Consider the following contingency table, which relates the number of applicants accepted to a college and gender.

(a) Construct a conditional distribution of acceptance status by gender.
(b) What proportion of males was accepted? What proportion of females was accepted?
(c) What might you conclude about the admittance policies of the school?
A lurking variable is the type of school applied to. This particular college has two programs of study: business and social work. The following table shows applications
by type of school.

(d) What proportion of males who applied to the business school was accepted? What proportion of females who applied to the business school was accepted?
(e) What proportion of males who applied to the social work school was accepted? What proportion of females who applied to the social work school was accepted?
(f ) Explain carefully how the bias disappears when type of school is considered.

Accepted Denied Male 98 522 Female 90 200 Business School Social Work School Accepted DeniedAccepted Denied Male 90 510 12 Female 10 60 80 140