Chapter 27, Problem 6E

a)

To determine

To check the assumptions and conditions for inference.

Explanation of Solution

Given:

  

  

The conditions are: straight enough, Independence, Randomization, Random residual, Does plot thicken? and Nearly normal condition.

We will check it one by one.

Straight enough condition: Satisfied, because no curvature is present in the scatterplot.

Independence assumption: Satisfied, assuming that the houses are independent.

Randomization condition: Satisfied, as houses were randomly selected.

Random residuals condition: Satisfied, because there is no obvious pattern in the residual plot.

Does the plot thicken? condition: Satisfied, because the vertical spread in the residual plot is not increasing or decreasing.

Nearly normal condition: Satisfied, because the histogram of the residual is roughly symmetric and unimodal.

b)

To determine

To find the 95% confidence interval for slope.

Answer to Problem 6E

The 95% confidence interval for slope is,

  $(89.7636,99.1442)$

Explanation of Solution

Given:

  

  

Formula:

Confidence interval for slope is,

  $(b-t_c\times S{E}_b,b+t_c\times S{E}_b)$

First, need to find critical value $t_c$ .

Critical value for df = 1012 and confidence level = 0.95 is,

  $t_c=1.96$ …Using excel formula, =TINV(0.05,1012)

Therefore, the 95% confidence interval for slope is,

  $\begin{array}{l}(94.4539-1.96\times 2.393,94.4539+1.96\times 2.393)\\ (89.7636,99.1442)\end{array}$