A statistics instructor is interested in examining the relationship between students' level of statistics anxiety and their academic self-efficacy and statistics performance. A class of N = 10 students was asked to respond to a self-efficacy scale and an anxiety scale. Each student's average statistics exam score was also recorded.

The results are as follows:

Efficacy Anxiety Stats Exam

Efficacy Pearson Correlation 1.00 -.617 .888***

Sig. (2-tailed) .000 .057 .001

N 10 10 10

Anxiety Pearson Correlation -.617 1.00 -.661*

Sig. (2-tailed) .057 .000 .038

N 10 10 10

Stats Exam Pearson Correlation .888** -.661* 1.00

Sig. (2-tailed) .001 .038 .000

N 10 10 10

a. Explain what is meant by a correlation coefficient using one of the correlations as an example.

b. Study the table and comment on the patterns of results in terms of which variables are

relatively strongly correlated and which are not very strongly correlated.

c. Comment on the limitations of making conclusions about direction of causality based on these data. In other words, discuss the issue of making cause-effect statements using correlations.