Question

A student wonders if tall women tend to date taller men than do short women. She measures herself, her dormitory roommate, and the women in the adjoining rooms; then she measures the next man each woman dates. The data (heights in inches) are listed below. Women (x) 67 65 69 63 68 67 Men (y) 71 67 69 67 68 66

(a) Make a scatterplot of these data. (Do this on paper. Your instructor may ask you to turn this in.) Based on the scatterplot, do you expect the correlation to be positive or negative? Near ± 1 or not?

The correlation should be positive. It should be near 1.

The correlation should be negative. It should be near -1.

The correlation should be positive. It should not be near 1.

The correlation should be negative. It should not be near -1.

(b) Find the correlation r between the heights of the men and women. (Round your answer to three decimal places.)

(c) How would r change if all the men were 6 inches shorter than the heights given in the table? Does the correlation tell us whether women tend to date men taller than themselves?

r will not change. This correlation does imply that women tend to date men taller than themselves

. r will increase. This correlation does not imply that women tend to date men taller than themselves.

r will not change. This correlation does not imply that women tend to date men taller than themselves.

r will decrease. This correlation does imply that women tend to date men taller than themselves.

(d) If heights were measured in centimeters rather than inches, how would the correlation change? (There are 2.54 centimeters in an inch.)

r will decrease by 2.54. r will be divided by 2.54.

r will increase by 2.54.

r will not change.

r will be multiplied by 2.54.

(e) If every woman dated a man exactly 3 inches taller than herself, what would be the correlation between male and female heights?

r will be equal to -1.

r will be equal to 1.

r will be the same as the value in (b).

r will be equal to 0.

Answer 1

Solution :  

a) Scatter Plot

Answer:  The correlation should be positive. It should not be near 1.

b) Correlation Coefficient :

Answer: The correlation coefficient is r = 0.413

c)

Answer:  r will not change. This correlation does imply that women tend to date men taller than themselves

d)

Answer: r will not change.

Because correlation coefficient is change of origin and scale

e)

Answer: r will be equal to 1.