Chapter PII, Problem 29RE

(a)

To determine

To describe the association.

Explanation of Solution

It is given in the question that the researchers want to know how Olympics performances in various events related to each other are. And the plot is also given which shows winning long-jump and high-jump distances in inches for the summer Olympics. Thus, by looking at the scatterplot we can see that the points in the scatterplot is moving in the upward direction from left to right. So, the association between the variables is positive and they have positive correlation and also they are fairly linear and pretty strong as the points are in a straight line.

(b)

To determine

To explain do long-jump performances somehow influence the high jumpers and also explain how do you account for the relationship you see.

Answer to Problem 29RE

Yes, the long-jump performances somehow influence the high jumpers.

Explanation of Solution

It is given in the question that the researchers want to know how Olympics performances in various events related to each other are. And the plot is also given which shows winning long-jump and high-jump distances in inches for the summer Olympics. Thus, the long-jump performances somehow influence the high jumpers by that there is association probably training methods and variables like strength and technique and that is the kind of relationship we see between them.

(c)

To determine

To explain does that make actual correlation higher or lower.

Answer to Problem 29RE

No, it does not affect the correlation.

Explanation of Solution

It is given in the question that the researchers want to know how Olympics performances in various events related to each other are. And the plot is also given which shows winning long-jump and high-jump distances in inches for the summer Olympics. Thus, the correlation for the given scatterplot is $0.925$ , but at the Olympics these jumps are actually measured in meters rather than inches, so this does not affect the correlation because the correlation does not take into account the units of the variables.

(d)

To determine

To explain what do you predict about the long jump in a year when the high-jumper jumped one standard deviation better than the average high jump.

Answer to Problem 29RE

It is $0.925$ standard deviation above the average long jump.

Explanation of Solution

It is given in the question that the researchers want to know how Olympics performances in various events related to each other are. And the plot is also given which shows winning long-jump and high-jump distances in inches for the summer Olympics. We predict about the long jump in a year when the high-jumper jumped one standard deviation better than the average high jump that it is $0.925$ standard deviation above the average long jump as it is one standard deviation.