A group of doctors published an article in the New England Journal of Medicine. In the article they revealed the findings of a study to determine if there is a difference in survival rates for men who undergo surgery for localized prostate cancer and those who are treated with observation only. The researchers randomly assigned 731 men with localized prostate cancer to radical prostatectomy or observation. During the years of follow-up, 245 of 367 (66.8%) assigned to surgery survived for at least 5 years and 223 of 364 men (61.3%) assigned to observation survived for at least 5 years. Required:
a. Construct and interpret a 99% confidence interval for the difference in the true proportion of men like these that would survive for at least 5 years after receiving surgery and the proportion that would survive for at least 5 years when only being observed.
b. How does the confidence interval from part a tell you that there is not sufficient evidence at the a=.01 level that there is a difference in the proportion of men with localized prostate cancer who survive at least five years after receiving surgery and the proportion of men with localized prostate cancer who survive at least five years when only being observed. In other words, how would you know that the p-value for a 2 proportion z test would not be significant at the 0.01 level?