Concept explainers
AIDS and AZT In a study (reported in the New York Times, February 15, 1991) on the effects of AZT in slowing the development of AIDS symptoms, 338 veterans whose immune systems were beginning to falter after infection with the AIDS virus were randomly assigned either to receive AZT immediately or to wait until their T cells showed severe immune weakness. The study classified the veterans’ race, whether they received AZT immediately, and whether they developed AIDS symptoms during the three-year study. Let x1 denote whether they used AZT (1 = yes, 0 = no) and let x2 denote race (1 = white, 0 = black). A logistic
- a. Interpret the sign of the effect of AZT.
- b. Show how to interpret the AZT effect for a particular race by comparing the estimated probability of AIDS symptoms for black veterans with and without immediate AZT use.
- c. The se value was 0.279 for the AZT use effect. Does AZT use have a significant effect at the 0.05 significance level? Show all steps of a test to justify your answer.
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- A cross-sectional study is conducted to investigate cardiovascular disease (CVD) risk factors among a sample of patients seeking medical care at one of three local hospitals. A total of 500500 patients are enrolled. Based on the following data, we would like to determine if there is a significant association between the family history of CVD and the enrollment site. Enrollment Site Family History of CVD Hospital 1 Hospital 2 Hospital 3 Total Yes 34 8 58 100 No 104 72 224 400 Total 138 80 282 500 Given: The value of the test statistic is χ2= 6.912 Use α=0.1 as the level of significance. The superintendent of Hospital 2 performed the Goodness of Fit Test to test whether 25% of the patients go to Hospital 1, 15% of the patients go to Hospital 2 and 60% of the patients go to Hospital 3. Given: The superintendent found that the pp-value for the test is 0.25091 Let: p1=p1= be the proportion of patients at Hospital 1 p2=p2= be the proportion of patients at…arrow_forwardVasectomies and Prostate Cancer. In the United States, approximately 450,000 vasectomies are performed each year. In this surgical procedure for contraception, the tube carrying sperm from the testicles is cut and tied. Several studies have been conducted to analyze the relationship between vasectomies and prostate cancer. The results of one such study by E. Giovannucci et al. appeared in the paper “A Retrospective Cohort Study of Vasectomy and Prostate Cancer in U.S. Men” (Journal of the American Medical Association, Vol. 269(7), pp. 878–882). Of 21,300 men who had not had a vasectomy, 69 were found to have prostate cancer; of 22,000 men who had had a vasectomy, 113 were found to have prostate cancer. a. At the 1% significance level, do the data provide sufficient evidence to conclude that men who have had a vasectomy are at greater risk of having prostate cancer? Consider men who had had a vasectomy Population 2. b. Is this study a designed experiment or an observational study?…arrow_forwardQuit Smoking: The New England Journal of Medicine published the results of a double-blind, placebo-controlled experiment to study the effect of nicotine patches and the antidepressant bupropion on quitting smoking. The target for quitting smoking was the 8th day of the experiment. In this experiment researchers randomly assigned smokers to treatments. We conducted a hypothesis test to determine if the side effect rates are significantly different for nicotine patches versus bupropion at a 5% level of significance. (The normality conditions are met by the data.) The P-value is 0.04. What can we conclude? We reject the null hypothesis. The side effects are more painful for people taking bupropion. We reject the null hypothesis. The side effect rate for bupropion is significantly higher than the side effect rate for the nicotine patches. We fail to reject the null hypothesis. The side effect rates are different, but not significantly different. We reject the null hypothesis. The…arrow_forward
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