Chapter 7, Problem 28E

(a)

To determine

To explain whether or not each of these possible conclusions is justified.

Answer to Problem 28E

Not justified.

Explanation of Solution

The correlation between fuel efficiency and price of $150$ cars at a large dealershipis $r=-0.34$ . From this the conclusion is given as:

The more you pay, the lower the fuel efficiency of your car will be.

This conclusion is not justified because there is not a direct relationship between the fuel efficiency and the price of cars at a large leadership as the correlation, $r\ne -1$ . This means that the correlation cannot say about the price and fuel efficiency relationship as it is less than $-1$ .

(b)

To determine

To explain whether or not each of these possible conclusions is justified.

Answer to Problem 28E

Not justified.

Explanation of Solution

The correlation between fuel efficiency and price of $150$ cars at a large dealershipis $r=-0.34$ . From this the conclusion is given as:

The form of relationship between fuel efficiency and price is moderately straight.

This conclusion is not justified because there is not a direct relationship between the fuel efficiency and the price of cars at a large leadership as the correlation, $r\ne -1$ . And as the correlation r is low values that shows a weekly association between the two and therefore, the relationship between fuel efficiency and the price is not really straight.

(c)

To determine

To explain whether or not each of these possible conclusions is justified.

Answer to Problem 28E

Not justified.

Explanation of Solution

The correlation between fuel efficiency and price of $150$ cars at a large dealershipis $r=-0.34$ . From this the conclusion is given as:

There are several outliers that explains the low correlation.

This conclusion is not justified because we do not know from the correlation coefficient that they will be containing outliers or not. As correlation coefficient does not define the outliers, it there are or there are no outliers.

(d)

To determine

To explain whether or not each of these possible conclusions is justified.

Answer to Problem 28E

Not justified.

Explanation of Solution

The correlation between fuel efficiency and price of $150$ cars at a large dealershipis $r=-0.34$ . From this the conclusion is given as:

If we measure fuel efficiency in kilometres per liter instead of miles per gallon, the correlation will increase.

This conclusion is not justified because the correlation does not depend on the units used to measure the variables. Thus, correlation is not considered in units. So, if we measure fuel efficiency in kilometres per liter instead of miles per gallon, the correlation will not increase.