(Solved): 1. Using data from 2013 on 64 black females, the estimated log-linear regression between WAGE (earn ...

1. Using data from 2013 on 64 black females, the estimated log-linear regression between WAGE (earnings per hour, in \$) and years of education, EDUC is $\ln (\widehat{WAGE})=1.58+0.09EDUC$. The reported t-statistic for the slope coefficient is 3.95 . (a) Test at the $5\%$ level of significance, the null hypothesis that the return to an additional year of education is equal to $8\%$ against the alternative that the rate of return to education is more than $8\%$. In your answer, show (i) the formal null and alternative hypotheses, (ii) the test statistic and its distribution under the null hypothesis, (iii) the critical value from the $t$ table and the rejection region (in a figure), (iv) the calculated value of the test statistic, and (v) state your conclusion, with its economic interpretation. [Hint: From the information you should be able to figure out the standard error of the slope coefficient (se $\left(b_2\right)$ ). Then, with the calculated standard error, you should be able to find the $t$ statistic.] (b) Construct a $95\%$ interval estimate for the return to an additional year of education and state its interpretation. Hint: To answer the questions here you will need the standard error for the slope coefficient. At first glance, that information is not given. But we can retrieve that information from the conditions given in the question. The reported $t$-statistic for the slope coefficient is provided. Remember that the reported t-stats are used to test the coefficients are zeros. So you can recover the standard error there. And then you use the standard error for your own t-test and such.