STAT
3.1-3.2 solutions

# 7 the dean of a college of business with five

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your population if interest is internet users we do not have undercoverege. 7. The dean of a college of business with five departments wants to estimate the student- hours lost per month due to illness of professors and compare them. Describe a sampling plan that would be suitable for estimating the college-wide loss and for comparing departments. Stratified sample; take a simple random sample from each of the 5 depts. If you just take a simple random sample from the whole college, you may miss a department that is small, for example, and they will have no representation. Stratified sampling forces there to be representation from each group. 8. A politician wants to estimate the mean age of registered voters in her district. Unfortunately, she does not have a complete list of households. Describe a sampling plan that would be suitable for her purposes. Many different answers possible here. One idea would be look at the list of precincts in the district (a precinct is a specific area within a city designed for voting purposes-if you live in precinct A, you all vote in the same place and you are all on the same list.) From there you can get a list of everyone in each precinct that is registered to vote, and take a random sample from that. If that’s not allowed you could divide the district into regions and use a map to randomly select households to sample from (more difficult!) You’d have to eliminate anyone not registered to vote. 9. You are on the staff of a member of Congress who has 5,000 constituents (voters in her district.) She is considering a bill that would require all employers to provide health insurance for their employees. She sends a survey to all 5,000 constituents asking them their opinion on this bill (support, oppose, no opinion.) Of the 1,128 surveys received, 871 of them oppose the bill (which equals 77.2%.) a. What is the response rate for this survey? 1128/5000 = 0.2256=22.56%                                            2

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b. Looking at these results you are not convinced that a majority ( > 50%) of all the voters in her district necessarily oppose this bill. State briefly how you would explain this to the congresswoman. Use an argument based on statistical ideas. There is a very high rate of nonresponse to this survey. You don’t know how those people would have responded to the question. You cannot assume that the responses from the nonrespondents would be the same as for the respondents. It could be that they didn’t care; so if you did have the data from all 5,000 people sampled, you wouldn’t have 77.2% opposing the bill; it would likely be lower in that case. 10. An online dating service has a quick poll on its website showing the following results. Which of the following correctly describes the problems with this survey? Do you agree with having mandatory background checks as a condition of becoming a member of an online dating service?
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