In given Exercise, data were given for admissions to two graduate programs for men and women. The data are given again here for use in this exercise, with the combined data presented as well.
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Program A
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Program B
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Combined
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Admit
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Deny
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Admit
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Deny
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Admit
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Deny
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Men
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400
|
250
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50
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300
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450
|
550
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|
Women
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50
|
25
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125
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300
|
175
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325
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a. Give the odds of being admitted versus being denied to program A separately for the men and women who applied to that program. Then give the odds ratio for women compared to men. Write a sentence explaining the odds ratio in words.
b. Give the odds of being admitted versus being denied for the combined programs separately for men and women. Then give the odds ratio for women compared to men. Write a sentence explaining the odds ratio in words.
c. Using the results from parts (a) and (b), write one sentence that sounds as if the university favors female applicants and another sentence that sounds as if the university favors male applicants.
Exercise
Suppose two hospitals are willing to participate in an experiment to test a new treatment, and both hospitals agree to include 1100 patients in the study. Because the researchers who are conducting the experiment are on the staff of hospital A, they decide to perform the majority of cases with the new procedure. They randomly assign 1000 patients to the new treatment, with the remaining 100 receiving the standard treatment. Hospital B, which is a bit reluctant to try something new on too many patients, agrees to randomly assign 100 patients to the new treatment, leaving 1000 to receive the standard treatment. The following table displays the results:
a. Which treatment was more successful in hospital A? Justify your answer with relevant percents.
b. Which treatment was more successful in hospital B? Justify your answer with relevant percents.
c. Combine the data from the two hospitals into a single contingency table that shows the relationship between treatment and outcome. Which treatment has the higher survival rate in this combined table? Justify your answer.
d. Explain how this exercise is an example of Simpson's paradox.