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# 1. Using data from 2013 on 64 black females, the estimated log-linear regression

Sep 1, 2021 | mathematics / statistics

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(WAGE d ) = 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(b2)). Then, with the calculated standard error, you should be able to find the t statistic.]

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(b) Construct a 95% interval estimate for the return to an additional year of education and state its interpretation.