3. An instructor asked five students how many hours they had studied for an exam.

Here are the hours studied and the students’ grades:

Hours Studied Test Grade 0 52 10 95 6 83 8 71 6 64

(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).