The following admission data are for the graduate program in the six largest maj
ID: 3202281 • Letter: T
Question
The following admission data are for the graduate program in the six largest majors at the University of California at Berkeley for the fall 1973 quarter. (a) What is the overall probability of being admitted for males? For females? What is the standard deviation for males and for females? (b) Write down the hypothesis test that the overall probability of admission is higher for men than for women. (c) Conduct a t-test of the hypothesis from part (b) and report the p-value. (d) Is the result significant at the 5% level? Does it provide evidence of discrimination? (e) Committee chairpersons claim they are more likely to admit women than men. Is this claim true? Compute acceptance rates for men and women by graduate program. (f) Do these data suggest that the university is guilty of gender discrimination in its admission policy? Explain briefly.Explanation / Answer
a.) Total number of males admitted = 1198
Total number of males rejected = 1493
Total number of males = 1198 + 1493 = 2691
P(being admitted for male) = 1198 / 2691 = 0.4451
Total number of females admitted = 557
Total number of males rejected = 1278
Total number of females = 1835
P(being admitted for male) = 557 / 1835 = 0.3035
SD = n*p*(1-p)
SDmales = 2691*0.4451*(1-0.4451) = 25.78
SDfemales = 1835*0.3035*(1-0.3035) = 19.69
b) Hypothesis
H: pm > pf
H: pm pf
c) p = (p1 * n1 + p2 * n2) / (n1 + n2) = 0.3876
SE = sqrt{ p * ( 1 - p ) * [ (1/n1) + (1/n2) ] } = 0.01475
t = (p1 - p2) / SE = 9.95
d) Yes
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