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A situation where a theory-based approach doesnât work Example 1.3: Heart Transplant Operations In an article published in the British Medical Journal (2004), researchers Poloniecki, Sismanidis, Bland, and Jones reported that heart transplantations at St. Georgeâs Hospital in London had been suspended in September 2000, after a sudden spike in mortality rate. Of the last 10 heart transplants, 80% had resulted in deaths within 30 days of the transplant. Newspapers reported that this mortality rate was over five times the national average. Based on historical national data, the researchers used 15% as a reasonable value for comparison. Think about it: Why do you think the Theory-based (One proportion z-test; Normal approximation) approach will not work well for this data? Applying the 3S Strategy Using the 3S Strategy from the previous section, we observed 0.80 as our statistic and now we will simulate one thousand repetitions from a process where ð = 0.15 (under the null hypothesis). We did this using the One Proportion applet as shown in Figure 1.2. Figure 1.2: Null distribution (could-have-been simulated sample proportions) for 1000 repetitions of drawing samples of 10 âpatientsâ from a process where the probability of death is equal to 0.15. âSuccessâ has been defined to be patient death. 9. How well does the CLT predict the center, SD, and shape of the null distribution of sample proportion of deaths among a sample of 10 heart transplant cases, as displayed in Figure 1.2? a. Center: Does it make sense? b. SD: c. Shape: June 27, 2014 MAA PREP workshop 38