The Stanford University Heart Transplant Study was conducted

The Stanford University Heart Transplant Study was conducted to determine whether an experimental heart transplant program increased lifespan. Each patient entering the program was officially designated a heart transplant candidate, meaning that he was gravely ill and might benefit from a new heart. Patients were randomly assigned into treatment and control groups. Patients in the treatment group received a transplant, and those in the control group did not. The table below displays how many patients survived and died in each group

___ control______treatment___
alive 4 | 24

dead 30 | 45

A hypothesis test would reject the conclusion that the survival rate is the same in each group,
and so we might like to calculate a confidence interval. Explain why we cannot construct such an
interval using the normal approximation. What might go wrong if we constructed the confidence interval despite this problem?

Solution

Normal distribution is the approximation for large distribution from binomial poisson etc.

Here the variables are discrete and numbers are less.

Chi square will be more appropriate to test this.

As chi square test is used we can check whether the two groups are the same or diferent. Conf interval cannot be created.

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H0: The two groups are having the same average

Ha: the two groups averages are different

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?² Calculations

Two-way Contingency Table

?² = 6.096,     df = 1,     ?²/df = 6.10 ,         P(?² > 6.096) = 0.0135

warning:  some observed or expected frequencies are less than 5; thus the Central Limit Theorem may not apply and the resultant ?² may be invalid

As p value <0.05 reject null hypothesis.

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The confidence interval if constructed is not reliable and any conclusion made based on that may be a gambling or pure chance without statistical base.