Men with localized prostate cancer (median age = 67) were randomly assigned to either radical prostatectomy (removal) or observation. During the follow-up time (median time, 10 years), 31 of 367 assigned to observation had died from prostate cancer, and 21 of the 364 assigned to surgery had died from prostate cancer.
a. Find the percentage that died from prostate cancer in each group, and compare these percentages.
b. Test the hypothesis that treatment and death from prostate cancer are independent using a significance level of 0.05. You may choose a chi square test of homogeneity or a two-proportion z-test.
c. Suppose the sample sizes and deaths were doubled so that the death rates remained the same. Hypothetically, 42 out of 728 who had surgery died from prostate cancer, and 62 out of 734 who were observed died from prostate cancer. Repeat the test, reporting the new p-value and conclusion.
d. Explain the difference in results between parts b and c.