21.21 

A social scientist wishes to determine whether there is a relationship

between the attractiveness scores (on a 100-point scale) assigned to college students by a panel of peers and their scores on a paper-and-pencil test of anxiety.

The data is quantitative since they are based on attractiveness scores and anxiety scores. 

Suppose a number of students are selected. A social scientist wishes to determine whether there is a relationship between attractiveness scores (on a 100-oint scale) and their scores on a paper-and-pencil test of anxiety. We have 3 groups or 3 observations on each student and the observations are paired and hence not independent. 

Therefore, apply the t-test for the population correlation coefficient in testing whether there is any relation between the paired observations of the attractiveness scores. And their scores on a paper-and-pencil test of anxiety. Assume the relationship between the 2 variables can be described with a straight line and that the sample originates from a normal bivariable population in applying the t-test for a single correlation coefficient. 

t for a correlation coefficient

Observational study, no manipulation of variables. Compare data.