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 each woman dates. Here are the data (heights in inches).
Women 66 64 66 65 70 65
Men 72 68 70 68 74 69
Which of the following statements is true?
A. The variables measured are all categorical.
B. There is a strong positive correlation between the heights of men and women since the women are always smaller than the men they date.
C. There is a positive correlation between the heights of men and women.
D. Correlation makes no sense here since gender is a categorical variable.

n=6  

So then the correlation coefficient would be r =0.913

And as we can see the value for r is very high and near to 1. so the correct option for this case would be:

C. There is a positive correlation between the heights of men and women.

Step-by-step explanation:

Previous concepts

The correlation coefficient is a "statistical measure that calculates the strength of the relationship between the relative movements of two variables". It's denoted by r and its always between -1 and 1.

And in order to calculate the correlation coefficient we can use this formula:  

We have the following data:

Women (X): 66 64 66 65 70 65

Men(Y): 72 68 70 68 74 69

We have quantitative data so no makes sense say that we have categorical data.

For our case we have this:

n=6  

So then the correlation coefficient would be r =0.913

And as we can see the value for r is very high and near to 1. so the correct option for this case would be:

C. There is a positive correlation between the heights of men and women.

d. 8

step-by-step explanation:

the given radical expression is:

we can rewrite this as:

we express as square numbers to get;

the exponents will now cancel out to give.

the correct answer is d