2. A researcher studied the relation between psychotherapists’ degree of empathy and their patients’ satisfaction with therapy. As a pilot study, four patient–therapist pairs were studied. Here are the results:

Pair Number Therapist Empathy Patient Satisfaction 1 70 4 2 94 5 3 36 2 4 48 1

(a) Make a scatter diagram of the scores;

(b) describe in words the general pattern of correlation, if any;

(c) figure the correlation coefficient;

(d) figure whether the correlation is statistically significant (use the .05 significance level, two-tailed);

(e) explain the logic of what you have done, writing as if you are speaking to someone who has never heard of correlation (but who does understand the mean, standard deviation, Z scores, and hypothesis testing); and

(f) give three logically possible directions of causality, saying for each whether it is a reasonable direction in light of the variables involved (and why).