Chapter 27, Problem 20E

a)

To determine

To find the 90% confidence interval for the slope of the regression line.

Answer to Problem 20E

  $(0.5811,0.7690)$

Explanation of Solution

Given:

  

Formula:

Confidence interval for slope is,

  $(Coefficient(b)\mp t_c\times S{E}_b)$

The confidence level = 0.90

So, level of significance = $\alpha$ = 0.10

First need to find critical t value.

tc = 1.654 …Using excel formula, =TINV(0.1,160)

Using formula, 90% confidence interval for the slope of the regression line.

  $\begin{array}{l}(0.675075-1.654\times 0.0568,0.675075+1.654\times 0.0568)\\ (0.5811,0.7690)\end{array}$

b)

To determine

To explain the 90% confidence interval for the slope of the regression line.

Answer to Problem 20E

We are 90% confident that the slope of the population regression line is between 0.5811 and 0.7690.

Explanation of Solution

Given:

  

90% confidence interval for the slope of the regression line:

  $(0.5811,0.7690)$

We are 90% confident that the slope of the population regression line is between 0.5811 and 0.7690