Rec 1 - SOLUTIONS

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Ohio State University *

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1430

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Statistics

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Apr 3, 2024

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STAT 1430 Recitation 1B SOLUTIONS 1. A pharmaceutical company interested in measuring how often physicians prescribe a certain drug has selected a simple random sample from each of two groups: M.D. (Medical Doctors) and D.O. (Doctors of Osteopathic). What is this type of sampling called? a. Simple random sampling. b. Stratified random sampling. c. None of the above. 2. Detailed surveys are sent to 13,000 organizations on the Internet to determine who uses the Internet more (women or men). 1,468 responses were received. The margin of error was 2.8 percent, with a confidence level of 95%. What was the response rate for this survey? a. 1,468 b. 95% c. 2.8% d. 11.29% 3. A survey asks 500 randomly selected U.S. taxpayers whether they have ever cheated on their taxes. Which of the following is an example of response bias in this situation? a. Bob does not respond to the survey. b. Bob answers “no” even though he really has cheated on his taxes. c. Bob was not selected to participate in the survey. d. All of the above are examples of response bias. 4. A sample of Americans was surveyed and asked to report the amount of money spent annually on reading materials. Suppose they originally sampled 200 people but the data set actually contains 133 values. What kind problem is represented as a result? a. Nonresponse b. Possible bias in the data we do have c. Lower level of precision in the results due to smaller actual sample than planned d. All of the above 5. A survey of 15 randomly selected employees from Bob’s factory was taken to find out how many sick days they took due to colds and flu last year. Suppose Bob didn’t take a random sample. Suppose the employees in the sample were those who responded to an advertisement Bob put out to the whole company, looking for volunteers to participate in the survey. What kind of error would be made here? THERE IS ONLY ONE CORRECT ANSWER – CHECK YOUR LECTURE NOTES. a. Undercoverage b. Nonresponse c. Bias due to a self-selected sample d. None of the above 6. A statistics student wants to know what OSU students think about parking on campus. To obtain a sample of 20 students, he knocks on the doors of residents in his dorm until he finds 20 people home who can take his survey about parking. This is a: a. Simple random sample b. Stratified sample c. Convenience sample

STAT 1430 Recitation 1B SOLUTIONS 7. When every possible sample with the same number of observations is equally likely to be chosen, the selected sample is called: a. Simple random sample. b. Stratified sample c. Biased sample 8. The website for ESPN is interested in who the greatest baseball player of all time was. They run an internet poll to figure this out. They ask every visitor to the site if they would like to participate in the poll, and then ask them who the greatest ballplayer of all time was. They show the results at the end of the polling period. This is a: a. Simple random sample b. Stratified sample c. Volunteer sample d. Convenience sample 9. Which of the following problems in surveys can cause bias? a. Nonresponse b. Undercoverage c. Question wording d. All of the above 10. The following question is being considered for inclusion in a survey regarding cell-phones. “Some cell phone users have developed brain cancer. Should all cell phones come with a warning label explaining the danger of using cell phones?” You don’t want this question to be included as written. Explain why this question is biased AND create a new question that avoids bias yet still helps the researcher find out what they want to know? Answers will vary. Check with your TA if you have questions about your answers. 11. A politician wants to estimate the mean age of registered voters in her district. Unfortunately, she does not have a complete list of households. How can she go about attempting to do a random sample to get the information she needs and represent the population? More than one possible answer here as long as it’s justifiable and reasonable. Next 2 problems: 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%.) 12. What is the response rate for this survey? 22.56% (1,128 / 5,000) 13. 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 so much possible bias due to the nonresponse that you do not know what would happen if everyone actually answered the question.

STAT 1430 Recitation 1B SOLUTIONS 14. Look up one of the latest graphs shown in today’s USA TODAY SNAPSHOTS website: http://www.usatoday.com/picture-gallery/news/2015/04/07/usa-today-snapshots/6340793/ . Pick one that can be represented as a graph, sketch the graph, and critique the sample and the graph in terms of the criteria we discussed in class. If there is not enough information to evaluate certain things, describe what else is needed. Answers will vary. Check with your TA if you have questions about your answers. For next 4 problems: Use the “Mobile Mindset Study” done by Lookout, Inc., a cybersecurity company, on the topic of Smart Phone usage which we looked at in recitation 1A (the PDF is on Carmen). Answers to the following questions (19-22) will vary. As long as they are reasonable, they should be acceptable. Check with your TA if you have questions about your answer. 15. Looking at the five graphs in the report, give an example of a question that could result in a lot of nonresponse bias . – Remember, nonresponse bias is usually defined as a survey-wide issue and not a specific question issue. 16. Looking at the five graphs in the report, give an example of a question that could result in a lot of response bias . 17. Looking at the survey methodology section at the bottom, is there undercoverage ? Why or why not? Use the definition of undercoverage from your notes to answer this question. 18. Is it possible to know the response rate of this survey? Why or why not? 19. A researcher wants to study the effects of computer activities vs. pencil and paper activities on learning math for preschool children. Thirty children will participate in her study; 15 children using computer activities and 15 children using pencil and paper activities. She wants to compare the performance of the two groups. To form the two groups, she will choose between two procedures. Which procedure is the best to use and why? (If they are equally effective explain why.) Procedure 1 : She brings the children into a room with 30 desks; 15 desks have computers and 15 desks have a paper and pencil. She tells the children to go to whichever table they want. Procedure 2: She flips a coin for each child. Heads = computer group and Tails = paper and pencil group. Each child goes to their assigned group; when one group is filled the rest go to the other group. Procedure 2 is better because it randomly assigns subjects to treatments, avoiding bias. (Children may tend to go toward the method they are best at or most interested in.)

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Rec 1 - SOLUTIONS

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