounds

$$\begin{gathered} b−t^{*}×S{E}_b=−2.6350−2.042×0.1769=−2.9962298 \\ b+t^{*}×S{E}_b=−2.6350+2.042×0.1769=−2.2737702 \end{gathered}$$

There are $95\%$ confident that the slope of the regression line is between $-2.9962298$ and $-2.2737702$.