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The Buteyko method is a shallow breathing technique developed by Konstantin Buteyko, a Russian doctor, in 1952. Anecdotal evidence suggests that the Buteyko method can reduce asthma symptoms and improve quality of life. In a scientific study to determine the effectiveness of this method, researchers recruited 600 asthma patients aged \(18-69\) who relied on medication for asthma treatment. These patients were randomnly split into two research groups: one practiced the Buteyko method and the other did not. Patients were scored on quality of life, activity, asthma symptoms, and medication reduction on a scale from 0 to 10 . On average, the participants in the Buteyko group experienced a significant reduction in asthma symptoms and an improvement in quality of life. \({ }^{13}\) (a) Identify the main research question of the study. (b) Who are the subjects in this study, and how many are included? (c) What are the variables in the study? Identify each variable as numerical or categorical. If numerical, state whether the variable is discrete or continuous. If categorical, state whether the variable is ordinal.

A study that surveyed a random sample of otherwise healthy high school students found that they are more likely to get muscle cramps when they are stressed. The study also noted that students drink more coffee and sleep less when they are stressed. (a) What type of study is this? (b) Can this study be used to conclude a causal relationship between increased stress and muscle cramps? (c) State possible confounding variables that might explain the observed relationship between increased stress and muscle cramps.

To assess the effectiveness of taking large doses of vitamin \(\mathrm{C}\) in reducing the duration of the common cold, researchers recruited 400 healthy volunteers from staff and students at a university. A quarter of the patients were assigned a placebo, and the rest were evenly divided between \(1 \mathrm{~g}\) Vitamin \(\mathrm{C}, 3 \mathrm{~g}\) Vitamin \(\mathrm{C},\) or \(3 \mathrm{~g}\) Vitamin C plus additives to be taken at onset of a cold for the following two days. All tablets had identical appearance and packaging. The nurses who handed the prescribed pills to the patients knew which patient received which treatment, but the researchers assessing the patients when they were sick did not. No significant differences were observed in any measure of cold duration or severity 43 between the four medication groups, and the placebo group had the shortest duration of symptoms. (a) Was this an experiment or an observational study? Why? (b) What are the explanatory and response variables in this study? (c) Were the patients blinded to their treatment? (d) Was this study double-blind? (e) Participants are ultimately able to choose whether or not to use the pills prescribed to them. We might expect that not all of them will adhere and take their pills. Does this introduce a confounding variable to the study? Explain your reasoning.

In a public health study on the effects of consumption of fruits and vegetables on psychological well-being in young adults, participants were randomly assigned to three groups: (1) dietas-usual, (2) an ecological momentary intervention involving text message reminders to increase their fruits and vegetable consumption plus a voucher to purchase them, or (3) a fruit and vegetable intervention in which participants were given two additional daily servings of fresh fruits and vegetables to consume on top of their normal diet. Participants were asked to take a nightly survey on their smartphones. Participants were student volunteers at the University of Otago, New Zealand. At the end of the 14 -day study, only participants in the third group showed improvements to their psychological well-being across the 14 -days relative to the other groups. \({ }^{45}\) (a) What type of study is this? (b) Identify the explanatory and response variables. (c) Comment on whether the results of the study can be generalized to the population. (d) Comment on whether the results of the study can be used to establish causal relationships. (e) A newspaper article reporting on the study states, "The results of this study provide proof that giving young adults fresh fruits and vegetables to eat can have psychological benefits, even over a brief period of time." How would you suggest revising this statement so that it can be supported by the study?