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A statistics student who is curious about the relationship between the amount of time students spend on social networking sites and their performance at school decides to conduct a survey. Three research strategies for collecting data are described below. In each, name the sampling method proposed and any bias you might expect. (a) He randomly samples 40 students from the study's population, gives them the survey, asks them to fill it out and bring it back the next day. (b) He gives out the survey only to his friends, and makes sure each one of them fills out the Survey. (c) He posts a link to an online survey on his Facebook wall and asks his friends to fill out the survey.

Suppose we want to estimate family size, where family is defined as one or more parents living with children. If we select students at random at an elementary school and ask them what their family size is, will our average be biased? If so, will it overestimate or underestimate the true value?

In order 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 \(\mathrm{C}\) 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 between the four medication groups, and the placebo group had the shortest duration of symptoms. \(^{60}\) (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.

1.42 Distributions and appropriate statistics. For each of the following, describe whether you expect the distribution to be symmetric, right skewed, or left skewed. Also specify whether the mean or median would best represent a typical observation in the data, and whether the variability of observations would be best represented using the standard deviation or IQR. (a) Housing prices in a country where \(25 \%\) of the houses cost below $$\$ 350,000,50 \%$$ of the houses cost below $$\$ 450,000,75 \%$$ of the houses cost below $$\$ 1,000,000$$ and there are a meaningful number of houses that cost more than $$\$ 6,000,000$$ (b) Housing prices in a country where \(25 \%\) of the houses cost below $$\$ 300,000,50 \%$$ of the houses cost below $$\$ 600,000,75 \%$$ of the houses cost below $$\$ 900,000$$ and very few houses that cost more than $$\$ 1,200,000$$ (c) Number of alcoholic drinks consumed by college students in a given week. (d) Annual salaries of the employees at a Fortune 500 company.