Econ 1150
Applied Econometrics
Mini-Exam 2
1. A standardized test is given to two different school districts. In High School 1, 100 (n1) students are randomly selected to take the test and the sample mean of test scores is 75 (Y¯
1
act) and the sample variance is 196 (s
2
1
). In High School 2, 90 (n2) students are randomly selected to take the test and the sample mean of test scores is 72 (Y¯
2
act) and the sample variance is 100 (s
2
2
).
(a) For High School 1, we want to test the hypothesis that the population mean of test scores is equal to 72. State the null and alternative hypotheses and calculate the p-value for this test. Can you reject the null hypothesis at the 5% significance level? What about at the 1% significance level?
(b) We want to conduct a hypothesis test to see if the mean test scores differ between High School 1 and High School 2. Construct the 90% confidence interval for the observed difference in sample means Y¯
1
act − Y¯
2
act. Using the confidence interval, can you reject the null hypothesis that mean test scores do not differ between High School 1 and High School 2 at the 10% significance level?
2. You’re trying to estimate the effect of work experience (tenurei), measured in number of years, on hourly wages (wagei) and you’ve estimated the following regression equation (standard errors in parentheses):
(a) Calculate the value of the observed t-statistic (t
act) for the null hypothesis that the coefficient on tenurei
is equal to zero. Can you reject the null hypothesis at the 5% significance level?
(b) Interpret the constant term and the coefficient.
7.124 is the expected wage rate of someone with 0 years of experience. One more year of experience increases the wage rate by $0.162.
3. You run a regression of hourly wages (wagei) on college-status (collgradi) in Stata. collgradi
is a random variable that is equal to 0 if individual i is not a college graduate and equal to 1 if individual i is a college graduate. This is the regression output:
(a) From the table above, can you reject the null hypothesis that the coefficient on collgradi
is equal to zero at the 1% significance level? Which part of the table tells you this?
(b) Interpret the coefficient on collgradi and the constant term.
(c) What is the predicted hourly wage for a college graduate?