C7.12 Use the data set in BEAUTY.RAW, which contains a subset of the variables (but more usable observations than in the regressions) reported by Hamermesh and Biddle (1994). (i) Find the separate fractions of men and women that are classified as having above average looks. Are more people rated as having above average or below average looks? (ii) Test the null hypothesis that the population fractions of above-average- looking women and men are the same. Report the one-sided p-value that the fraction is higher for women. (Hint: Estimating a simple linear prob- ability model is easiest.) (iii) Now estimate the model log (wage) B+B,belavg + Babvavgu separately for men and women, and report the results in the usual form. In both cases, interpret the coefficient on belavg. Explain in words what the hypothesis Ho: B = 0 against H: B <0 means, and find the p-values for men and women. FAKING (iv) Is there convincing evidence that women with above average looks earn more than women with average looks? Explain. (v) For both men and women, add the explanatory variables educ, exper, union, goodhlth, black, married, south, bigcity, smllcity, and service. Do the effects of the "looks" variables change in important ways?