We cannot construct such an interval using the normal approximation.
Null Hypothesis: The heart transplant procedure did not alter the survival rates of the observed patients. Alternate Hypothesis, Ha: The claim was that the patients getting a heart transplant were more likely to survive than those who did not.
Normal distribution is the approximation for large distribution from binomial, poisson distribution etc. Moreover, the variables are discrete and few; and instead of the actual observations we are working on counts data. In the given situation it is preferred to use chi square distribution. As chi square test is used we can check whether the two groups are the same or different. Therefore, it is not possible to construct a confidence interval.
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