Question

independent? in 2015, the report on the UC berkley faculty salary equity study shows that 87 of the university's 222 assistant professors were women, along with 137 of the 324 associate professors and 243 of the 972 full professor

a. what is the probability that a randomly chosen berkeley professor (of any rank) is a woman?

b. What is the conditional probability that a randomly chosen professor is a woman, given that the person chosen is a full professor?

c. are the rand and sex of berkely professors independent\? how do you know?

Answer 1

Ans: Assistant Associate professors professors full professors Total Women 87 137 243 467 Men 135 187 729 1051 Total 222 324 972 1518 467 1518 a) probabiliday that a randomly chosen berkeley professor is a woman - = 10.3076 we know, B(A/B) - P(ADB) PB) ol I full purofessor) - plumenn full professo) P p(full professor) 243 / 1518 025 972 / 1518 c) Ho Rand and Sex of berikely professors are not Independent Ha: Rand and sex of beskeling professors are Andependent.

l Expected value Assistant professors Row totaly colorm total Grand Total Associate professors Dhofessors 99.68 299.03 267 224.32 672.97 105 full Total Women 68.30 Men 153.70 2 x² = (263–29903 E ((0.6)..) - (87-18.3) + t 299.03 68.3 5.12+ 13.98€ 10.5 +2.28+6.21+4.66=142.767 P-value (0.0000 refect Ho, yes, we can say Smee pcd, we defect Ho, Vand and sex of berkely professors so dependent