Chapter 4.1, Problem 4.14E

(a)

To determine

To describe how would the r change if all the men were $6$ inches shorter than the heights given in the table and does the correlation tell us whether women tend to date men taller than themselves.

Explanation of Solution

If all the men were $6$ inches shorter than the heights given in the table then r does not change the correlation coefficient, because the proportions of the heights among the men do not change. Thus the correlation does not tell us whether women tend to date men taller than themselves.

(b)

To determine

To describe how does the correlation change if the heights were measured in centimeters rather than inches.

Explanation of Solution

If the heights were measured in centimeters rather than inches then r would not change, because the proportions of the heights among the men do not change.

(c)

To determine

To describe what would be the correlation between the male and female heights if every women dates a men three inches taller than herself.

Answer to Problem 4.14E

The correlation coefficient would be one

Explanation of Solution

If every women dates a men three inches taller than herself, then the correlation coefficient would be one, because there is an extremely strong positive association in this case.