Math 256, Hallstone More Inference for Proportions (11.3 and extras not in text) Spring 2016

1.  11.3 How many lefties play college baseball? A survey of 60 randomly chosen players found 15 of them to be left handed. Compute a 95% confidence interval for the true proportion of all left handed college baseball players.

2.  Recall: J Not paying off your credit card bill at the end of the month is one of the worst financial decisions you can make. A growing share of Americans are regularly paying off their full credit card balances than were prior to the recession, according to data recently released (2013) by the American Bankers Association. However, the figure that they released was lower than I could believe, having “improved” to 29%. I think that the percentage has probably changed, so I asked 200 randomly chosen people if they paid off their balances. If 63 of them do pay off, estimate the true proportion of people who pay off their balances with a 95% confidence interval.

3.  In the National AIDS Behavioral Surveys sample of 2673 adult heterosexuals, 5 respondents had both received a blood transfusion and had a sexual partner from a group at high risk of AIDS.
a) You should not use the large-sample confidence interval for the proportion p in the population who share these two risk factors. Why not?
b) The plus four method adds four observations, two successes and two failures. What are the sample size and the count of successes after you do this? What is the plus four estimate of p. Give the plus four 95% confidence interval for p.

4.  HOMEWORK: A member of the GRCC women’s team made 71 out of 100 free throws in a fundraiser, after getting a pledge from me. Give a 95% confidence interval for the true proportion of free throws she makes. Also comment on the assumptions in doing this problem.

5.  HOMEWORK: Repeat the previous problem for Stephen Curry if he makes 93 out of 100.

6.  What should be the margin of error in this poll? Which of these estimates does the margin of error actually apply to? Assume 95% confidence in all nationwide polls, unless otherwise stated.

7.  A few years ago, Washington became the second state to have an assisted suicide law. We want to find out what percentage of Washingtonians approve of this law, and we want our margin of error to be at most 3%, with 95% confidence. How big should our sample be? Say we want to find out the same information for the people in Seattle. How would that affect the sample size?

8.  Two Proportions (We will do separately; OLI does as special case of 14.1) A manufacturer experiments with two production methods. The first method produces 18 defects out of 275 sample items, while the second method produces 27 defects out of 320 samples. At the a = .05 level, test the claim that there is no difference between the proportions of defects.

9.  To study the long-term effects of preschool programs for poor children, the High/Scope Educational Research Foundation has followed two groups of Michigan children since early childhood. One group of 62 attended preschool as 3- and 4-year-olds. A control group of 61 children from the same area and similar backgrounds did not attend preschool. Over a ten-year period as adults, 38 of the preschool sample and 49 of the control sample needed social services (mainly welfare). Does the study provide significant evidence at the 0.05 level that children who attend preschool have less need for social services as adults?

10.  HOMEWORK: A survey was conducted of randomly selected television viewers to determine the composition of the audience for a certain show. Of 200 people with college educations, 30 indicated that they watched the show. Of 600 people without college educations, 210 indicated that they watched the show. At the a = .01 level, test the claim that a smaller proportion of college educated people watch the show.

11.  The above poll gives information about the feelings of people in the US. We want to estimate the difference in the proportion of Republicans and Democrats who feel that the Senate should hold hearings on Obama’s nominee. After searching the Pew Research website I found that there were 286 Republicans, 299 Democrats, and 345 (presumably mostly) Independents. (The number of people in the two parties is hard to pin down, but my best estimate is 47% Democrat, 41% Republican, and 12% true independent/other.)

a.  What is the best single number estimate of that difference?

b.  Construct a 95% confidence interval for the difference between the proportion of Republicans and Democrats who feel that the Senate should hold hearings on Obama’s nominee.

c.  (Fill in the blanks: With 95% confidence, the percentage of Republicans who feel the Senate should hold hearings on Obama’s nominee is ______(bigger or smaller) than the percentage of Democrats who feel the Senate should hold hearings on Obama’s nominee by between ______% and ______% .)

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