sity 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 he was gravely ill and would most likely benefit from a new heart. Patients in the treatment group got a transplant and those in the control group did not. Of the 34 patients in the control group, 4 were alive at

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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 he was gravely ill and would most likely benefit from a new heart. Patients in the treatment group got a transplant and those in the control group 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.

 

 

5. We write treatment on
cards representing patients who were in the treatment group, and control on
cards representing patients
in the control group. Then, we shuffle these cards and split them into two groups: one group of size
representing patients who survived, and
another group of size
representing patients who died. We calculate the difference between the proportion of patients in the treatment group
who survived and the proportion of patients in the control group who survived to get Psim.treatment – Psim.control and record this value. We repeat this
many times to build a distribution centered at
Lastly, we calculate the fraction of simulations where the simulated differences in proportions
are 0.23 or higher v. 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.
Transcribed Image Text:5. We write treatment on cards representing patients who were in the treatment group, and control on cards representing patients in the control group. Then, we shuffle these cards and split them into two groups: one group of size representing patients who survived, and another group of size representing patients who died. We calculate the difference between the proportion of patients in the treatment group who survived and the proportion of patients in the control group who survived to get Psim.treatment – Psim.control and record this value. We repeat this many times to build a distribution centered at Lastly, we calculate the fraction of simulations where the simulated differences in proportions are 0.23 or higher v. 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.
Group
Alive
Dead
Total
Treatment
24
45
69
Control
4
30
34
Total
28
75
103
Round all calculated answers to four decimal places.
1. What proportion of patients in the treatment group survived? 0.35
2. What proportion of patients in the control group survived? 0.12
Transcribed Image Text:Group Alive Dead Total Treatment 24 45 69 Control 4 30 34 Total 28 75 103 Round all calculated answers to four decimal places. 1. What proportion of patients in the treatment group survived? 0.35 2. What proportion of patients in the control group survived? 0.12
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