Solution to Exercise 1.5.

  Problem Statement: Many universities and colleges have instituted supplemental instruction (SI) programs, in which a student facilitator meets regularly with a small group of students enrolled in the course to promote discussion of course material and enhance subject mastery. Suppose that students in a large statistics course (what else?) are randomly divided into a control group that will not participate in SI and a treatment group that will participate. At the end of the term, each student's total score in the course determined.

a. Are the scores fiom the SI group a sample from existing population? If so, what is it? lf not, what is the relevant conceptual population?

Solution: If they are a sample from an existing population, that would be the population of students who are taking the course in question and who had supplemental instruction. Well, that would be pretty much the same as the sample. I guess this has to be a conceptual population - the students who might take the class and get SI.

b. What do you think is tbe advantage of randomly dividing the students into the two groups rather than letting each student choose which group to join?

Solution: Some students might be more motivated, and choose to spend the extra time in the SI sessions and do better, but then they may have done better anyway because of their motivation. Or maybe some students have a weak background and know it and take the SI, but still don't do as well as the others. Whatever happens, you can't separate out the effect of the SI from a lot of possibilities if you allow students to choose. Random assignment guarantees ``unbiased'' results - good students and bad are just as likely to get the SI or control.

c. Why didn't the investigators put all students in treatment group?

Solution: There wouldn't be any basis for comparison otherwise.