analyze data, it is to design a study that you could conduct with existing data or data you collect. Your dependent variable in this case is whether a student goes to public vs. private school. Therefore, your literature review should be about the characteristics that differentiate whether kids go to public or private school.

You do a good job describing the HSB data set and the variables you use.

Rather than analyzing the data, you should describe how you would analyze and validate the study.

You should also talk about threats to internal validity. What other variables or factors aside from the ones you listed might account for differences in whether students go to public or private schools?