Exercise 1.50 introduces the Stanford Heart Transplant Study. Of the 34 patients
ID: 3273775 • Letter: E
Question
Exercise 1.50 introduces the Stanford Heart Transplant Study. 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. (a) What proportion of patients in the treatment group and what proportion of patients in the control group died? (b) One approach for investigating whether or not the treatment is effective is to use a randomization technique. i. What are the claims being tested? Use the same null and alternative hypothesis notation used in the section. ii. The paragraph 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. We write alive on ___ cards representing patients who were alive at the end of the study, and dead on ___ cards representing patients who were not. Then, we shuffle these cards and split them into two groups: one group of size ___ representing treatment, and another group of size ___ representing control. We calculate the difference between the proportion of dead cards in the treatment and control groups (treatment -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 ___. 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. iii. What do the simulation results shown below suggest about the effectiveness of the transplant program?Explanation / Answer
a. There were records of 75 death, of which 30 belonged to control group and 45 belonged to treatment group.
Thus, P(death|treatment)=45/75=0.6, and P(death|control group)=30/75=0.4
b. i) The claim to be tested is that there is no difference in proportion of dead patients between treatment and control group. The null hypothesis is the hypothesis of no difference. Therefore, null hypothesis is as follows:
H0:p1-p2=0
The alternative hypothesis is the tentative proposition, the researcher wishes to establish. That is it says that there is significant difference in proportion of dead patients between treatment and control group. The alternative hypothesis is as follows:
H1:p1-p2=/=0
ii) blanks are filled with following words.
28 (there were 28 patients alive at the end of the experiment), 75 (75 people died at the end of the experiment), 69 (there were 69 patients in total in the treatment group), 34 (representing control), 0.2 (0.6-0.4), atleast as extreme as 0.2.
part iii) image is not visible when opened in another window.
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.