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STATS Modeling The World

David E. Bock, Paul F. Velleman, Richard D. De Veaux

Chapter 1

Exploring and Understanding Data

Educators


Problem 1

A February 2010 Gallup Poll question asked, "In politics, as of today, do you consider yourself a
Republican, a Democrat, or an Independent?' The possible responses were "Democrat", "Republican",
"Independent', "Other", and "No Response'. What kind of variable is the response?

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Problem 2

A June 2011 Gallup Poll asked Americans, “Thinking about the job situation in America today,
would you say that it is now a good time or a bad time to find a quality jobs?” The choices were “Good
time” or “Bad time”. What kind of variable is the response?

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Problem 3

A pharmaceutical company conducts an experiment in which a subject takes 100 mg of a substance orally. The researchers measure how many minutes it takes for half of the substance to exit the
bloodstream. What kind of variable is the company studying?

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Problem 4

A medical researcher measures the increase in heart rate of patients under a stress test. What kind of
variable is the researcher studying?

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Problem 5

(Exercises 5–12) For each description of data, identify Who and What were investigated and the population of interest.

Find a newspaper or magazine article in which some data are reported. For the data discussed in the
article, answer the questions above. Include a copy of the article with your report.

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Problem 6

(Exercises 5–12) For each description of data, identify Who and What were investigated and the population of interest.

Find an Internet source that reports on a study and describes the data. Print out the description and
answer the questions above.

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Problem 7

(Exercises 5–12) For each description of data, identify Who and What were investigated and the population of interest.

Ian Walker, a psychologist at the University of Bath, wondered whether drivers treat bicycle riders differently when they wear helmets. He rigged his bicycle with an ultrasonic sensor that could measure how close each car was that passed him. He then rode on alternating days with and without a helmet. Out of 2500 cars passing him, he found that when he wore his helmet, motorists passed 3.35 inches closer to him, on average, than when his head was bare. [NY Times, Dec. 10, 2006]

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Problem 8

(Exercises 5–12) For each description of data, identify Who and What were investigated and the population of interest.
Investments Some companies offer 401$(\mathrm{k})$ retirement plans to employees, permitting them to shift part of their before-tax salaries into investments such as mutual funds. Employers typically match 50$\%$ of the employees contribution up to about 6$\%$ of salary. One company, concerned with what it believed was a low employee participation rate in its 401$(\mathrm{k})$ plan, sampled 30 other companies with similar plans and asked for their 401$(\mathrm{k})$ participation rates.

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Problem 9

(Exercises 5–12) For each description of data, identify Who and What were investigated and the population of interest.

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 alternately taped two posters over the coffee station. During one week, it was a picture of flowers; during the other, it was a pair of staring eyes. They found that the average contribution was significantly higher when the eyes poster was up than when the flowers were there. Apparently, the mere feeling of being watched—even by eyes that were not real—was enough to encourage people to behave more honestly. [NY Times, Dec. 10, 2006]

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Problem 10

(Exercises 5–12) For each description of data, identify Who and What were investigated and the population of interest.

A study conducted by a team of American and Canadian researchers found that during ovulation, a woman can tell whether a man is gay or straight by looking at his face. To explore the subject, the authors conducted three investigations, the first of which involved 40 undergraduate women who were asked to guess the sexual orientation of 80 men based on photos of their face. Half of the men were gay, and the other half were straight. All held similar expressions in the photos or were deemed to be equally attractive. None of the women were using any contraceptive drugs at the time of the test. The result: the closer a woman was to her peak ovulation the more accurate her guess.

(Source: news.yahoo.com/does-ovulation-boost-womans-gaydar-210405621.html)

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Problem 11

(Exercises 5–12) For each description of data, identify Who and What were investigated and the population of interest.

A study begun in 2011 examines the use of stem cells in treating two forms of blindness, Stargardt’s
disease, and dry age-related macular degeneration. Each of the 24 patients entered one of two separate trials in which embryonic stem cells were to be used to treat the condition.

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Problem 12

(Exercises 5–12) For each description of data, identify Who and What were investigated and the population of interest.

The Cleveland Casting Plant is a large, highly automated producer of gray and nodular iron automotive castings for Ford Motor Company. The company is interested in keeping the pouring temperature of the molten iron (in degrees Fahrenheit) close to the specified value of 2550 degrees. Cleveland Casting
measured the pouring temperature for 10 randomly selected crankshafts.

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Problem 13

(Exercises 13–26) For each description of data, identify the W’s, name the variables, specify for each variable whether its use indicates that it should be treated as categorical or quantitative, and, for any quantitative variable, identify the units in which it was measured (or note that they were not provided).

Because of the difficulty of weighing a bear in the woods, researchers caught and measured 54
bears, recording their weight, neck size, length, and sex. They hoped to find a way to estimate weight from the other, more easily determined quantities.

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Problem 14

(Exercises 13–26) For each description of data, identify the W’s, name the variables, specify for each variable whether its use indicates that it should be treated as categorical or quantitative, and, for any quantitative variable, identify the units in which it was measured (or note that they were not provided).

The State Education Department requires local school districts to keep these records on all students: age, race or ethnicity, days absent, current grade level, standardized test scores in reading and mathematics, and any disabilities or special educational needs.

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Problem 15

(Exercises 13–26) For each description of data, identify the W’s, name the variables, specify for each variable whether its use indicates that it should be treated as categorical or quantitative, and, for any quantitative variable, identify the units in which it was measured (or note that they were not provided).

A listing posted by the Arby’s restaurant chain gives, for each of the sandwiches it sells, the type
of meat in the sandwich, the number of calories, and the serving size in ounces. The data might be used to assess the nutritional value of the different sandwiches.

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Problem 16

(Exercises 13–26) For each description of data, identify the W’s, name the variables, specify for each variable whether its use indicates that it should be treated as categorical or quantitative, and, for any quantitative variable, identify the units in which it was measured (or note that they were not provided).

Gallup conducted a series of telephone polls involving 20,392 American adults during 2011.
Among the reported results were the voters’ gender, age, race, party affiliation, whether they were of Hispanic ethnicity, education, region, adults in the household, and phone status (cell phone only/landline only/both, cell phone mostly, and having an unlisted landline number).

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Problem 17

(Exercises 13–26) For each description of data, identify the W’s, name the variables, specify for each variable whether its use indicates that it should be treated as categorical or quantitative, and, for any quantitative variable, identify the units in which it was measured (or note that they were not provided).

Medical researchers at a large city hospital investigating the impact of prenatal care on newborn health collected data from 882 births during 1998–2000. They kept track of the mother’s age, the number of weeks the pregnancy lasted, the type of birth (cesarean, induced, natural), the level of prenatal care the mother had (none, minimal, adequate), the birth weight and sex of the baby,
and whether the baby exhibited health problems (none, minor, major).

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Problem 18

(Exercises 13–26) For each description of data, identify the W’s, name the variables, specify for each variable whether its use indicates that it should be treated as categorical or quantitative, and, for any quantitative variable, identify the units in which it was measured (or note that they were not provided).

In a study appearing in the journal Science, a research team reports that plants in southern England are flowering earlier in the spring. Records of the first flowering dates for 385 species over a period of 47 years show that flowering has advanced an average of 15 days per decade, an indication of climate warming, according to the authors.

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Problem 19

(Exercises 13–26) For each description of data, identify the W’s, name the variables, specify for each variable whether its use indicates that it should be treated as categorical or quantitative, and, for any quantitative variable, identify the units in which it was measured (or note that they were not provided).

Scientists at a major pharmaceutical firm conducted an experiment to study the effectiveness of an herbal compound to treat the common cold. They exposed each patient to a cold virus, then gave them either the herbal compound or a sugar solution known to have no effect on colds. Several days later they assessed each patient’s condition, using a cold severity scale ranging from 0 to 5. They found no evidence of the benefits of the compound.

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Problem 20

(Exercises 13–26) For each description of data, identify the W’s, name the variables, specify for each variable whether its use indicates that it should be treated as categorical or quantitative, and, for any quantitative variable, identify the units in which it was measured (or note that they were not provided).

Business analysts hoping to provide information helpful to American grape growers compiled these
data about vineyards: size (acres), number of years in existence, state, varieties of grapes grown, average case price, gross sales, and percent profit.

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Problem 21

(Exercises 13–26) For each description of data, identify the W’s, name the variables, specify for each variable whether its use indicates that it should be treated as categorical or quantitative, and, for any quantitative variable, identify the units in which it was measured (or note that they were not provided).

In performing research for an ecology class, students at a college in upstate New York collect data on local streams each year. They record a number of biological, chemical, and physical variables, including the stream name, the substrate of the stream (limestone, shale, or mixed), the acidity of the water (pH), the temperature (°C), and the BCI (a numerical measure of biological diversity).

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Problem 22

(Exercises 13–26) For each description of data, identify the W’s, name the variables, specify for each variable whether its use indicates that it should be treated as categorical or quantitative, and, for any quantitative variable, identify the units in which it was measured (or note that they were not provided).

The Environmental Protection Agency (EPA) tracks fuel economy of automobiles based on information from the manufacturers (Ford, Toyota, etc.). Among the data the agency collects are the manufacturer,
vehicle type (car, SUV, etc.), weight, horsepower, and gas mileage (mpg) for city and highway driving.

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Problem 23

(Exercises 13–26) For each description of data, identify the W’s, name the variables, specify for each variable whether its use indicates that it should be treated as categorical or quantitative, and, for any quantitative variable, identify the units in which it was measured (or note that they were not provided).

In 2012, Consumer Reports rated bottom-freezer refrigerators. It listed 102 models, giving the brand, cost, size (cu ft), temperature performance, noise (poor, fair, etc.), ease of use, energy efficiency, estimated annual energy cost, an overall rating (good, excellent, etc.), and the exterior dimensions.

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Problem 24

(Exercises 13–26) For each description of data, identify the W’s, name the variables, specify for each variable whether its use indicates that it should be treated as categorical or quantitative, and, for any quantitative variable, identify the units in which it was measured (or note that they were not provided).

People who get lost in the desert, mountains, or woods often seem to wander in circles rather than walk in straight lines. To see whether people naturally walk in circles in the absence of visual clues, researcher Andrea Axtell tested 32 people on a football field. One at a time, they stood at the center of one goal line, were blindfolded, and then tried to walk to the other goal line. She recorded each individual’s sex, height, handedness, the number of yards each was able to walk before going out of bounds, and whether each wandered off course to the left or the right. No one made it all the way to the far end of the field without crossing one of the sidelines. [STATS No. 39, Winter 2004]

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Problem 25

(Exercises 13–26) For each description of data, identify the W’s, name the variables, specify for each variable whether its use indicates that it should be treated as categorical or quantitative, and, for any quantitative variable, identify the units in which it was measured (or note that they were not provided).

The Kentucky Derby is a horse race that has been run every year since 1875 at Churchill
Downs, Louisville, Kentucky. The race started as a 1.5-mile race, but in 1896, it was shortened to 1.25 miles because experts felt that 3-year-old horses shouldn’t run such a long race that early in the season. (It has been run in May every year but one—1901—when it took place on April 29). Here are the data for the first four and several recent races.

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Problem 26

(Exercises 13–26) For each description of data, identify the W’s, name the variables, specify for each variable whether its use indicates that it should be treated as categorical or quantitative, and, for any quantitative variable, identify the units in which it was measured (or note that they were not provided).

The 2.5-mile Indianapolis Motor Speedway has been the home to a race on Memorial Day weekend
nearly every year since 1911. Even during the first race, there were controversies. Ralph Mulford was
given the checkered flag first but took three extra laps just to make sure he’d completed 500 miles. When he finished, another driver, Ray Harroun, was being presented with the winner’s trophy, and Mulford’s protests were ignored. Harroun averaged 74.6 mph for the 500 miles. In 2013, the winner, Tony Kanaan, averaged 187.433 mph. Here are the data for the first five races and five recent
Indianapolis 500 races.

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