STAT 211 HW6: Sex discrimination? You may work with in a group of as many as three students on this assignment, handing in one report with all names, provided that you all contribute to the work. You must submit a word- processed report, with computer output integrated into your report as appropriate. In 1973 a lawsuit was filed against the University of California at Berkeley, alleging sex discrimination in its graduate admissions policies. The following 2x2 table classifies applicants to two of the largest graduate programs at the university in that year: Men Women Accepted | 533 113 Denied 665 336 a) Identify the explanatory and response variables in this study/table. b) Determine the proportion of men who were accepted and the proportion of women who were accepted. (In other words, calculate the acceptance rates for each gender.) c) Produce (with Excel's 100% stacked column chart) a segmented bar graph to compare the acceptance rates of men and women. d) Does it appear that there is an association between gender and admission decision? Explain. The following table classifies the same applicants according to an additional variable: which program they applied to: Men accepted Men denied | Women accepted Women denied Program A 511 314 89 19 Program F 22 351 24 317 e) For each program, determine the proportion of male applicants who were accepted and also the proportion of female applicants who were accepted. f) Comment on how the acceptance rate for men compares to the acceptance rate for women in these two programs. g) Is the overall acceptance rate for women equal to the average of the acceptance rates for women in the the two programs? Explain why or why not. h) Identify two ways, related to the issue of possible gender discrimination in graduate admissions, in which Program A differs from Program F. 1) Your calculations should reveal a bit of a "paradox" in that men have a much higher acceptance rate than women overall, yet women have a higher acceptance rate than men in both programs.Write a paragraph that uses the data provided to explain Why the apparent \"paradox\" occurs, as if to a judge or jun; struggling to understand what these data reveal. j} Explain how the idea of a confounding 1liariahle applies to these data and the apparent \"paradox.\