1. Suppose you are interested in finding the relationship between a worker's age and earnings. After obtaining data on worker ages and average hourly earnings (AHE), you also control for gender (Female = 1 if female; 0 otherwise) and whether each worker has a bachelor's degree (Bachelor = 1 if worker has Bachelor's; 0 otherwise). You want to estimate the following model (notated Regression (1)): AHE, = 0 + 1 Agei+ 2Agei^2 + 3Femalei + 4 Bachelor i+ 5Female i Bachelor i + ui (1) (a) (3 points) You hypothesize that as workers grow older and more experienced, their earnings rise, but as they get closer to retirement, they are less willing to move to a higher- paying job or may opt to work less hours as they become less productive or choose more leisure time. Discuss the anticipated coefficient signs for both , and 2. (b) (3 points) Suppose you want to test whether a bachelor's degree has a significant impact on earnings (AHE). State and describe the null hypothesis. (c) (3 points) Assuming a large data sample, what is the critical value for the previous hypothesis test on whether a bachelor's degree has a significant impact on earnings (AHE)? Assume a 5% significance level. Describe how you derive this critical value. (d) (3 points) You want to check if age has a differential effect on earnings for men and women. How will you change the model (in Regression 1 above) to test for this condition