Imagine that students in an introductory statistics course complete 20 assignments during two semesters. Each assignment is worth 1% of a student’s final grade, and students get credit for assignments...

Imagine that students in an introductory statistics course complete 20 assignments during two semesters. Each assignment is worth 1% of a student’s final grade, and students get credit for assignments that are turned in on time and that show reasonable effort. The instructor of the course is interested in whether doing the homework contributes to learning, and (anticipating material to be taken up in Chapters 5 and 6), she observes a linear, moderately strong, and highly statistically significant relationship between the students’ grades on the final exam in the course and the number of homework assignments that they completed. For concreteness, imagine that for each additional assignment completed, the students’ grades on average were 1.5 higher (so that, e.g., students completing all of the assignments on average scored 30 points higher on the exam than those who completed none of the assignments).

(a) Can this result be taken as evidence that completing homework assignments causes higher grades on the final exam? Why or why not?

(b) Is it possible to design an experimental study that could provide more convincing evidence that completing homework assignments causes higher exam grades? If not, why not? If so, how might such an experiment be designed?

(c) Is it possible to marshal stronger observational evidence that completing homework assignments causes higher exam grades? If not, why not? If so, how?