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How Many People Wash Their Hands After Using the Washroom? In Example 1.10 on page \(16,\) we introduce a study by researchers from Harris Interactive who were interested in determining what percent of people wash their hands after using the washroom. They collected data by standing in public restrooms and pretending to comb their hair or put on make-up as they observed patrons' behavior. \({ }^{27}\) Public restrooms were observed at Turner's Field in Atlanta, Penn Station and Grand Central Station in New York, the Museum of Science and Industry and the Shedd Aquarium in Chicago, and the Ferry Terminal Farmers Market in San Francisco. Of the over 6000 people whose behavior was observed, \(85 \%\) washed their hands. Women were more likely to wash their hands: \(93 \%\) of women washed, while only \(77 \%\) of men did. The Museum of Science and Industry in Chicago had the highest hand-washing rate, while men at Turner's Field in Atlanta had the lowest. (a) What are the cases? What are the variables? Classify each variable as quantitative or categorical. (b) In a separate telephone survey of more than 1000 adults, more than \(96 \%\) said they always wash their hands after using a public restroom. Why do you think there is such a discrepancy in the percent from the telephone survey compared to the percent observed?

Teaching Ability In a sample survey of professors at the University of Nebraska, \(94 \%\) of them descrihed themselves as "ahove average" teachers. \({ }^{28}\) (a) What is the sample? What is the population? (b) Based on the information provided, can we conclude that the study suffers from sampling bias? (c) Is \(94 \%\) a good estimate for the percentage of above-average teachers at the University of Nebraska? If not, why not?

What Percent of Young Adults Move Back in with Their Parents? The Pew Research Center polled a random sample of \(n=808\) US residents between the ages of 18 and 34 . Of those in the sample, \(24 \%\) had moved back in with their parents for economic reasons after living on their own. \(^{30}\) Do you think that this sample of 808 people is a representative sample of all US residents between the ages of 18 and 34 ? Why or why not?

Do Cat Videos Improve Mood? As part of an "internet cat videos/photos" study, Dr. Jessica Gall Myrick posted an on-line survey to Facebook and Twitter asking a series of questions regarding how individuals felt before and after the last time they watched a cat video on the Internet. \(^{31}\) One of the goals of the study was to determine how watching cat videos affects an individual's energy and emotional state. People were asked to share the link, and everyone who clicked the link and completed the survey was included in the sample. More than 6,000 individuals completed the survey, and the study found that after watching a cat video people generally reported more energy, fewer negative emotions, and more positive emotions. (a) Would this be considered a simple random sample from a target population? Why or why not? (b) Ignoring sampling bias, what other ways could bias have been introduced into this study?

Diet Cola and Weight Gain in Rats A study \(^{32}\) fed one group of rats a diet that included yogurt sweetened with sugar, and another group of rats a diet that included yogurt sweetened with a zerocalorie artificial sweetener commonly found in diet cola. The rats that were fed a zero-calorie sweetener gained more weight and more body fat compared to the rats that were fed sugar. After the study was published, many news articles discussed the implication that people who drink diet soda gain more weight. Explain why we cannot conclude that this is necessarily true.

Armoring Military Planes During the Second World War, the U.S. military collected data on bullet holes found in B-24 bombers that returned from flight missions. The data showed that most bullet holes were found in the wings and tail of the aircraft. Therefore, the military reasoned that more armor should be added to these regions, as they are more likely to be shot. Abraham Wold, a famous statistician of the era, is reported to have argued against this reasoning. In fact, he argued that based on these data more armor should be added to the center of the plane, and NOT the wings and tail. What was Wald's argument?

National Health Statistics The Centers for Disease Control and Prevention (CDC) administers a large number of survey programs for monitoring the status of health and health care in the US. One of these programs is the National Health and Nutrition Examination Survey (NHANES), which interviews and examines a random sample of about 5000 people in the US each year. The survey includes questions about health, nutrition, and behavior, while the examination includes physical measurements and lab tests. Another program is the National Hospital Ambulatory Medical Care Survey (NHAMCS), which includes information from hospital records for a random sample of individuals treated in hospital emergency rooms around the country. (a) To what population can we reasonably generalize findings from the NHANES? (b) To what population can we reasonably generalize findings from the NHAMCS? (c) For each of the questions below, indicate which survey, NHANES or NHAMCS, would probably be more appropriate to address the issue. ii. What proportion of emergency room visits in the US involve sports-related injuries? iii. Is there a difference in the average waiting time to be seen by an emergency room physician between male and female patients? iv. What proportion of US residents have visited an emergency room within the past year?

Describe an association between two variables. Give a confounding variable that may help to account for this association. More ice cream sales have been linked to more deaths by drowning.

Describe an association between two variables. Give a confounding variable that may help to account for this association. People who own a yacht are more likely to buy a sports car.

Describe an association between two variables. Give a confounding variable that may help to account for this association. Air pollution is higher in places with a higher proportion of paved ground relative to grassy ground.