In 1973 a lawsuit was filed against the University of California at Berkeley, alleging sex discrimination in its graduate admissions policies. The following table pertains to two of the graduate programs at the university. For each program, it lists the number of men accepted, the number of men denied, the number of women accepted, and the number of women denied:

a. Start with the combined data. Determine the proportion of men applicants who were accepted and compare this to the proportion of women applicants who were accepted. Which proportion is larger?
b. Now consider only Program A. Did men or women have a higher proportion of applicants who were accepted? Provide calculations to justify your answer.

c. Repeat (b) for Program F.
d. Is this an example of Simpson€™s paradox (see the previous exercise)? Explain.
e. Explain how this paradox happens, based on the data, as if to someone who doesn€™t know much about statistics.

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Women Women Men Men accepted denied accepted denied 314 Program A Program F Combined 511 89 19 351 24 317 22 665 533 336 113