CHAPTER 1 EXERCISES

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Question 1.8

1.8 Miles per gallon. Here is a small part of a data set that describes the fuel economy (in miles per gallon) of 2015 model motor vehicles.

  1. (a) What are the individuals in this data set?

  2. (b) For each individual, what variables are given? Which of these variables take numerical values?

Make and
model
Vehicle
type
Transmission
type
Number of
cylinders
City
mpg
Highway
mpg
BMW 328i Compact car Manual 6 22 34
BMW 335i Compact car Manual 6 20 30
Buick LaCrosse Midsize car Automatic 6 18 28
Chevrolet Traverse Sport utility vehicle (FWD) Automatic 6 17 24

Question 1.9

1.9 Athletes’ salaries. Here is a small part of a data set that describes Major League Baseball players as of opening day of the 2015 season.

  1. (a) What individuals does this data set describe?

  2. (b) In addition to the player’s name, how many variables does the data set contain? Which of these variables take numerical values?

  3. (c) What do you think are the units in which each of the numerical variables is expressed? For example, what does it mean to give Bryce Harper’s annual salary as 3,750? (Hint: The average annual salary of a Major League Baseball player on opening day 2015 was, with roundoff, $4,250,000.)

Player Team Position Age Salary
Kershaw, Clayton Dodgers Pitcher 27 31,000
Harper, Bryce Nationals Outfielder 22 3,750
Sabathia, C. C. Yankees Pitcher 34 24,286
Rodriguez, Alex Yankees Designated Hitter 39 22,000

Question 1.10

1.10 Who recycles? In Example 1, weight is not a good measure of the participation of households in different neighborhoods in a city recycling program. What variables would you measure in its place?

Question 1.11

1.11 Sampling moms. Pregnant and breast-feeding women should eat at least 12 ounces of fish and seafood per week to ensure their babies’ optimal brain development, according to a coalition of top scientists from private groups and federal agencies. A nutritionist wants to know whether pregnant women are eating at least 12 ounces of fish per week. To do so, she obtains a list of the 340 members of a local chain of prenatal fitness clubs and mails a questionnaire to 60 of these women selected at random. Only 21 questionnaires are returned. What is the population in this study? What is the sample from which information is actually obtained? What percentage of the women whom the nutritionist tried to contact responded?

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Question 1.12

image1.12 The death penalty. A press release by the Gallup News Service says that, based on a poll conducted on October 12–15, 2014, it found that 63% of Americans respond Yes when asked this question: “Are you in favor of the death penalty for a person convicted of murder?” Toward the end of the article, you read: “Results for this Gallup poll are based on 1017 telephone interviews” and “based on a random sample of adults, 18 years and older living in all 50 U.S. states and the District of Columbia.” What variable did this poll measure? What population do you think Gallup wants information about? What was the sample?

Question 1.13

1.13 The political gender gap. There may be a “gender gap” in political party preference in the United States, with women more likely than men to prefer Democratic candidates. A political scientist interviews a large sample of registered voters, both men and women. She asks each voter whether he or she voted for the Democratic or the Republican candidate in the last presidential election. Is this study an experiment? Why or why not? What variables does the study measure?

Question 1.14

1.14 What is the population? For each of the following sampling situations, identify the population as exactly as possible. That is, say what kind of individuals the population consists of and say exactly which individuals fall in the population. If the information given is not sufficient, complete the description of the population by making reasonable assumptions about any missing information.

  1. (a) An opinion poll contacts 972 American adults and asks them, “Would you rather have a job working for the government or working for business?”

  2. (b) Video adapter cables have pins that plug into slots in a computer monitor. The adapter will not work if pins are bent or broken. A computer store buys video adapter cables in large lots from a supplier. The store chooses five cables from each lot and inspects the pins. If any of the cables have bent or broken pins, the entire lot is sent back.

  3. (c) The American Community Survey contacts 3.5 million households, including some in every county in the United States. This Census Bureau survey asks each household questions about their housing, economic, and social status.

Question 1.15

1.15 What is the population? For each of the following sampling situations, identify the population as exactly as possible. That is, say what kind of individuals the population consists of and say exactly which individuals fall in the population. If the information given is not sufficient, complete the description of the population in a reasonable way.

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  1. (a) A sociologist is interested in determining what proportion of teens believe the drinking age should be lowered to 18 in all the states. She selects a sample of five high schools in a large city and interviews all 12th-graders in each of the schools.

  2. (b) A medical researcher is interested in the rate of dementia among former NFL football players. From a list of living, former players he selects a sample of 20 and interviews them to determine if signs of dementia are present.

  3. (c) The host of a local radio talk show wonders if people who are actively religious are more likely to trust their neighbors than those who are not. The station receives calls from 51 listeners who voice their opinions.

Question 1.16

image1.16 Teens’ sleep needs. A Washington Post article reported on a study about the sleep needs of teenagers. In the study, researchers measured the presence of the sleep-promoting hormone melatonin in teenagers’ saliva at different times of the day. They learned that the melatonin levels rise later at night than they do in children and adults and remain at a higher level later in the morning. The teenagers who took part in the study were volunteers. Higher levels of melatonin indicate sleepiness. The researchers recommended that high schools start later in the day to accommodate the sleep needs of teens. Is this study an experiment, a sample survey, or an observational study that is not a sample survey? Explain your answer.

Question 1.17

1.17 Power lines and leukemia. The study of power lines and leukemia in Example 3 compared two groups of individuals and measured many variables that might influence differences between the groups. Explain carefully why this study is not an experiment.

Question 1.18

1.18 Treating prostate disease. A large study used records from Canada’s national health care system to compare the effectiveness of two ways to treat prostate disease. The two treatments are traditional surgery and a new method that does not require surgery. The records described many patients whose doctors had chosen one or the other method. The study found that patients treated by the new method were more likely to die within eight years.

  1. (a) Explain why this is an observational study, not an experiment.

  2. (b) Briefly describe the nature of an experiment to compare the two ways to treat prostate disease.

Question 1.19

1.19 Walnuts and cholesterol. Does eating walnuts increase the level of good cholesterol (HDL) and reduce the level of bad cholesterol (LDL)? Here are two ways to study this question.

  1. 1. Researchers in Australia recruited 58 adults with diabetes for a research study. These subjects were randomly assigned to two treatment groups: a low-modified-fat diet group and a low-modified-fat diet group that included a handful of walnuts each day. After six months, researchers compared changes in HDL and LDL levels for the two groups.

  2. 2. Another team of researchers recruited 58 adults with diabetes who regularly eat walnuts as part of their diet. The researchers match each with a similar adult with diabetes who does not regularly eat walnuts. The researchers measured the HDL and LDL for each adult and compared the results for both groups.

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  1. (a) Explain why the first is an experiment and the second is an observational study.

  2. (b) Why does the experiment give more useful information about whether walnuts increase HDL and reduce LDL?

Question 1.20

image1.20 Alcohol and cancer in women. A Washington Post article reported on a study about alcohol consumption and cancer in women. Since 1996, a team of British researchers has been gathering detailed information from 1.28 million women aged 50 to 64. The researchers recorded how much alcohol the women reported consuming when they volunteered for the study and again three years later. The researchers then examined whether there was any link with the 68,775 cancers the women developed over an average of the next seven years. They found that even among women who consumed as little as 10 grams of alcohol a day on average (the equivalent of about one drink), the risk for cancer of the breast, liver, and rectum was elevated.

  1. (a) Is this an experiment? Explain your answer.

  2. (b) We would prefer a sample survey to using women who volunteer for a study. What population does it appear that the researchers were interested in? What variables did they measure?

Question 1.21

image1.21 Bullying. Researchers tracked 2668 people from early childhood through adulthood and found that 13-year-olds who are frequent targets of bullies were three times more likely than their nonvictimized peers to be depressed later as adults. What is the population in this study? What is the sample? What variables do the researchers measure?

Question 1.22

1.22 Choose your study type. What is the best way to answer each of the questions below: an experiment, a sample survey, or an observational study that is not a sample survey? Explain your choices.

  1. (a) Is your school’s football team called for fewer penalties in home games than in away games?

  2. (b) Are college students satisfied with the cost of textbooks that they are required to purchase?

  3. (c) Do college students who have access to video recordings of course lectures perform better in the course than those who don’t?

Question 1.23

1.23 Choose your study purpose. Give an example of a question about pet owners, their behavior, or their opinions that would best be answered by

  1. (a) a sample survey.

  2. (b) an observational study that is not a sample survey.

  3. (c) an experiment.

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