2. (10 points) Test the hypothesis that the population mean log wage is equal for black and nonblack men. First, write down the null and alternative hypotheses. Second, use Stata to do a t-test for the difference between the mean log wage of black men and the mean log wage of nonblack men. [Hint: Use the Stata command ttest varl, by (var2). In this case, var is wage and var2 is black; so what you need to type in Stata's command window is: ttest Iwage, by (black).] Third, tell us what the t-statistic is for the difference between the mean log wages of black and nonblack men, and also indicate the corresponding p-value. Fourth, using a significance level of 5 percent (0.05), what do you conclude and why? . ttest lwage, by (black) Two-sample t test with equal variances Group Obs Mean Std. err. Std. dev.. [95% conf. interval] 0 815 6.816486 .0144368 1 120 6.524434 .0359601 .4121446 .3939236 6.788149 6.844824 6.45323 6.595639 Combined 935 6.779004 .0137729 .4211439 6.751974 6.806033 diff .2920523 .0400754 .2134039 .3707006 diff mean (0) mean (1) t = H0 diff = 0 Degrees of freedom = 7.2876 933 Ha: diff < 0 Pr(T 0 Pr(Tt) = 0.0000 3. (5 points) Test the hypothesis that the population mean years of education (variable educ) is equal for black and nonblack men. Use a significance level of 5 percent (0.05). What do you