4 When the prevalence of a disease in the population is very low, such as HIV infection or certain cancers, there is controversy about the benefits of screening everyone for the disease. In this problem, you will see why this is the case. The table below shows what is likely to happen if all roughly 300,000,000 Americans each were given an inexpensive enzyme immunoassay screening test for HIV infection. Test Positive 1,339,370 4,479,849 5,819,219 Test Negative 4,030 Total Have HIV 1,343,400 Do Not Have HIV 294,176,751 298,656,600 Total 294,180,781 300,000,000 Sources: www.cdc.gov, R. Chou et al. (July 2005). "Screening for HIV: A Review of the Evidence for the U.S. Preventive Services Task Force," Annals of Internal Medicine, Vol. 143, July 2005, pp. 55-73, www.annals.org/content/143/1/55.full a. How many false positives were there? Explain the consequence of a false positive for the person tested. b. How many false negatives were there? Explain the consequence of a false negative for the person tested. c. What is the sensitivity of this test? Explain the meaning of this statistic, in the context of this test. d. What is the specificity of this test? Explain the meaning of this statistic, in the context of this test. e. What is the positive predictive value (PPV)? Use this value in a sentence explaining to a person what his or her positive test might indicate. f. What is the negative predictive value (NPV)? Use this value in a sentence explaining to a person what his or her negative test might indicate. g. Based on your results, explain why people are reluctant to recommend universal screening for HIV.

The rabies vaccine for dogs can save your dog's life. If your dog bites another animal or is on the receiving end of a bite, the vaccine can protect them from a dangerous and potentially fatal illness. Furthermore, in most places, the rabies vaccine for dogs is legally required. The NYC Department of Health wants to know if LESS than 95% of the dogs in the city have been vaccinated with their rabies vaccine.  158,045 of the 165,000 dogs examined had their rabies shots.  Risk no more than 5% Type I error.  What kind of test will you need to perform?  A   A right, one-tailed z-test B   A left, one-tailed z-test C   A two-tailed z- test

Practice question #3 Investigators want to know if those who work long hours have more trouble sleeping. In one sample of 190 British civil servants who worked more than 40 hours a week, 95 of them said they usually get less than 7 hours of sleep per night. In a second sample of 150 British civil servants who worked between 35 and 40 hours per week, 63 of them said they usually get less than 7 hours of sleep per night. The investigators believe these are represent samples of the populations. Find a 95% Confidence Interval for the difference in proportions of these two populations that get less than 7 hours of sleep per night. Then interpret the confidence interval. Be sure to check that any necessary conditions are met first. Round final answers to 3 decimal places. Verify conditions are appropriate for method: Interval: ________________________ Does the interval contain zero? __________ What does this information lead you to conclude?

The following table shows some data from a study on substance use among 10th graders in the United States and Europe. Smoked Cigarettes Cigarette-Free Totals U.S. 14,000 Europe 96,000 Total 71,210 110,000

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In 1993 approximately 62.1 million Americans suffered injuries, as reported by the National Center for Health Statistics in Vital and Health Statistics. More males (33.4 million) were injured than females (28.7 million). Those statistics do not tell us whether males and females tend to be injured in similar circumstances. One set of categories commonly used for accident circumstances. One set of categories commonly used for accident circumstance is "while at work," "home", "motor vehicle", and "other". A random sample of accident reports gave the data in contingency table below. Male Female While at work 19 24 27 Home 14 Motor Vehicle 26 Other At the 5% significance level, do the data provide sufficient evidence to conclude that an association exists between accident circumstances and sex? Type in Canvas the grand total. 35