Question

A student wonders if people of similar heights tend to date each other. She measures herself, her dormitory roommate, and the women in the adjoining rooms, then she measures the next man whom each woman dates. Here are the data (heights in inches): Women: 64 65 65 66 66 70 Men: 68 68 69 70 72 74 Determine whether each of the following statements is true (T) orfalse (F). (a) If we had measured the heights of the men and women in centimeters (1 inch= 2.54 cm), the correlation coefficient would have been 2.54 times larger. (b) There is a strong negative association between the heights of men and women because women are always smaller than the men they date. (c) There is a positive association between the heights of men and women.

Answer 1

(a) False

(b) False

(c) True

Explanation:

(a) If we had measured the heights of the men and women in centimeters (1 inch= 2.54 cm), the correlation coefficient would have been 2.54 times larger.

No, since changing the units of measurement does not change the correlation coefficient

(b) There is a strong negative association between the heights of men and women because women are always smaller than the men they date.

Negative association means that as one variable increases, the other decreases, Here, we see that as the heights of the men increase, the height of the women do not reliably decrease, hence there is no strong negative asscoiation

(c) There is a positive association between the heights of men and women.

We see from the values given that as the heights of men increase, so do the heights of women and vise versa, so there is a positive association between the heights of men and women