1. SAT prep courses. Can special study courses actually help raise SAT scores? One organization says that the 30 students they tutored achieved an average gain of 60 points when they retook the test.

a) Explain why this does not necessarily prove that the special course caused the scores to go up.

b) Propose a design for an experiment that could test the effectiveness of the tutorial course.

c) Suppose you suspect that the tutorial course might be more helpful for students whose initial scores were particu- larly low. How would this affect your proposed design?

2. Safety switch. An industrial machine requires an emer- gency shutoff switch that must be designed so that it can be easily operated with either hand. Design an experiment to find out whether workers will be able to deactivate the ma- chine as quickly with their left hands as with their right hands. Be sure to explain the role of randomization in your design.