The Stanford University Heart Transplant Study was conducted to determine whether an experimental heart transplant program increased lifespan Each patient entering the program was designated an official heart transplant candidate meaning that they were gravely ill and would most likely benefit from a new heart Some patients got a transplant and some did not The variable transplant indicates which group the patients were in patients in the treatment group got a transplant and those in the control group did not Of the 34 patients in the control group 30 died Of the 69 people in the treatment group 45 died Another variable called survived was used to indicate whether the patient was alive at the end of the study Turnbull Brown and Hu 1974 a What is the difference between the proportion of patients who died in the treatment and control groups treatment control 0 231 o b One approach for investigating whether the treatment is effective is to use a randomization technique Fill in the blanks with a number or phrase whichever is appropriate We write alive on 28 cards representing all the patients in the sample who were alive at the end of the study and deceased on 75 ocards representing patients who were not Then we shuffle these cards and split them into two groups one group of size 69 of representing treatment and another group of size 34 o representing control We calculate the difference between the proportion of cards in the treatment and control groups treatment control and record this value We repeat this 100 times to build a distribution centered at 0 o Lastly we calculate the fraction of simulations where the simulated differences in proportions are lower than the difference of observed in our sample If this fraction is low we conclude that it is unlikely to have observed such an outcome by chance and that the null hypothesis should be rejected in favor of the alternative