Question: Let revisit the school system described in

> Exercises 21, 35, and 37 describe an experiment investigating the effectiveness of omega-3 fats in treating bipolar disorder. Suppose some of the 30 subjects were very active people who walked a lot or got vigorous exercise several times a week, while ot

> Exercises 24 and 36 describe an experiment investigating the effectiveness of exercise in combating insomnia. Researchers randomly assigned half of the 40 volunteers to an exercise program. 1. Why was it important to randomize in deciding who would exerc

> Exercises 21 and 35 describe an experiment investigating a dietary approach to treating bipolar disorder. Researchers randomly assigned 30 subjects to two treatment groups, one group taking a high dose of omega-3 fats and the other a placebo. 1. Why was

> Exercise 24 describes an experiment showing that exercise helped people sleep better. The experiment involved other groups of subjects who didn’t exercise. Why didn’t the experimenters just have everyone exercise and see if their ability to sleep improve

> The correlation between Fuel Efficiency (as measured by miles per gallon) and Price of 150 cars at a large dealership is r=0.34. Explain whether or not each of these possible conclusions is justified: 1. The more you pay, the lower the fuel efficiency of

> Exercise 21 describes an experiment that showed that high doses of omega-3 fats might be of benefit to people with bipolar disorder. The experiment involved a control group of subjects who received a placebo. Why didn’t the experimenters just give everyo

> Pew Research compared respondents to an ordinary 5-day telephone survey with respondents to a 4-month-long rigorous survey designed to generate the highest possible response rate. They were especially interested in identifying any variables for which tho

> Athletes who had suffered hamstring injuries were randomly assigned to one of two exercise programs. Those who engaged in static stretching returned to sports activity in a mean of 15.2 days faster than those assigned to a program of agility and trunk st

> A dog food company wants to compare a new lower-calorie food with their standard dog food to see if it effective in helping inactive dogs maintain a healthy weight. They have found several dog owners willing to participate in the trial. The dogs have bee

> Some people claim they can get relief from migraine headache pain by drinking a large glass of ice water. Researchers plan to enlist several people who suffer from migraines in a test. When a participant experiences a migraine headache, he or she will ta

> Some people who race greyhounds give the dogs large doses of vitamin C in the belief that the dogs will run faster. Investigators at the University of Florida tried three different diets in random order on each of five racing greyhounds. They were surpri

> The May 4, 2000, issue of Science News reported that, contrary to popular belief, depressed individuals cry no more often in response to sad situations than non-depressed people. Researchers studied 23 men and 48 women with major depression and 9 men and

> Scientists at a major pharmaceutical firm investigated the effectiveness of an herbal compound to treat the common cold. They exposed each subject to a cold virus, then gave him or her either the herbal compound or a sugar solution known to have no effec

> In 2002, the journal Science reported that a study of women in Finland indicated that having sons shortened the life spans of mothers by about 34 weeks per son, but that daughters helped to lengthen the mother lives. The data came from church records fro

> Researchers have linked an increase in the incidence of breast cancer in Italy to dioxin released by an industrial accident in 1976. The study identified 981 women who lived near the site of the accident and were under age 40 at the time. Fifteen of the

> The correlation between Age and Income as measured on 100 people is r=0.75. Explain whether or not each of these possible conclusions is justified: 1. When Age increases, Income increases as well. 2. The form of the relationship between Age and Income is

> After menopause, some women take supplemental estrogen. There is some concern that if these women also drink alcohol, their estrogen levels will rise too high. Twelve volunteers who were receiving supplemental estrogen were randomly divided into two grou

> Is diet or exercise effective in combating insomnia? Some believe that cutting out desserts can help alleviate the problem, while others recommend exercise. Forty volunteers suffering from insomnia agreed to participate in a month-long test. Half were ra

> In a test of roughly 200 men and women, those with moderately high blood pressure (averaging 164/89 mm Hg) did worse on tests of memory and reaction time than those with normal blood pressure. (Hypertension 36 [2000]: 1079)

> Among a group of disabled women aged 65 and older who were tracked for several years, those who had a vitamin B12 deficiency were twice as likely to suffer severe depression as those who did not. (American Journal of Psychiatry 157 [2000]: 715)

> Over a 4-month period, among 30 people with bipolar disorder, patients who were given a high dose (10 g/day) of omega-3 fats from fish oil improved more than those given a placebo. (Archives of General Psychiatry 56 [1999]: 407)

> Coffee stations in offices often just ask users to leave money in a tray to pay for their coffee, but many people cheat. Researchers at Newcastle University replaced the picture of flowers on the wall behind the coffee station with a picture of staring e

> Researchers studied the herb black cohosh as a treatment for hot flashes caused by menopause. They randomly assigned 351 women aged 45 to 55 who reported at least two hot flashes a day to one of five groups: (1) black cohosh, (2) a multiherb supplement

> When spending large amounts to purchase advertising time, companies want to know what audience they’ll reach. In January 2011, a poll asked 1008 American adults whether they planned to watch the upcoming Super Bowl. Men and women were asked separately wh

> Multiple sclerosis (MS) is an autoimmune disease that strikes more often the farther people live from the equator. Could vitamin D which most people get from the sun ultraviolet rays be a factor? Researchers compared vitamin D levels in blood samples fro

> Researchers who examined health records of thousands of males found that men who died of myocardial infarction (heart attack) tended to be shorter than men who did not. 1. Is this an experiment? If not, what kind of study is it? 2. Is it correct to concl

> A survey of the world nations in 2014 shows a strong positive correlation between percentage of the country using smartphones and life expectancy in years at birth. 1. Does this mean that smartphones are good for your health? 2. What might explain the st

> For his statistics class experiment, researcher J. Gilbert decided to study how parents income affects children performance on standardized tests like the SAT. He proposed to collect information from a random sample of test takers and examine the relatio

> Consider each of these situations. Do you think the proposed sampling method is appropriate? Explain. 1. We want to know if there is neighborhood support to turn a vacant lot into a playground. We spend a Saturday afternoon going door-to-door in the neig

> Consider each of these situations. Do you think the proposed sampling method is appropriate? Explain. 1. We want to know what percentage of local doctors accept Medicaid patients. We call the offices of 50 doctors randomly selected from local Yellow Page

> In recent years, beaches around the world have seen fish washing up on shore in large numbers. One group of scientists thought that leakage from the damaged Fukushima nuclear power plant in Japan might be a cause. They propose to measure the mean amount

> Concerned about reports of discolored scales on fish caught downstream from a newly sited chemical plant, scientists set up a field station in a shoreline public park. For one week, they asked fishermen there to bring any fish they caught to the field st

> Sammy Salsa, a small local company, produces 20 cases of salsa a day. Each case contains 12 jars and is imprinted with a code indicating the date and batch number. To help maintain consistency, at the end of each day, Sammy selects three jars of salsa, w

> A manufacturing company employs 14 project managers, 48 supervisors, and 377 laborers. In an effort to keep informed about any possible sources of employee discontent, management wants to conduct job satisfaction interviews with a sample of employees eve

> Between quarterly audits, a company likes to check on its accounting procedures to address any problems before they become serious. The accounting staff processes payments on about 120 orders each day. The next day, the supervisor rechecks 10 of the tran

> Occasionally, when I fill my car with gas, I figure out how many miles per gallon my car got. I wrote down those results after six fill-ups in the past few months. Overall, it appears my car gets 28.8 miles per gallon. 1. What statistic have I calculated

> How long is your arm compared with your hand size? Put your right thumb at your left shoulder bone, stretch your hand open wide, and extend your hand down your arm. Put your thumb at the place where your little finger is, and extend down the arm again. R

> A researcher studies children in elementary school and finds a strong positive linear association between height and reading scores. 1. Does this mean that taller children are generally better readers? 2. What might explain the strong correlation?

> What about drawing a random sample only from cell phone exchanges? Discuss the advantages and disadvantages of such a sampling method compared with surveying randomly generated telephone numbers from non-cell phone exchanges. Do you think these advantage

> Any time we conduct a survey, we must take care to avoid under coverage. Suppose we plan to select 500 names from the city phone book, call their homes between noon and 4 pm, and interview whoever answers, anticipating contacts with at least 200 people.

> Examine each of the following questions for possible bias. If you think the question is biased, indicate how and propose a better question. 1. Do you think high school students should be required to wear uniforms? 2. Given humanity great tradition of exp

> Examine each of the following questions for possible bias. If you think the question is biased, indicate how and propose a better question. 1. Should companies that pollute the environment be compelled to pay the costs of cleanup? 2. Given that 18-year-o

> An online poll on a website asked: A nationwide ban of the diet supplement ephedra went into effect recently. The herbal stimulant has been linked to 155 deaths and many more heart attacks and strokes. Ephedra manufacturer NVE Pharmaceuticals, claiming t

> Two members of the PTA committee in Exercises 26 and 27 have proposed different questions to ask in seeking parents opinions. Question 1: Should elementary school age children have to pass high-stakes tests in order to remain with their classmates? Quest

> The survey described in Exercise 29 asked: Many people believe this playground is too small and in need of repair. Do you think the playground should be repaired and expanded even if that means raising the entrance fee to the park? Describe two ways this

> An amusement park has opened a new roller coaster. It is so popular that people are waiting for up to 3 hours for a 2-minute ride. Concerned about how patrons (who paid a large amount to enter the park and ride on the rides) feel about this, they survey

> Some people have been complaining that the children playground at a municipal park is too small and is in need of repair. Managers of the park decide to survey city residents to see if they believe the playground should be rebuilt. They hand out question

> For your political science class, you’d like to take a survey from a sample of all the Catholic church members in your city. A list of churches shows 17 Catholic churches within the city limits. Rather than try to obtain a list of all members of all thes

> Students in the economics class discussed in Exercise 31 also wrote these conclusions. Explain the mistakes they made. 1. There was a very strong correlation of 1.22 between Life Expectancy and GDP. 2. The correlation between Literacy Rate and GDP was 0.

> In a large city school system with 20 elementary schools, the school board is considering the adoption of a new policy that would require elementary students to pass a test in order to be promoted to the next grade. The PTA wants to find out whether pare

> Prior to the mayoral election discussed in Exercise 24, the newspaper also conducted a poll. The paper surveyed a random sample of registered voters stratified by political party, age, sex, and area of residence. This poll predicted that Amabo would win

> A local TV station conducted a PulsePoll about the upcoming mayoral election. Evening news viewers were invited to text in their votes, with the results to be announced on the late-night news. Based on the texts, the station predicted that Amabo would wi

> Dairy inspectors visit farms unannounced and take samples of the milk to test for contamination. If the milk is found to contain dirt, antibiotics, or other foreign matter, the milk will be destroyed and the farm re-inspected until purity is restored.

> A company packaging snack foods maintains quality control by randomly selecting 10 cases from each day production and weighing the bags. Then they open one bag from each case and inspect the contents.

> State police set up a roadblock to estimate the percentage of cars with up-to-date registration, insurance, and safety inspection stickers. They usually find problems with about 10% of the cars they stop.

> The Environmental Protection Agency took soil samples at 16 locations near a former industrial waste dump and checked each for evidence of toxic chemicals. They found no elevated levels of any harmful substances.

> Hoping to learn what issues may resonate with voters in the coming election, the campaign director for a mayoral candidate selects one block from each of the city election districts. Staff members go there and interview all the adult residents they can f

> A question posted on the gamefaqs.com website asked visitors to the site, Do you have an active social life outside the Internet? 22% of the 55,581 respondents said No or Not really, most of my personal contact is online.

> Your economics instructor assigns your class to investigate factors associated with the gross domestic product (GDP) of nations. Each student examines a different factor (such as Life Expectancy, Literacy Rate, etc.) for a few countries and reports to th

> Consumers Union asked all subscribers whether they had used alternative medical treatments and, if so, whether they had benefited from them. For almost all of the treatments, approximately 20% of those responding reported cures or substantial improvement

> At its website (www.gallup.com), the Gallup Poll publishes results of a new survey each day. Scroll down to the end, and you find a statement that includes words such as these: Results are based on telephone interviews with 1016 national adults, aged 18

> Major League Baseball tests players to see whether they are using performance-enhancing drugs. Officials select a team at random, and a drug-testing crew shows up unannounced to test all 40 players on the team. Each testing day can be considered a study

> For their class project, a group of statistics students decide to survey the student body to assess opinions about the proposed new student center. Their sample of 200 contained 50 first-year students, 50 sophomores, 50 juniors, and 50 seniors. 1. Do you

> Through their Roper Reports Worldwide, GfK Roper conducts a global consumer survey to help multinational companies understand different consumer attitudes throughout the world. Within 30 countries, the researchers interview 1000 people aged 1365. Their s

> Consider again the post-1950 trend in U.S. GDP we examined in Exercise 61. Here are regression output and a residual plot when we use the log of GDP in the model. Is this a better model for GDP? Explain. Would you want to consider a different re-expressi

> The scatterplot shows the gross domestic product (GDP) of the United States in trillions of 2009 dollars plotted against years since 1950 A linear model fit to the relationship looks like this: Dependent variable is: GDP($T) R-squared = 96.9% s = 0.8137

> In Exercise 58 we looked at United Nations data about a country GDP and the average number of people per room (Crowdedness) in housing there. For a re-expression, a student tried the reciprocal 10000|sol|GDP, representing the number of people per $10,000

> Let try the re-expressed variable Fuel Consumption (gal/100 mi) to examine the fuel efficiency of the 11 cars in Exercise 57. Here are the revised regression analysis and residuals plot: Dependent variable is: Fuel Consumption R-squared = 89.2% 1. Explai

> In a Chance magazine article (Summer 2005), Danielle Vasilescu and Howard Wainer used data from the United Nations Center for Human Settlements to investigate aspects of living conditions for several countries. Among the variables they looked at were the

> Hurricane Katrina hurricane force winds extended 120 miles from its center. Katrina was a big storm, and that affects how we think about the prediction errors. Suppose we add 120 miles to each error to get an idea of how far from the predicted track we m

> Now consider the variables igÆ’ and weight in the data set Igf13. 1. Fit a regression model. If the data violate any assumptions, find a suitable re-expression of igÆ’. 2. Add sex to the model in part a as a predictor. Interpret the coefficient of sex. 3

> As the example in the chapter indicates, one of the important factors determining a car Fuel Efficiency is its Weight. Let examine this relationship again, for 11 cars. 1. Describe the association between these variables shown in the scatterplot at the t

> In Chapter 4, we examined Consider the wind speeds in the Hopkins Forest over the course of a year. Here the scatterplot we saw then: (Data in Hopkins Forest) 1. Describe the pattern you see here. 2. Should we try re-expressing either variable to make th

> In Exercise 29, we considered whether a linear model would be appropriate to describe the trend in the number of passengers departing from the Oakland (CA) airport each month since the start of 1997. If we fit a regression model, we obtain this residual

> Look once more at the data from Tour de France 2016. In Exercise 52, we looked at the whole history of the race, but now let consider just the modern era from 1967 on. 1. Make a scatterplot and find the regression of Avg Speed by Year only for years from

> The Consumer Price Index (CPI) tracks the prices of consumer goods in the United States, as shown in the following table. The CPI is reported monthly, but we can look at selected values. The table shows the January CPI at five-year intervals. It indicate

> We met the Tour de France dataset in Chapter 1 (in Just Checking). Look at the Tour de France dataset. One hundred years ago, the fastest rider finished the course at an average speed of about 25.3 kph (around 15.8 mph). By the 21st century, winning ride

> The World Bank reports many demographic statistics about countries of the world. The data file holds the Fertility rate (births per woman) and the female Life Expectancy at birth (in years) for 200 countries of the world. Response variable is: Life expec

> In Chapter 7, we There is found a relationship between the age of a bridge in Tompkins County, New York, and its condition as found by inspection. (Data in Tompkins County Bridges 2016) But we considered only bridges built or replaced since 1900. Tompkin

> Look again at the graph of the age at first marriage for women in Exercise 42. Here is a regression model for the data on women, along with a residuals plot: Response variable is: Women R-squared = 61.1% s = 1.474 1. Based on this model, what would you p

> In Exercise 46, we saw in the Swim the Lake 2016 data that Vicki Keith round-trip swim of Lake Ontario was an obvious outlier among the other one-way times. Here is the new regression after this unusual point is removed: Dependent variable is Time R-Squa

> The errors in predicting hurricane tracks (examined in this chapter) were given in nautical miles. A statutory mile is 0.86898 nautical mile. Most people living on the Gulf Coast of the United States would prefer to know the prediction errors in statutor

> We removed humans from the scatterplot of the Gestation data in Exercise 45 because our species was an outlier in life expectancy. The resulting scatterplot (below) shows two points that now may be of concern. The point in the upper right corner of this

> People swam across Lake Ontario from Niagara-on-the-Lake to Toronto (52 km, or about 32.3 mi) 62 times between 1954 and 2016. We might be interested in whether the swimmers are getting any faster or slower. Here are the regression of the crossing Times (

> For humans, pregnancy lasts about 280 days. In other species of animals, the length of time from conception to birth varies. Is there any evidence that the gestation period is related to the animal life span? The first scatterplot shows Gestation Period

> Has the trend of decreasing difference in age at first marriage seen in Exercise 42 gotten stronger recently? The scatterplot and residual plot for the data from 1980 through 2015, along with a regression for just those years, are below. 1. Is this linea

> In Exercise 41, you investigated the federal rate on 3-month Treasury bills between 1950 and 1980. The scatterplot below shows that the trend changed dramatically after 1980, so we computed a new regression model for the years 1981 to 2015. Here the mode

> The graph shows the ages of both men and women at first marriage (www.census.gov). Clearly, the patterns for men and women are similar. But are the two lines getting closer together? Here are a timeplot showing the difference in average age (menÃ&

> Here are a plot and regression output showing the federal rate on 3-month Treasury bills from 1950 to 1980, and a regression model fit to the relationship between the Rate (in %) and Years Since 1950 (www.gpoaccess.gov/eop/). 1. What is the correlation b

> How does the speed at which you drive affect your fuel economy? To find out, researchers drove a compact car for 200 miles at speeds ranging from 35 to 75 miles per hour. From their data, they created the model Fuel Efficiency=320.1 Speed and created thi

> After keeping track of his heating expenses for several winters, a homeowner believes he can estimate the monthly cost from the average daily Fahrenheit temperature by using the model Cost=133 2.13 Temp. Here is the residuals plot for his data: 1. Interp

> A college admissions officer, defending the college use of SAT scores in the admissions process, produced the following graph. It shows the mean GPAs for last year freshmen, grouped by SAT scores. How strong is the evidence that SAT Score is a good predi

> A researcher investigating the association between two variables collected some data and was surprised when he calculated the correlation. He had expected to find a fairly strong association, yet the correlation was near 0. Discouraged, he didn’t bother

> To measure progress in reading ability, students at an elementary school take a reading comprehension test every year. Scores are measured in grade-level units; that is, a score of 4.2 means that a student is reading at slightly above the expected level

> A researcher studying violent behavior in elementary school children asks the children parents how much time each child spends playing computer games and has their teachers rate each child on the level of aggressiveness they display while playing with ot

> Suppose a researcher studying health issues measures blood pressure and the percentage of body fat for several adult males and finds a strong positive association. Describe three different possible cause-and-effect relationships that might be present.

> The original five points in Exercise 33 produce a regression line with slope 0. Match each of the red points (ae) with the slope of the line after that one point is added: 1. 0.45 2. 0.30 3. 0.00 4. 0.05 5. 0.85

> The scatterplot shows five blue data points at the left. Not surprisingly, the correlation for these points is r=0. Suppose one additional data point is added at one of the five positions suggested below in red. Match each point (ae) with the correct new

> Each of the following scatterplots shows a cluster of points and one stray point. For each, answer these questions: 1. In what way is the point unusual? Does it have high leverage, a large residual, or both? 2. Do you think that point is an influential p

> Each of these four scatterplots shows a cluster of points and one stray point. For each, answer these questions: 1. In what way is the point unusual? Does it have high leverage, a large residual, or both? 2. Do you think that point is an influential poin