Stats Data and Models

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

Chapter 1

Stats Starts Here - all with Video Answers

Educators

Chapter Questions

Problem 1

Grocery shopping Many grocery store chains offer customers a card they can scan when they check out and offer discounts to people who do so. To get the card, customers must give information, including a mailing address and e-mail address. The actual purpose is not to reward loyal customers but to gather data. What data do these cards allow stores to gather, and why would they want that data?

James Kiss

James Kiss

Numerade Educator

Problem 2

Online shopping Online retailers such as Amazon.com keep data on products that customers buy, and even products they look at. What does Amazon hope to gain from such information?

James Kiss

Numerade Educator

Problem 3

Super Bowl Sports announcers love to quote statistics. During the Super Bowl, they particularly love to announce when a record has been broken. They might have a list of all Super Bowl games, along with the scores of each team, total scores for the two teams, margin of victory, passing yards for the quarterbacks, and many more bits of information. Identify the who in this list.

James Kiss

Numerade Educator

Problem 4

Nobel laureates The website www.nobelprize.org allows you to look up all the Nobel prizes awarded in any year. The data are not listed in a table. Rather you drag a slider to the year and see a list of the awardees for that year. Describe the who in this scenario.

James Kiss

Numerade Educator

Problem 5

Grade levels A person's grade in school is generally identified by a number.
a) Give an example of a why in which grade level is treated as categorical.
b) Give an example of a why in which grade level is treated as quantitative.

James Kiss

Numerade Educator

Problem 6

ZIP codes The Postal Service uses five-digit ZIP codes to identify locations to assist in delivering mail.
a) In what sense are ZIP codes categorical?
b) Is there any ordinal sense to ZIP codes? In other words, does a larger ZIP code tell you anything about a location compared to a smaller ZIP code?

James Kiss

Numerade Educator

Problem 7

Voters 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?

James Kiss

Numerade Educator

Problem 8

Voters 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?

James Kiss

Numerade Educator

Problem 9

Medicine A pharmaceutical company conducts an experiment in which a subject takes $100 \mathrm{mg}$ 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?

James Kiss

Numerade Educator

Problem 10

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

Yingtai Xiao

Numerade Educator

Problem 11

The news Find a newspaper or magazine article in which some data are reported. For the data discussed in the article, identify as many of the W's as you can. Include a copy of the article with your report.

Nick Johnson

Numerade Educator

Problem 12

The Internet Find an Internet source that reports on a study and describes the data. Print out the description and identify as many of the W's as you can.

Dominador Tan

Numerade Educator

Problem 13

For each description of data, identify Who and What were investigated and the Population of interest.
Height? A study conducted by a team of researchers found that during pregnancy, a woman can tell whether a man is short or tall 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 likely height of 80 men based on photos of their face. Half of the men were short, and the other half were tall. All held similar expressions in the photos or were deemed to be equally attractive. None of the women were in their third trimester at the time of the test. The result: the closer a woman was to her third trimester the more accurate her guess.

James Kiss

Numerade Educator

Problem 14

For each description of data, identify Who and What were investigated and the Population of interest.
Hula-hoops The hula-hoop, a popular children's toy in the $1950 \mathrm{~s}$, has gained popularity as an exercise in recent years. But does it work? To answer this question, the American Council on Exercise conducted a study to evaluate the cardio and calorie-burning benefits of "hooping." Researchers recorded heart rate and oxygen consumption of participants, as well as their individual ratings of perceived exertion, at regular intervals during a 30 -minute workout. (www.acefitness.org/certifiednewsarticle/1094/)

James Kiss

Numerade Educator

Problem 15

For each description of data, identify Who and What were investigated and the Population of interest.
Bicycle safety 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 3500 cars passing him, he found that when he wore his helmet, motorists passed 3.29 inches closer to him, on average, than when his head was bare. (Source: $N Y$ Times, Dec. 10,2006$)$

James Kiss

Numerade Educator

Problem 16

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.

James Kiss

Numerade Educator

Problem 17

For each description of data, identify Who and What were investigated and the Population of interest.
Honesty 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.

James Kiss

Numerade Educator

Problem 18

For each description of data, identify Who and What were investigated and the Population of interest.
Blindness A study begun in 2011 examines the use of stem cells in treating two forms of osteopenia. Each of the 24 patients entered one of two separate trials in which embryonic stem cells were to be used to treat the condition.

James Kiss

Numerade Educator

Problem 19

For each description of data, identify Who and What were investigated and the Population of interest.
Candy bars A look at 515 participants found that participants who ate two or more candy bars a day "experienced waist size increases six times greater than those of people who didn't eat the candy bars."

James Kiss

Numerade Educator

Problem 20

For each description of data, identify Who and What were investigated and the Population of interest.
Molten iron 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.

James Kiss

Numerade Educator

Problem 21

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).
Weighing hummingbirds Because of the difficulty of weighing a hummingbird in the mountains, researchers caught and measured 34 hummingbirds, recording their weight, wingspan, body length, and sex. They hoped to find a way to estimate weight from the other, more easily determined quantities.

James Kiss

Numerade Educator

Problem 22

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.

James Kiss

Numerade Educator

Problem 23

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.

James Kiss

Numerade Educator

Problem 24

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 Gallup Poll conducted a representative telephone survey of 1180 American voters during the first quarter of 2007 . Among the reported results were the voter's region (Northeast, South, etc.), age, party affiliation, and whether or not the person had voted in the 2006 midterm congressional election.

James Kiss

Numerade Educator

Problem 25

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).
Researchers investigating the impact of training on sprinting collected data from 668 training sessions during $1998-2000$. They kept track of the runner's age, the number of weeks the training lasted, the type of training (interval, endurance, combined), the level of training the runner had (none, moderate, intense), the weight and sex of the runners, and whether the runners exhibited improvements (none, minor, major).

James Kiss

Numerade Educator

Problem 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.

James Kiss

Numerade Educator

Problem 27

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 benefits of the compound.

James Kiss

Numerade Educator

Problem 28

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 cherry growers compiled these data about cherry trees: size (square kilometers), number of months in existence, state, varieties of cherries grown, average price per ton, gross sales, and percent profit.

James Kiss

Numerade Educator

Problem 29

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 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 $\left({ }^{\circ} \mathrm{C}\right)$, and the $\mathrm{BCI}$ (a numerical measure of biological diversity).

James Kiss

Numerade Educator

Problem 30

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.

James Kiss

Numerade Educator

Problem 31

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 $2013,$ Consumer Reports published an article evaluating refrigerators. It listed 353 models, giving the brand, cost, size (cu ft), type (such as top freezer), estimated annual energy cost, an overall rating (good, excellent, etc.), and the repair history for that brand (percentage requiring repairs over the past 5 years).

James Kiss

Numerade Educator

Problem 32

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. (Source: STATS No. 39, Winter 2004)

James Kiss

Numerade Educator

Problem 33

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.

James Kiss

Numerade Educator

Problem 34

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 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 over $187 \mathrm{mph}$, beating the previous record by over $17 \mathrm{mph}$ ! Here are the data for the first five races and five recent Indianapolis 500 races.

James Kiss

Numerade Educator