Chapter 12, Problem 3CRE

To determine

To construct: and explain a 95 percent confidence interval for the slope of the regression line for the population and describe how this interval is R12.2 compatible.

Answer to Problem 3CRE

(78.31496, 471.24504)

Explanation of Solution

Given:

  

  $\begin{array}{l}n=12\\ b=274.78\\ S{E}_b=88.18\end{array}$

Formula used:

For the boundaries are

  $\begin{array}{l}b-t^{\ast }\times S{E}_b\\ b+t^{\ast }\times S{E}_b\end{array}$

Calculation:

The degrees of freedom

  $df=n-2=12-2=10$

The critical t-value using the table with help of the row of $df=10$ and the column of $c=95\%$

  $t^{\ast }=2.228$

The boundaries are

  $\begin{array}{l}b-t^{\ast }\times S{E}_b=274.78-2.228\times 88.18=78.31496\\ b+t^{\ast }\times S{E}_b=274.78+2.228\times 88.18=471.24504\end{array}$

It is 95 % sure that between 78.31496 and 471.24504 the actual slope of the population regression line.