Refer to Exercise 3.10. Not all surgery cases, even of the same type, are equally serious. Large research hospitals tend to get the most serious surgery cases, whereas community hospitals tend to get more of the routine cases. Suppose that patients can be classified as being in either "Good" or "Poor" condition and the outcomes of surgery are as shown in the table on the next page.
(a) Calculate the proportions that survive for each hospital and each condition.
(b) From these data, which hospital would you choose if you were in good condition? If you were in bad condition?
(c) Compare your answer with that to Exercise 3.10. Explain this reversal as an example of Simpson's paradox and identify the lurking variable in Exercise 3.10.

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Survival Rates by Condition Good Condition Poor Condition Died SurvivedTotal 15 Died SurvivedTotal 75 Research hospital Community hospital16 Total 685 584 700 600 Research hospital Community hospital7 Total 14251 93 100 31 12691300 82 1518 1600