Answer to Question #234730 in Statistics and Probability for humza

Question

The Association of American Medical Colleges (AAMC) compiles data on medical school faculty and publishes the results in AAMC Faculty Roster. The following contingency table cross-classifies medical school faculty by the characteristics gender and rank Table 4A a. Find P(R3) b. Find P(R3|G1) c. Are events G1 and R3 are independent? Explain your answer d. For a medical school faculty member, is the event that the person is female independent of the event that the person is an associate professor? Explain your answer.

Answer 1

a.

P(R₃)=40379/98993= 0.4079 (to 4 decimal places)

b.

P(R₃|G₁)= P(R₃&G₁)/P(G₁)

=(25888/98993)/(70000/98993)

=25888/70000

=0.3698

c.

Events G₁ and R₃ are not independent. for independence to hold,

P(R₃&G₁) = P(R₃)*P(G₁).

P(R₃&G₁)=25888/98993=0.2615 and

P(R₃)=40379/98993=0.4079, P(G₁)=70000/98993=0.7071

Therefore, 0.2616 is not equal to 0.4079*0.7071=0.2884

hence, G₁ and R₃ are not independent since the condition above is not satisfied.

d.

Event that the person is female (G₂) is not independent of the event that the person is an associate professor(R₂). This is because,

the joint distribution (P(R₂&G₂)) is not equal to the product of their marginal distribution that is, P(R₂)*P(G₂).

to illustrate this,

P(R₂&G₂)= 5400/98993=0.0545, and

P(R₂)*P(G₂)= (21732/98993)*(28993/98993)=0.0643

which are not equal, hence the two events are not independent.