Chapter 12, Problem T12.7SPT

To determine

To find out which of the following is the $95\%$ confidence interval for the slope ${\beta }_1$ of the population regression line.

Answer to Problem T12.7SPT

Option (e) is the correct option.

Explanation of Solution

It is given that the good putting is more important than long driving for shooting low scores and hence winning money. To see if this is the case, then the random sample of players are selected for examining. They have assumed that the inference conditions about the slope are met and the data is calculated by the computer output is given in the question. Suppose the researcher test the hypothesis. The P-value of the test statistic is $0.0087$ . Thus, it is given that

  $\begin{array}{l}n=69\\ c=95\%\end{array}$

The estimate of the slope $b_1$ is given in the row “Avg. putts” and in the row “Coef” of the given computer output:

  $b_1=-4139198$

The estimated standard deviation of the slope $S{E}_{b_1}$ is given in the row “Tapping time” and in the column “Se coef” of the given output:

  $S{E}_{b_1}=1698371$

The critical t-value can be found in the Student’s T distribution table in the appendix in the row, then the degrees of freedom is:

  $\begin{array}{l}df=n-2\\ =69-2\\ =67\end{array}$

Thus, $t^{*}=2$ .

The boundaries of the confidence interval then become:

  $\begin{array}{l}{b}_1\pm t^{*}\times S{E}_{b_1}\\ =-4139198\pm 2\times 1698371\end{array}$

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