For Table 5.2 on admissions decisions for Florida graduate school applicants, let yig = 1 denote a subject in department i of gender g (1 = females, 0 = males) being admitted. The model logit[P(Yig = 1)] = ui + α + βg has βˆ = 0.163 (SE =

0.111). The model of form (10.4) that allows the gender effect to vary randomly by department has βˆ = 0.176 (SE = 0.132), with σˆv = 0.20. Interpret and explain why SE for βˆ is larger for the second model.