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
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
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
![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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4745af79-0155-486b-8f61-53121b7c4ee4%2F1d174630-458a-4fe4-afb5-99f46d2cde7e%2Fj8wswxe_processed.png&w=3840&q=75)
![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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4745af79-0155-486b-8f61-53121b7c4ee4%2F1d174630-458a-4fe4-afb5-99f46d2cde7e%2Fpqiz2a_processed.png&w=3840&q=75)
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