Problem 5 [23 Pts]

How hard was it in 1973 for women to get into Berkeley? In that year, their graduate school admitted 1950

out of 6300 men applicants, and 1490 out of 5510 women applicants (Bickel and O'Connell, 1975).

(a)

(2 pts) Make a two-way table representing this information.

(b)

(2 pts) What is the probability of being male and admitted?

(c)

(2 pts) What is the probability of being a female and admitted?

(d)

(2 pts) Are gender and admission into Berkeley independent?

(e)

(2 pts) Are gender and admission into Berkeley mutually exclusive?

(f)

(2 pts) Is there evidence of gender discrimination?

To further investigate this phenomenon, we break down the admission results based on department. We

will assume that there are only two departments: Arts (Department of Arts) and Science (Department of

Science). There were 120 men out of 480 admitted to the Arts department and there were 1830 men out

of 5820 admitted to the Science department. There were 1040 women out of 4110 admitted into the Arts

department and there were 450 women out of 1400 admitted into the Science department.

(g)

(2 pts) Summarize this information in a table.

(h)

(4 pts) What is the difference in the probability of admission rates between men and women for Arts?

and for Science?

(i)

(5 pts) Explain why your answers to parts (b) and (c) are different from those in part (h)?