Chapter 9, Problem 25E

(a)

To determine

To explain do you think the association would be stronger or weaker if humans were removed and the $r=0.54$ , not a very strong relationship.

Answer to Problem 25E

It will be stronger.

Explanation of Solution

In the given question, the scatterplot shows the gestation period in days versus life expectancy in years for eighteen species of mammals. And in the scatterplot the point highlighted at the far right represents humans. Now, it is given that $r=0.54$ that shows it is not a very strong relationship. Thus, we can say that the association is stronger because both the slope and the correlation would increase. Thus, the association between the gestation period and the life expectancy is stronger.

(b)

To determine

To explain is there reasonable justification for removing humans from the data set.

Answer to Problem 25E

Yes, it can be.

Explanation of Solution

In the given question, the scatterplot shows the gestation period in days versus life expectancy in years for eighteen species of mammals. And in the scatterplot the point highlighted at the far right represents humans. There is a reasonable justification to remove the humans from the data set, it is just that the researchers wants to restrict their study to the non-humans only. So that they can study the results appropriately.

(c)

To determine

To comment on the strength of the association.

Explanation of Solution

In the given question, the scatterplot shows the gestation period in days versus life expectancy in years for eighteen species of mammals. And in the scatterplot the point highlighted at the far right represents humans. In this part a second scatterplot is given that shows the gestation period and the life expectancy of seventeen non-humans species and the dependent variable is gestation period. Also, it is given:

  $\begin{array}{l}{R}^2=72.2\%\\ \text{Constant}=-39.5175\\ \text{Life expectancy}=15.4980\end{array}$

The strength of the association is moderately strong as the variations is more as per the residual. And the pattern in the scatterplot shows positive relation and it is going in upward direction.

(d)

To determine

To interpret the slope of the line.

Answer to Problem 25E

For every year increase in life expectancy, the gestation period increases by about $15.5$ days, on average.

Explanation of Solution

In the given question, the scatterplot shows the gestation period in days versus life expectancy in years for eighteen species of mammals. And in the scatterplot the point highlighted at the far right represents humans. The slope of the line interprets that for every year increase in life expectancy, the gestation period increases by about $15.5$ days, on average.

(e)

To determine

To estimate the expected gestation period of one of these monkeys.

Answer to Problem 25E

The expected gestation period of one of these monkeys given is $270.5$ days.

Explanation of Solution

In the given question, the scatterplot shows the gestation period in days versus life expectancy in years for eighteen species of mammals. And in the scatterplot the point highlighted at the far right represents humans. It is given that some species of monkeys have a life expectancy of about $20$ years. Thus, we can estimate that:

  $\begin{array}{l}\text{Gestation period}=-39.5175+15.4980x\\ =-39.5175+15.4980(20)\\ =270.5\end{array}$

Thus, the expected gestation period of one of these monkeys given is $270.5$ days.