STATS Modeling the World

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

Chapter 2

Data - all with Video Answers

Educators

Chapter Questions

Problem 1

Voters. A February 2007 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

James Kiss

Numerade Educator

Problem 2

Mood. A January 2007 Gallup Poll question asked, "In general, do you think things have gotten better or gotten worse in this country in the last five years?" Possible answers were "Better", "Worse", "No Change", "Don't Know", and "No Response". What kind of variable is the response?

Yingtai Xiao

Numerade Educator

Problem 3

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 4

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 5

The news. 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.

Nick Johnson

Numerade Educator

Problem 6

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

Dominador Tan

Numerade Educator

Problem 7

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 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$]$

James Kiss

Numerade Educator

Problem 8

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.

Lynn Larson

Numerade Educator

Problem 9

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. [NY Times, Dec. 10,2006$]$

James Kiss

Numerade Educator

Problem 10

Movies. Some motion pictures are profitable and others are not. Understandably, the movie industry would like to know what makes a movie successful. Data from 120 first-run movies released in 2005 suggest that longer movies actually make less profit.

Nick Johnson

Numerade Educator

Problem 11

Fitness. Are physically fit people less likely to die of cancer? An article in the May 2002 issue of Medicine and Science in Sports and Exercise reported results of a study that followed 25,892 men aged 30 to 87 for 10 years. The most physically fit men had a $55 \%$ lower risk of death from cancer than the least fit group.

Joanna Quigley

Numerade Educator

Problem 12

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 13

Weighing bears. 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.

Rashmi Sinha

Numerade Educator

Problem 14

Schools. 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.

Lynn Larson

Numerade Educator

Problem 15

Arby's menu. 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.

Joannie Wang

Numerade Educator

Problem 16

Age and party. 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.

Andrija Isakov

Numerade Educator

Problem 17

Babies. 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).

Nick Johnson

Numerade Educator

Problem 18

Flowers. 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.

Linda Winkler

Numerade Educator

Problem 19

Herbal medicine. 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.

Foster Wisusik

Numerade Educator

Problem 20

Vineyards. 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.

James Kiss

Numerade Educator

Problem 21

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

Rashmi Sinha

Numerade Educator

Problem 22

Fuel economy. 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 23

Refrigerators. In 2006, Consumer Reports published an article evaluating refrigerators. It listed 41 models, giving the brand, cost, size (cu $\mathrm{ft}$ ), 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

Shoukat Ali

Other Schools

Problem 24

Walking in circles. 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$]$

Lucas Finney

Numerade Educator

Problem 25

Horse race 2008. 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.

Patrick Connors

Patrick Connors

Numerade Educator

Problem 26

Indy 2008. 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 $74.6 \mathrm{mph}$ for the 500 miles. $\ln 2008$, the winner, Scott Dixon, averaged $143.567 \mathrm{mph}$.

Here are the data for the first five races and five recent Indianapolis 500 races. Included also are the pole winners (the winners of the trial races, when each driver drives alone to determine the position on race day).

Rylie Howey

Numerade Educator