Chapter 14: Q 14.137 (page 586)

Acreage and Value. The data from Exercise 14.37 for lot size (in acres) and assessed value (in thousands of dollars) of a sample of homes in a particular area are on the WeissStats site. Do the data provide sufficient evidence to conclude that, for homes in this particular area, lot size and assessed value are positively linearly correlated?

Short Answer

Expert verified

Thus, the data do not provide sufficient evidence to conclude that, for homes in this particular area, lot size and assessed value are positively linearly correlated at $5 %$ significance level.

Step by step solution

Step 1:Given information

The data from Exercise 14.37 for lot size (in acres) and assessed value (in thousands of dollars) of a sample of homes in a particular area are on the WeissStats site

Step 2:Explaination

Check whether or not it is reasonably apply the correlation $t$ -test procedure by using the data from Exercise 14.37.

- From the residual plot, it is clear that the residuals are falls in the horizontal band.

- From the normal probability plot of residuals, it is clear that the residuals are roughly linear pattern.

Hence, the assumptions 1-3 for the regression inferences are not violated for the variables value and lot size. But from Exercise 14.73, it is clear that the observations are not linear pattern.

Check whether the data provide sufficient evidence to conclude that, for homes in this particular area, lot size and assessed value are positively linearly correlated.

The test hypotheses are as follows:

Null hypothesis:

$H_{0} : ρ = 0$

That is, lot size and assessed value for homes are not positively linearly correlated.

Alternative hypothesis:

$H_{a} : ρ > 0$

That is, lot size and assessed value for homes are positively linearly correlated.

Obtain the correlation and p-value between lot size and value by using MINITAB.

MINITAB procedure:

Step 1: Select Stat >Basic Statistics > Correlation.

Step 2: In Variables, select lot size and value from the box on the left.

Step 3: Click OK.

MINITAB output:

Conclusion:

Use the significance level, $α = 0.05$ .

Here, p-value is greater than the level of significance.

That is, p-value $(= 0.1345) > α (= 0.05)$ .

Therefore, by the rejection rule, it can be concluded that there is no evidence to reject the null hypothesis $(H_{0})$ at $α = 0.05$ .

Thus, the data do not provide sufficient evidence to conclude that, for homes in this particular area, lot size and assessed value are positively linearly correlated at $5 %$ significance level.