We have data on 609 students who entered Vanderbilt University as freshmen between 1983 and 1986 and took an intermediate microeconomics course. Only students who had previously taken a calculus course and two semesters of introductory economics were included in the dataset. These data were used for the study [J.S. Butler, T.A. Finegan, and J.J. Siegfried (1998). Does More Calculus Improve Student Learning in Intermediate Micro and Macro Economic Theory. Journal of Applied Econometrics, 13, 185-202]. The data were obtained from the Journal of Applied Econometrics Data Archive. The dataset contains 609 rows, one for each student, and the following four columns:
Variable Name Description
Math The student's Math SAT score
Verbal The student's Verbal SAT score
GPA The student's GPA as a freshman
Gender F = female, M = male
For the questions below, do I use 1 sample t-test, 2 sample t-test, or the paired t-test?
1. Do microeconomics students at Vanderbilt score significantly higher on the Verbal SAT than the national average (which in the mid-1980s was around 425)?
2. Do microeconomics students at Vanderbilt score significantly higher on the Math SAT than the national average (which in the mid-1980s was around 470)?
3. Report a 95 percent confidence interval for the true mean Verbal SAT score. Do 95 percent of students have Verbal SAT scores that fall within this interval? Explain your answer.
4. Is there a statistically significant difference between the Verbal and Math scores of microeconomics students at Vanderbilt?
5. Is there a statistically significant difference between the freshman GPAs of males and females? Construct a 95 percent confidence interval for the difference. Does it include zero? Relate this to the conclusion of your test.
6. Is there a statistically significant difference between the performances of males and females on the Math SAT? Construct a 95 percent confidence interval for the difference. Does it include zero? Relate this to the conclusion of your test.
7. Is there a statistically significant difference between the performances of males and females on the Verbal SAT? Construct a 95 percent confidence interval for the difference. Does it include zero? Relate this to the conclusion of your test.