1. You've been given a data set that contains information on educational attainment and criminal behavior. Along with the data set, you are told that crime and education have a (sample) covariance of 3, that the variance of crime is 3, and that the variance of education is 12. With this information, compute the correlation between education and crime.

2. What is selection? Why does self-selection make it difficult to measure the effect of education policies?

3. Explain how randomized controlled trials overcome selection bias.

4. Consider the following scenarios and explain why the correlation described need not imply that one factor causes the other. Be explicit about the other factors that might be at play. a. Students in charter schools have higher test scores than their counterparts in nearby public schools. b. A negative correlation between maternal smoking and their children's birth weight. c. On average, students with relatively large student loans are less likely to default. d. Within a school, students in smaller classes have lower end of year test scores. e. Children in families that spend more time on educational activities do not have better educational outcomes than children in families who spend less time on educational activities.

5. You come across a scientific study reported in the New York Times. The study says that adults who played varsity sports in high school are 20 percentage points more likely to have graduated college with a bachelor's degree than adults who did not. a. Identify the outcome variable in this study b. Identify the treatment variable (or policy variable) in this study c. What is the counterfactual scenario for high school varsity athletes? d. Why is it important to think about the counterfactual scenario? e. Do you think that the correlation reported in this study is a causal effect? Why or why not? f. What is the value of the naive average treatment effect (ATE) of this study, assuming that the correlation is causal? What is its interpretation? g. If someone constructed an experiment to answer this question, what would it look like? Is such an experiment possible? Explain.

6. Below is a table from a scientific study in Tennessee called Project STAR (Schanzenbach, 2006, Table 2). The table contains averages for the treatment and control groups over various characteristics. The final column reports the p-value from a t-test for equality of the two means. The experiment sought to document educational gains from students in small-sized classes. The outcome variable is reported in the final row, while the treatment variable is listed in the penultimate row. The other rows are pretreatment (a.k.a. control) variables.