Chapter 27, Problem 40E

a)

To determine

To state the variables and hypotheses about the slope.

Answer to Problem 40E

  $\begin{array}{l}{H}_0:{\beta }_1=0\\ H_a:{\beta }_1\ne 0\end{array}$

Explanation of Solution

Given:

  

  

From the output, we want to know if there is an association between Retail price and MPG.

The variables are Retail price and MPG.

The null and alternative hypotheses:

  $\begin{array}{l}{H}_0:{\beta }_1=0\\ H_a:{\beta }_1\ne 0\end{array}$

That means,

  $H_0:$ There is no association between Retail price and MPG.

  $H_a:$ There is an association between Retail price and MPG.

b)

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, because the 84 cars are less than 10% of the population of all cars.

Randomization condition: Satisfied, assuming that the cars 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, assuming that the residuals are roughly Normally distributed.

c)

To determine

To perform the hypothesis test.

Answer to Problem 40E

Standard error of slope is 0 so test not possible for this analysis.

Explanation of Solution

Given:

  

  

Formula:

Test statistic:

  $t=\frac{b-{\beta }_0}{S{E}_b}$

Standard error of slope is 0 so test not possible for this analysis.