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# Download Introduction to Chance Models (Section 1.1) Introduction A key step

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```A situation where a theory-based approach doesnât 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. Georgeâs 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 âpatientsâ from a process where the probability of death is
equal to 0.15. âSuccessâ 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
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