3. People in surveys tend to underreport their participation in social assistance programs. Suppose that the probability of actually participating is 20%, but based on survey data, the probability appears to be only 15%. (Assume no one reports that they are a participant if they aren't, but some people report they aren't participating even when they are). a) Suppose you survey a simple random sample of 200 respondents. How many of them would you expect to report being participants in social assistance, and how many would you expect are actually receiving social assistance? b) What is the probability that a person who participates actually reports their participation? c) Suppose you survey just 3 people, and those three people are actually receiving social assistance (you may know this by, say, getting access to state administrative records for the people in your sample). What is the probability that at least one of them will say they do not receive assistance? 4. Read the attached 1-page summary of a recent study done on vaccination and health outcomes. a) Discuss (in a few sentences) any concerns you would have with the sampling method used for the study. b) Does the study seem to be convincing in terms of establishing causality between vaccinations and health outcomes? Why or why not? 5. There is a nice set of policy briefs produced at Syracuse University by two policy-related centers on campus: the Lerner Center for Public Health Promotion and Population Health and the Center on Aging and Policy Studies (CAPS). If you go to their website, you can find a list of these "bulletins": https://asi.syr.edu/caps/lerner-center-caps-bulletins/ Look through this list and find an brief (most are a few pages) that interests you and seems to reflect some statistical work. Ask yourself: Do the researchers use a sample? How was it gathered? What analysis do they do? Is there a relevant graph or figure that summarizes their findings? Summarize in a paragraph how the authors seem to be using statistical analysis to answer their question of interest