Chapter 12.1, Problem 2.2CYU

To determine

To explain would a $99\%$ confidence interval for the slope $\beta$ of the population regression line include zero.

Answer to Problem 2.2CYU

  $99\%$ confidence interval for the slope $\beta$ of the population regression line will include zero in it.

Explanation of Solution

It is given in output that:

  $\begin{array}{l}n=8\\ b=0.09080\\ {\text{SE}}_b=0.02831\end{array}$

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

  $\begin{array}{l}df=n-2\\ =8-2\\ =6\end{array}$

Thus, if we will carry out the $99\%$ confidence interval for the slope $\beta$ of the population regression line, then as it is more than the $95\%$ confidence interval for the slope of the population regression line then the confidence interval for the $99\%$ will be large than the $95\%$ confidence interval. So, it will have the possibility that it will contain zero in the confidence interval also the sample size is very small. Thus, $99\%$ confidence interval for the slope $\beta$ of the population regression line will include zero in it.