MTHM 168 Chapter 1

State whether the following claim is one of association and causation, association only, or neither association nor causation. Cat owners tend to be more educated than dog owners.

Association only

State whether the following claim is one of association and causation, association only, or neither association nor causation. Cell phone radiation leads to deaths in honey bees.

Association with causation

State whether the following claim is one of association and causation, association only, or neither association nor causation. Daily exercise improves mental performance.

Association with causation

State whether the following claim is one of association and causation, association only, or neither association nor causation. Want to lose weight? Eat more fiber!

Association with causation

Indicate whether we should trust the results of the following study. Is the method of data collection biased? Ask a random sample of students at the library on a Friday night "How many hours a week do you study?" to collect data to estimate the average number of hours a week that all college students study.

Biased

Indicate whether we should trust the results of the following study. Is the method of data collection biased? Take 16 apples off the top of a truckload of apples and measure the amount of bruising on those apples to estimate how much bruising there is, on average, in the whole truckload.

Biased

Is the following variable categorical or quantitative? Collect data from a sample of teenagers with a question that asks "Do you eat at least five servings a day of fruit and vegetables?"

Categorical

Is the following variable categorical or quantitative? People in a city are asked if they support a new recycling law.

Categorical

Is the following variable categorical or quantitative? Record whether or not the literacy rate is over 90% for each country in the world.

Categorical

Is the following an experiment or an observational study? To examine whether planting trees reduces air pollution, we find a sample of city blocks with similar levels of air pollution and we then plant trees in half of the blocks in the sample. After waiting an appropriate amount of time, we measure air pollution levels.

Experiment

Is the following an experiment or an observational study? To examine whether playing music in a store increases the amount customers spend, we randomly assign some stores to play music and some to stay silent and compare the average amount spent by customers.

Experiment

A relationship between two variables is described below. We can think of one variable as helping to explain the other. Is the indicated variable the explanatory variable or the response variable? Lung capacity and number of years smoking cigarettes. Number of years smoking cigarettes is the:

Explanatory Variable

State whether the following claim is one of association and causation, association only, or neither association nor causation. Among college students, no link found between number of friends on social networking websites and size of the university.

Neither association nor causation

Indicate whether we should trust the results of the following study. Is the method of data collection biased?T ake a random sample of one type of printer and test each printer to see how many pages of text each will print before the ink runs out. Use the average from the sample to estimate how many pages, on average, all printers of this type will last before the ink runs out.

Not biased

The population is adults between the ages of 18 and 22. A sample of 300 students is collected from a local university, and each student at the university had an equal chance of being selected for the sample. State whether or not the sampling method described produces a random sample from the given population.

Not random

The population is all people who visit the website CNN.com. All visitors to the website are invited to take part in the daily online poll. State whether or not the sampling method described produces a random sample from the given population.

Not random

Do the following data come from an experiment or an observational study? A gene called ACTN3 encodes a protein which functions in fast-twitch muscles. Some people have a variant of this gene that cannot yield this protein. (So we might call the gene variant a possible non-sprinting gene.) To address the question of whether this gene is associated with sprinting ability, geneticists tested people from three different groups: world-class sprinters, world-class marathon runners, and a control group of non-athletes. In the samples tested, 6% of the sprinters had the gene variant, compared with 18% of the non-athletes and 24% of the marathon runners. This study1 suggests that sprinters are less likely than non-sprinters to have the gene variant.

Observational study

Is the following an experiment or an observational study? To examine whether eating brown rice affects metabolism, we ask a random sample of people whether they eat brown rice and we also measure their metabolism rate.

Observational study

State whether the data are best described as a population or a sample. A subscription-based music website tracks its total number of active users.

Population

Is the following variable categorical or quantitative? Record the percentage change in the price of a stock for 300 stocks publicly traded on Wall Street.

Quantitative

The population is incoming students at a particular university. The name of each incoming student is thrown into a hat, the names are mixed, and 25 names (each corresponding to a different student) are drawn from the hat. State whether or not the sampling method described produces a random sample from the given population.

Random

The population is the approximately 25,000 protein-coding genes in human DNA. Each gene is assigned a number (from 1 to 25,000 ), and computer software is used to randomly select 300 of these numbers yielding a sample of 300 genes. State whether or not the sampling method described produces a random sample from the given population.

Random

A relationship between two variables is described below. We can think of one variable as helping to explain the other. Is the indicated variable the explanatory variable or the response variable? Blood alcohol content (BAC) and number of alcoholic drinks consumed. BAC is the:

Response Variable

A relationship between two variables is described below. We can think of one variable as helping to explain the other. Is the indicated variable the explanatory variable or the response variable? Amount of fertilizer used and the yield of a crop. Yield of the crop is:

Response variable

State whether the data are best described as a population or a sample. A questionnaire to understand athletic participation on a college campus is emailed to 40 college students, and all of them respond.

Sample

State whether the data are best described as a population or a sample. To estimate size of trout in a lake, an angler records the weight of 5 trout he catches over a weekend.

Sample

Nuts and Cholesterol Several studies have been performed to examine the relationship between nut consumption and cholesterol levels. Here we consider two such studies. In Study 1,1 participants were randomly assigned into two groups: one group was given nuts to eat each day, and the other group was told to consume a diet without nuts. In Study 2,2 participants were free to follow their own diet, and reported how many nuts they consumed. Cholesterol levels were measured for all participants, and both studies found that nut consumption was associated with lower levels of LDL ("bad") cholesterol. Based on the information above, which study do you think provides better evidence that nut consumption reduces LDL cholesterol?

Study 1

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. Do you think that this sample of 808 people is a representative sample of all US residents between the ages of 18 and 34?

Yes

Music Volume and Beer Consumption In 2008, a study was conducted measuring the impact that music volume has on beer consumption. The researchers went into bars, controlled the music volume, and measured how much beer was consumed. The article states that ''the sound level of the environmental music was manipulated according to a randomization scheme." It was found that louder music corresponds to more beer consumption. Does this provide evidence that louder music causes people to drink more beer? Why or why not?

Yes, it does, because an association was found and the result comes from a randomized experiment.

Don't Text While Studying! For the 2015 Intel Science Fair, two brothers in high school recruited 47 of their classmates to take part in a two-stage study. Participants had to read two different passages and then answer questions on them, and each person's score was recorded for each of the two tests. There were no distractions for one of the passages, but participants received text messages while they read the other passage. Participants scored significantly worse when distracted by incoming texts. Participants were also asked if they thought they were good at multitasking (yes or no) but "even students who were confident of their abilities did just as poorly on the test while texting."1 a) How many cases are there? b) How many variables are mentioned in the description? How many of these are categorical? How many are quantitative? c) If we created a dataset of the information with cases as rows and variables as columns, how many rows and how many columns would the dataset have?

a) 47 Cases b) 3 Variables Mentioned in the Description, 1 Categorical, 2 Quantitative c) 47 Rows, 3 Columns

Is Your Nose Getting Bigger? Next time you see an elderly man, check out his nose and ears! While most parts of the human body stop growing as we reach adulthood, studies show that noses and ears continue to grow larger throughout our lifetime. In one study1 examining noses, researchers report "Age significantly influenced all analyzed measurements:" including volume, surface area, height, and width of noses. The gender of the 859 participants in the study was also recorded, and the study reports that "male increments in nasal dimensions were larger than female ones." a) How many variables are mentioned in this description? b) How many of the variables are categorical? How many are quantitative? c) If we created a dataset of the information with cases as rows and variables as columns, how many rows and how many columns would the dataset have?

a) 6 b) 1 Categorical, 5 Quantitative c) 859 Rows, 6 Columns

Rowing Solo Across the Atlantic Ocean On January 14, 2012, Andrew Brown of Great Britain set the world record time (40 days) for rowing solo across the northern Atlantic Ocean. On March 14, 2010, Katie Spotz of the United States became the youngest person to ever row solo across the Atlantic when she completed it in 70 days at the age of 22 years old. Table 1 shows the times for males and females who rowed solo across the Atlantic Ocean in the last few years. Male Times: 40, 87, 78, 106, 67 Female Times: 70, 153, 81 a) How many cases are there in this dataset? b) How many variables are there in this dataset?

a) 8 b) 2

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 7000 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. i. Are overweight people more likely to develop diabetes? 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?

a) All people in the US b) All hospital emergency rooms in the US c) i. NHANES ii. NHAMCS iii. NHAMCS iv. NHANES

Be Sure to Get Your Beauty Sleep! New research1 supports the idea that people who get a good night's sleep look more attractive. In the study, 23 subjects ages 18 to 31 were photographed twice, once after a good night's sleep and once after being kept awake for 31 hours. Hair, make-up, clothing, and lighting were the same for both photographs. Observers then rated the photographs for attractiveness, and the average rating under the two conditions was compared. The researchers report in the British Medical Journal that "Our findings show that sleep-deprived people appear less attractive compared with when they are well rested." a) What is the explanatory variable? What is the response variable? b) Is this an experiment or an observational study? If it is an experiment, is it a randomized comparative design or a matched pairs design? c) Can we conclude that sleep deprivation causes people to look less attractive? Why or why not?

a) Amount of rest, Attractiveness rating b) Matched pairs experiment c) Yes, we can, because an association was found and the result comes from a randomized experiment

Trans-Generational Effects of Diet Can experiences of parents affect future children? New studies1 suggest that they can: Early life experiences of parents appear to cause permanent changes in sperm and eggs. In one study, some male rats were fed a high-fat diet with 43% of calories from fat (a typical American diet), while others were fed a normal healthy rat diet. Not surprisingly, the rats fed the high-fat diet were far more likely than the normal-diet rats to develop metabolic syndrome (characterized by such things as excess weight, excess fat, insulin resistance, and glucose intolerance.) What surprised the scientists was that the daughters of these rats were also far more likely to develop metabolic syndrome than the daughters of rats fed healthy diets. None of the daughters and none of the mothers ate a high-fat diet and the fathers did not have any contact with the daughters. The high-fat diet of the fathers appeared to cause negative effects for their daughters. One variable is whether or not the male was fed a high-fat diet or a normal diet and another variable is whether or not the daughters developed metabolic syndrome. a) Is the type of diet variable categorical or quantitative? b) Is metabolic status of the daughters variable categorical or quantitative? c) Is metabolic status of the daughters the explanatory variable or the response variable?

a) Categorical b) Categorical c) Response Variable

Late Night Eating It is well-known that lack of sleep impairs concentration and alertness, and this might be due partly to late night food consumption. A 2015 study1 took 44 people aged 21 to 50 and gave them unlimited access to food and drink during the day, but allowed them only 4 hours of sleep per night for three consecutive nights. On the fourth night, all participants again had to stay up until 4 am, but this time participants were randomized into two groups; one group was only given access to water from 10 pm until their bedtime at 4 am while the other group still had unlimited access to food and drink for all hours. The group forced to fast from 10 pm on performed significantly better on tests of reaction time and had fewer attention lapses than the group with access to late night food. a) Is the explanatory variable categorical or quantitative? b) Are the response variables categorical or quantitative? c) Is this an observational study or a randomized experiment? d) Can we conclude that eating late at night worsens some of the typical effects of sleep deprivation (reaction time and attention lapses)? e) Are there likely to be confounding variables?

a) Categorical b) Quantitative c) Experiment d) Yes e) No

Spider Sex Play Spiders regularly engage in spider foreplay that does not culminate in mating. Male spiders mature faster than female spiders and often practice the mating routine on not-yet-mature females. Since male spiders run the risk of getting eaten by female spiders, biologists wondered why spiders engage in this behavior. In one study,1 some spiders were allowed to participate in these near-matings, while other maturing spiders were isolated. When the spiders were fully mature, the scientists observed real matings. They discovered that if either partner had participated at least once in mock sex, the pair reached the point of real mating significantly faster than inexperienced spiders did. (Mating faster is, apparently, a real advantage in the spider world.) One variable is whether or not the spider engaged in mock-sex. Another is the length of time for real mating once the spider is fully mature. a) Is the variable whether or not the spider engaged in mock sex categorical or quantitative? b) Is the variable length of time for real mating categorical or quantitative? c) Is the variable length of time for real mating the explanatory variable or the response variable?

a) Categorical b) Quantitative c) Response Variable

How Many People Wash Their Hands After Using the Washroom? 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.1 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) Identify each of the following variables as categorical or quantitative: - The variable indicating whether or not the person washed their hands. - The variable indicating the gender of the individual. - The variable indicating the location of the observation. 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?

a) Categorical, Categorical, Categorical b) Self-reported behavior is often inaccurate and biased

Wearing a Uniform to Work The website fox6now.com held an online poll in June 2015 asking "What do you think about the concept of having an everyday uniform for work, like Steve Jobs did?" Of the people who answered the question, 24% said they loved the idea, 58% said they hated the idea, and 18% said that they already wore a uniform to work. (a) Are the people who answered the poll likely to be representative of all adult workers? (b) Is it reasonable to generalize this result and estimate that 24% of all adult workers would like to wear a uniform to work?

a) No b) No

To Spoon or Not to Spoon? Does cuddling after sex help boost sexual and relationship satisfaction? A study1 involving 335 participants involved in romantic relationships found that people who reported more time spent on cuddling and affection after sex were more satisfied with their sex lives and relationships. This fact held true for both men and women. The average amount of time spent cuddling after sex was 15 minutes, and time spent on after sex affection was more strongly associated with sexual and relationship satisfaction than time spent on either foreplay or sex itself. a) Is this an observational study or a randomized experiment? b) Can we conclude that spending more time on affection after sex increases sexual and relationship satisfaction? c) A headline for an article2 describing this study was titled "To Spoon or Not to Spoon? After-Sex Affection Boosts Sexual and Relationship Satisfaction." Does the study support this title? d) The title of the scientific article the study was originally published in is "Post Sex Affectionate Exchanges Promote Sexual and Relationship Satisfaction." Does the study support this title?

a) Observational Study b) No c) No d) No

Urban Brains and Rural Brains A study published in 2010 showed that city dwellers have a 21% higher risk of developing anxiety disorders and a 39% higher risk of developing mood disorders than those who live in the country. A follow-up study published in 2011 used brain scans of city dwellers and country dwellers as they took a difficult math test.1 To increase the stress of the participants, those conducting the study tried to humiliate the participants by telling them how poorly they were doing on the test. The brain scans showed very different levels of activity in stress centers of the brain, with the urban dwellers having greater brain activity than rural dwellers in areas that react to stress. a) Is the 2010 study an experiment or an observational study? b) Can we conclude from the 2010 study that living in a city increases a person's likelihood of developing an anxiety disorder or mood disorder? c) Is the 2011 study an experiment or an observational study? d) Can we conclude from the 2011 study that living in a city increases activity in stress centers of the brain when a person is under stress?

a) Observational study b) No c) Observational study d) No

Sitting is the New Smoking A 2014 headline reads "Sitting is the New Smoking: Ways a Sedentary Lifestyle is Killing You"1, and explains the mounting evidence for ways in which sitting is bad for you. A more recent large 2015 study2 contributed to this evidence by following 69,260 men and 77,462 women and finding that for women, those who spent more leisure time sitting were significantly more likely to get cancer. a) Is the explanatory variable categorical or quantitative? b) Is the response variable categorical or quantitative? c) Is the 2015 study an observational study or a randomized experiment? d) Can we conclude from the 2015 study that spending more leisure time sitting causes cancer in women? e) Can we conclude from the 2015 study that spending more leisure time sitting does not cause cancer in women?

a) Quantitative b) Categorical c) Observational Study d) No e) No

Hormones and Fish Fertility When women take birth control pills, some of the hormones found in the pills eventually make their way into lakes and waterways. In one study, a water sample was taken from various lakes. The data indicate that as the concentration of estrogen in the lake water goes up, the fertility level of fish in the lake goes down. The estrogen level is measured in parts per trillion (ppt) and the fertility level is recorded as the percent of eggs fertilized. One variable is concentration of estrogen in the water and another is fertility level of fish. a) Is estrogen concentration categorical or quantitative? b) Is fertility level categorical or quantitative?

a) Quantitative b) Quantitative

Green Spaces Make Kids Smarter A recent article claims that "Green Spaces Make Kids Smarter." The study described in the article involved 2623 schoolchildren in Barcelona. The researchers measured the amount of greenery around the children's schools and then measured the children's working memories and attention spans. The children who had more vegetation around their schools did better on the memory and attention tests. a) What are the cases in this study? b) What is the explanatory variable? c) What is the response variable? d) Does the headline imply causation? e) Is the study an experiment or an observational study? f) Is it appropriate to conclude causation in this case?

a) The 2623 schoolchildren in Barcelona b) Amount greenery around school c) A measure of the child's working memory and attention span d) Yes e) Observational Study f) No

Antibiotics in Infancy and Obesity in Adults "Antibiotics in infancy may cause obesity in adults", claims a recent headline.1 A study in mice randomly assigned infant mice to either be given antibiotics or not, and the mice given antibiotics were more likely to be obese as adults. A separate study in humans found that children who had been given antibiotics before they were a year old (for example, for an ear infection) were more likely to be obese as adults. (Researchers believe the effect may be due to changes in the gut microbiome.) Based on these studies, is the headline an appropriate conclusion to make: a) For mice? b) For humans?

a) Yes b) No

Canadians Stream Music In a random sample of 3500 Canadian consumers, about 71% report that they regularly stream music. a) Is the sample likely to be representative of all Canadian consumers? b) Is it reasonable to generalize this result and estimate that about 71% of all Canadian consumers regularly stream music?

a) Yes b) Yes

Climate Change In July 2015, a poll asked a random sample of 1236 registered voters in Iowa whether they agree or disagree that the world needs to do more to combat climate change. The results show that 65% agree, while 25% disagree and 10% don't know a) Is the sample likely to be representative of all registered voters in Iowa? (b) Is it reasonable to generalize this result and estimate that 65% of all registered voters in Iowa agree that the world needs to do more to combat climate change?

a) Yes b) Yes