1. Do a few simulations and see if you can determine a correspondence between an aspect of the graph and the standard deviation of the difference scores. Specifically, look at the degree to which the lines diverge from being parallel and the standard deviation.
   
   
2. Decrease the correlation to 0.1. What effect does that have on how non-parallel the lines are and the standard deviation.
   
   
3. Increase the correlation to 0.9. What effect does that have on the standard deviation and on how often the test is significant?