Section A.1 Introduction To Data
Solution 1. Exercise 1
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Treatment: \(10/43 = 0.23 \to 23\%\text{.}\)
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Control: \(2/46 = 0.04 \to 4\%\text{.}\)
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A higher percentage of patients in the treatment group were pain free 24 hours after receiving acupuncture.
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It is possible that the observed difference between the two group percentages is due to chance.
Solution 2. Exercise 3
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“Is there an association between air pollution exposure and preterm births?”.
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143,196 births in Southern California between 1989 and 1993.
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Measurements of carbon monoxide, nitrogen dioxide, ozone, and particulate matter less than 10\(\mu g/m^3\) (PM\(_{10}\)) collected at air-quality-monitoring stations as well as length of gestation. Continuous numerical variables.
Solution 3. Exercise 5
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“Does explicitly telling children not to cheat affect their likelihood to cheat?”.
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160 children between the ages of 5 and 15.
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Four variables: (1) age (numerical, continuous), (2) sex (categorical), (3) whether they were an only child or not (categorical), (4) whether they cheated or not (categorical).
Solution 4. Exercise 7
Solution 5. Exercise 9
Solution 6. Exercise 11
Solution 7. Exercise 13
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Population: all births, sample: 143,196 births between 1989 and 1993 in Southern California.
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If births in this time span at the geography can be considered to be representative of all births, then the results are generalizable to the population of Southern California. However, since the study is observational the findings cannot be used to establish causal relationships.
Solution 8. Exercise 15
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Population: all asthma patients aged 18-69 who rely on medication for asthma treatment. Sample: 600 such patients.
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If the patients in this sample, who are likely not randomly sampled, can be considered to be representative of all asthma patients aged 18-69 who rely on medication for asthma treatment, then the results are generalizable to the population defined above. Additionally, since the study is experimental, the findings can be used to establish causal relationships.
Solution 9. Exercise 17
Solution 10. Exercise 19
Solution 11. Exercise 21
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Positive, non-linear, somewhat strong. Countries in which a higher percentage of the population have access to the internet also tend to have higher average life expectancies, however rise in life expectancy trails off before around 80 years old.
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Observational.
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Wealth: countries with individuals who can widely afford the internet can probably also afford basic medical care. (Note: Answers may vary.).
Solution 12. Exercise 23
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Simple random sampling is okay. In fact, it’s rare for simple random sampling to not be a reasonable sampling method!.
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The student opinions may vary by field of study, so the stratifying by this variable makes sense and would be reasonable.
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Students of similar ages are probably going to have more similar opinions, and we want clusters to be diverse with respect to the outcome of interest, so this would not be a good approach. (Additional thought: the clusters in this case may also have very different numbers of people, which can also create unexpected sample sizes.).
Solution 13. Exercise 25
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The cases are 200 randomly sampled men and women.
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The response variable is attitude towards a fictional microwave oven.
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The explanatory variable is dispositional attitude.
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Yes, the cases are sampled randomly.
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This is an observational study since there is no random assignment to treatments.
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No, we cannot establish a causal link between the explanatory and response variables since the study is observational.
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Yes, the results of the study can be generalized to the population at large since the sample is random.
Solution 14. Exercise 27
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Simple random sample. Non-response bias, if only those people who have strong opinions about the survey responds his sample may not be representative of the population.
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Convenience sample. His sample may not be representative of the population since it consists only of his friends. It is also possible that the study will have non-response bias if some choose to not bring back the survey.
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Convenience sample. This will have a similar issues to handing out surveys to friends.
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Multi-stage sampling. If the classes are similar to each other with respect to student composition this approach should not introduce bias, other than potential non-response bias.
Solution 15. Exercise 29
Solution 16. Exercise 31
Solution 17. Exercise 33
Need randomization and blinding. One possible outline: (1) Prepare two cups for each participant, one containing regular Coke and the other containing Diet Coke. Make sure the cups are identical and contain equal amounts of soda. Label the cups A (regular) and B (diet). (Be sure to randomize A and B for each trial!) (2) Give each participant the two cups, one cup at a time, in random order, and ask the participant to record a value that indicates how much she liked the beverage. Be sure that neither the participant nor the person handing out the cups knows the identity of the beverage to make this a double- blind experiment. (Answers may vary.)
Solution 18. Exercise 35
Solution 19. Exercise 37
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Experiment.
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Treatment: 25 grams of chia seeds twice a day, control: placebo.
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Yes, gender.
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Yes, single blind since the patients were blinded to the treatment they received.
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Since this is an experiment, we can make a causal statement. However, since the sample is not random, the causal statement cannot be generalized to the population at large.
Solution 20. Exercise 39
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Non-responders may have a different response to this question, e.g. parents who returned the surveys likely don’t have difficulty spending time with their children.
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It is unlikely that the women who were reached at the same address 3 years later are a random sample. These missing responders are probably renters (as opposed to homeowners) which means that they might be in a lower socio- economic status than the respondents.
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There is no control group in this study, this is an observational study, and there may be confounding variables, e.g. these people may go running because they are generally healthier and/or do other exercises.
