The Stanford University Heart Transplant Study (1974) 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 he was gravely ill and would most likely benefit from a new heart. Some patients got a transplant and some did not. Of the 34 patients in the control group, 4 were alive at the end of the study. Of the 69 patients in the treatment group, 24 were alive. The contingency table below summarizes these results. Treatment Control Total Alive 24 4 28 Dead 45 30 75 Total 69 34 103 45 a) What proportion of patients in the treatment group died? 69 30 b) What proportion of patients in the control group died? 34 c) What are the claims being tested? Ho: The experimental heart transplant program does not increase HA: The experimental heart transplant program increases lifespan. lifespan. d) One approach for investigating whether or not the treatment is effective is to use a randomization technique. The steps below describes the set up for such approach, if we were to do it without using statistical software. Fill in the blanks with a number or phrase, whichever is appropriate. • First, we write alive on 28 V cards representing patients who were alive at the end of the study, and dead on 75 V cards representing patients who were not. • Second, we shuffle these cards and split them into two groups: one group of size representing treatment, and another group of size representing control. • Third, we calculate the difference between the proportion of dead cards in the treatment and control groups (Treatment - Control) and record this value. We repeat many times to build a distribution centered at the null value = • Fourth, we calculate the fraction of simulations where the simulated differences in proportions are less than the point estimate = the difference in proportions from the original sample (the difference in proportions from parts (a) and (b)). 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. e) What is the estimated p-value, based on the 99 simulation results below? (Locate the point estimate and find the proportion of simulations equal to the point estimate or away from the null value.) f) What do the simulation results suggest about the effectiveness of the transplant program? O The p-value is large, so differences between treatment and control were likely just random chance. There is no evidence that the experimental heart transplant program increased the average patient's lifespan. O The p-value is small, so the differences between treatment and control were not likely from random chance alone. It appears the experimental heart transplant program increased the average patient's lifespan. -0.25 -0.15 -0.05 0.05 0.15 0.25 Simulated differences in proportions