Each group has the following scenarios. In each scenario, answer the mathematical part using techniques we have discussed in the past week and a half. Answer the "social justice" part by reasoning out, considering different viewpoints (at least TWO different viewpoints per scenario), adopting a viewpoint if one is not suggested, and answering the question. Be prepared to either DEFEND your answer, or to CRITIQUE answers of other groups.

After a while, I will assign one scenario presentation to each group; for now, consider EACH scenario.

Scenario 1:  Baby Needs a New Pair of Shoes

A survey of 89 high school students in a Midwest city found that, on average, students paid $52.41 for a pair of athletic shoes, with a sample standard deviation of $14.38. How confident can you be that the average student paid over $50? If you were advocating that the local school board adopt a uniform policy with a limit of $50 on shoes, what confidence level would you use?

Scenario 2:  Something’s Fishy

The USDA inspected 60 walleye caught by commercial fishermen in Lake Michigan one day last summer. The average mercury contamination in the sample was 0.292 ppm, with a sample standard deviation of 0.096 ppm. The maximum safe mercury level for human consumption is 0.32 ppm. Should the USDA close Lake Michigan to commercial walleye fishing? How confident are you of your answer?

Scenario 3:  Gimme Some Air

A local restaurant surveyed 112 customers. Of those, 63 supported a ban on smoking in the restaurant. Should the restaurant ban smoking? What confidence level would you use? What is your margin of error?

29 of the 112 customers surveyed were smokers who did not support the ban. What confidence level would they want to use in order to convince the owner NOT to enact the ban?

What should the owner do? Is the majority always right?

Scenario 4:  Not By The Hair On Your Chinny-chin chin

In a survey of 243 U.S. households, 43 claimed to have no health insurance. In 1999, the CDC estimated that 14.2% had no insurance. You are a staffer for a candidate who wants to increase funding for public health insurance. What claim would you want to make, and what confidence level would you use to justify the claim?

Suppose, instead, that your candidate supported no additional funding. What claim and confidence level would you use?

In a different survey of 117 Hispanic households, 37 claimed to have no health insurance, while of 396 white households, 42 had no insurance.

(Data based on estimates from CDC web site, www.cdc.gov)

Scenario 5:  Lottery: A Regressive Tax

Do you know what a "regressive" tax is?

217 lottery ticket buyers were surveyed; their annual household income averaged $19,495, with standard deviation $7852. Of these ticket buyers, they bought an average of 104.2 tickets last year (cost $104.20) with standard deviation 71.13 tickets, and they won an average of $7.93, with a standard deviation of $77.54. In 2001 (the latest year for which figures are available), 20% of all U.S. households earned $17,970 or less, and 40% earned $33,314 or less. Estimated lottery income in the U.S.: $35 billion. Do the poorest people "give" the most money to governments through lotteries? Answer using a confidence interval…

Scenario 6:  Medicare Prescription Drug Plan

163 Social Security recipients over the age of 65 were sampled at random; their average annual prescription costs were $3160, with standard deviation $1212. Under a proposal once considered in Congress, Medicare patients would pay an upfront deductible of $250, 25% of the cost between $250 and $2250, all costs between $2250 and $5100 (the "coverage gap"), and 5% of costs above that. Is the "coverage gap" in the right place (use confidence intervals to answer). Should the government be concerned about prescription drug costs?