1 F12 STAT 110 Practice EXAM 1 SOLUTIONS Name__________________________________ Questions 1-3 are based on the following description You want to know the opinions of American teachers about establishing a test for high school graduation. You obtain a list of the members of the National Education Association (the largest teacher’s union) and mail a questionnaire to 2,500 teachers chosen at random from this list. In all, 1,357 teachers mail back completed surveys. 1. The population for this study is all American teachers 2. The sample for this study is the 1,357 teachers who mailed back completed surveys 3. The sampling frame for this study is teacher members of the National Education Association A list of graduate students for the department of statistics at the University of South Carolina are listed in the following table. 01. Chalmers 02. Chen, H 03. Cheng 04. Chen, Y 05. Clark 06. Du 07. Feng 08. Fu 09. Gao 10. Habinger 11. Hartnett 12. Hill 13. Ishikawa 14. Jang 15. Lauer 16. Lawrence 17. Lewis 18. Li, L 19. Li, T 20. Liu 21. McMahan 22. Moran 23. Peng 24. Rahman 25. Ren 26. Scott 27. Thompson 28. Wanda 29. Wang 30. Wu 31. Yang 4. Use the following list of random digits to find the 5th element for a simple random sample. 28576 10317 03(03 is a repeated code)314 67721 09265 McMahan Questions 5-11 are based on the following description A recent poll, conducted February 1-3, asked 1,072 randomly selected adults, “Do you plan on watch all, most, some, or none of the Superbowl this Sunday?” 740 responded they would watch at least part of Superbowl XLV. 5. Find the observed proportion (the sample proportion), p, of those who will watch at least part of the Superbowl XLV. ,  6. Find the estimated margin of error for 95% confidence √, 2 7. Suppose the polling company got their sample by standing outside of a football stadium after a game and asking the first 1,072 spectators as they leave the game. What type of sampling scheme would this be? Convenience Sample 8. If the polling company wanted to be able to make a statement by gender about who was planning to watch at least some of the Superbowl, they could use a Stratified Random Sample 9. In order to reduce bias in this study, the researchers would have to make sure to have the best random sampling scheme 10. In order to reduce variability of the sample proportion in this study, the researchers would have to increase the sample size 11. Suppose a respondent in this study answered they would watch at least some of the Superbowl only because they thought that is what they are supposed to say, but they were actually not planning to watch it. This study would suffer from a Non-Sampling Error: Response Error Questions 12-16 are based on the following description There is a long standing controversy surrounding mass vaccination of military personnel with anthrax vaccine. In the 1950’s Brachman Study, workers at four goat hair mills were recruited into a trial of an anthrax vaccine. Several reports of this study claim that the anthrax vaccine studied was effective, since the rate of anthrax was statistically significantly higher in the placebo group. 12. It turns out that randomization was not done properly and that workers in the placebo group had much higher exposure to anthrax spores. So, it cannot be determined whether the higher rate of anthrax in the placebo group was due to the lack of vaccination or the higher exposure to the anthrax spores. The fact that we cannot tell apart the effect of the anthrax exposure and lack of vaccination on contraction of anthrax is called confounding 13. Perhaps a better design for this study would have been to first divide the workers into groups by exposure, maybe a group for high exposure and a group for low exposure according to job duties. Then subjects within each exposure group could be randomly allocated to either the vaccinated or the placebo group. This would be an example of a block design 14. What does it mean that the rate of anthrax contraction is “statistically significantly higher” for those not vaccinated? The researchers noticed anthrax rate so much higher in the unvaccinated group, this would rarely occur by chance 15. This study is a(n) experiment 16. What would it mean to say that the rate of anthrax contraction is “not statistically significantly higher” for those not vaccinated? It would mean that the researchers could have noticed anthrax rate higher in the unvaccinated group, but may be explained by chance3 Questions 17-23 are based on the following description A study attempted to quantify the harm to children when their parents are exposed to lead at the job and may bring it home in their hair and on their clothing. The study matched (on age and neighborhood) 33 children of parents who worked at a battery factory to 33 unexposed children. Level of lead exposure and hygiene habits at the end of the workday of the parents were measured as well as the lead concentration in the children’s blood. 17. This is NOT an experiment because: The researcher did not assign the exposure to lead and hygiene habits for parents 18. The explanatory variable(s) in this study is(are) level of lead exposure and hygiene habits at the end of the workday 19. The response variable(s) in this study is (are) level of lead in children’s blood 20. Excess lead in the homes of the children could have an effect on the level of lead in the children’s blood. In this case, excess lead would be a lurking variable 21. What is the population? children 22. This study’s design is a matched pairs design 23. The study compared the mean (average) lead level for the children of the battery factory workers to that of the children in the control group and reported that children of parents who are exposed to lead at work (battery factory workers) have a significantly higher lead concentration than do children who have parents without exposure to lead at their workplace. This means that even if there was no difference in lead concentration under either situation, observing an average lead level in exposed group that much higher than for unexposed exposed would rarely occur by chance Questions 24-27 are based on the following description