Section 1.3 Exercises

33

CLARIFYING THE CONCEPTS

Question 1.97

1. Explain why convenience sampling usually does not result in a representative sample. (p. 25)

1.3.1

Convenience sampling usually only includes a select group of people. For example, surveying people at a mall on a workday during working hours would probably include few if any people who work full time.

Question 1.98

2. What type of bias did the Literary Digest poll (pp. 20–21) exhibit? How did it affect the results? (p. 26)

Question 1.99

3. How could the Literary Digest have decreased the bias in its poll? (p. 21)

1.3.3

Answers will vary; could have chosen a random sample of houses and apartments and surveying the people door to door, for instance.

Question 1.100

4. Was the Literary Digest poll a random sample? (p. 21)

Question 1.101

5. Describe what a random sample is. (p. 21)

1.3.5

A sample for which every element has an equal chance of being included.

Question 1.102

6. Describe the difference between an observational study and an experimental study. (p. 28)

PRACTICING THE TECHNIQUES

CHECK IT OUT!

To do Check out Topic
Exercises 7–10 Example 12 Random sampling
Exercises 11–14 Example 13 Systematic sampling
Exercises 15–18 Example 14 Stratified sampling
Exercises 19–20 Example 15 Cluster sampling
Exercises 21–22 Example 16 Convenience sampling
Exercises 23–26 Example 17 Recognize the sampling
method
Exercises 27–30 Example 18 Selection bias
Exercises 31–34 Example 19 Questionnaire design
Exercises 35–46 Example 20 Experimental study
Exercises 47–48 Example 21 Randomization and
replication
Exercises 49–50 Example 22 Observational study

Refer to Table 11 to obtain random samples in Exercises 7–10.

Table 1.24: TABLE 11 College football teams in four major conferences
Big Ten Southeastern Atlantic Coast Pacific 12
Illinois Alabama Boston College Arizona
Indiana Arkansas Clemson Ariz. State
Iowa Auburn Duke California
Michigan Florida Florida State Colorado
Mich. State Georgia Georgia Tech Oregon
Minnesota Kentucky Maryland Oregon State
Nebraska Louisiana State Miami Stanford
Northwestern Mississippi North Carolina UCLA
Ohio State Miss. State NC State USC
Penn State Missouri Pittsburgh Utah
Purdue South Carolina Syracuse Washington
Wisconsin Tennessee Virginia Wash. State
Texas A&M Virginia Tech
Vanderbilt Wake Forest

Question 1.103

7. Obtain a random sample of size 4 teams from the Big Ten Conference.

1.3.7

Answers will vary.

Question 1.104

8. Obtain a random sample of size 5 teams from the Southeastern Conference.

Question 1.105

9. Obtain a random sample of size 6 teams from the Atlantic Coast Conference.

1.3.9

Answers will vary.

Question 1.106

10. Obtain a random sample of size 7 teams from the Pacific 12 Conference.

Use Table 11 to obtain systematic samples in Exercises 11–14.

Question 1.107

11. Obtain a systematic sample of teams from the Big Ten Conference. Use and start with the 1st team.

1.3.11

Illinois, Iowa, Michigan State, Nebraska, Ohio State, Perdue

Question 1.108

12. Obtain a systematic sample of every 3rd team from the Southeastern Conference. Start with the 2nd team.

Question 1.109

13. Obtain a systematic sample of every 4th team from the Southeastern Conference. Start with the 1st team.

1.3.13

Alabama, Georgia, Mississippi State, Texas A&M

Question 1.110

14. Obtain a systematic sample of teams from the Pacific 12 Conference. Use and start with the 3rd team.

Use Table 11 to obtain stratified samples in Exercises 15–18.

Question 1.111

15. Obtain a stratified sample of two teams from each of the Big Ten Conference and the Southeastern Conference.

1.3.15

Answers will vary.

Question 1.112

16. Obtain a stratified sample of three teams from each of the Atlantic Coast Conference and the Pacific 12 Conference.

Question 1.113

17. Obtain a stratified sample of four teams from each of the Big Ten Conference and the Atlantic Coast Conference.

1.3.17

Answers will vary.

Question 1.114

18. Obtain a stratified sample of two teams from each of the four conferences.

Use Table 11 to obtain cluster samples in Exercises 19–20.

Question 1.115

19. Obtain a cluster sample of all the teams from two randomly selected conferences.

1.3.19

Answers will vary.

Question 1.116

20. Obtain a different cluster sample of all the teams from two randomly selected conferences.

Use Table 11 to obtain convenience samples in Exercises 21–22.

Question 1.117

21. It is convenient for the researcher to choose the first five teams from the Southeastern Conference for the sample, using alphabetical order. Is this likely to result in a representative sample?

1.3.21

No

Question 1.118

22. It is convenient for the researcher to choose only those teams in the state of Washington for the sample from the Pacific 12 conference. Is this likely to result in a representative sample?

For Exercises 23–26, state which type of sampling is represented.

Question 1.119

23. Students in your class are divided into freshmen, sophomores, juniors, and seniors. One of the groups is selected at random and all the students in that group are selected.

1.3.23

Cluster sampling

Question 1.120

24. An instructor in a large lecture course of 300 students wants to get a student sample, and he selects every 10th name from the class roster.

34

Question 1.121

25. You are researching the proportion of college students who prefer country music to other forms of music. You survey all the students in all the classes you are taking this semester.

1.3.25

Convenience sampling

Question 1.122

26. An instructor in a large lecture course of 300 students (two lectures, one lab per week) wants to get a student sample. He takes a random sample of three of the 15 lab sections and selects all of the students from those three sections.

Use the following information for Exercises 27 and 28. Brandon is trying to estimate the proportion of all college students who are physically fit. He obtains a sample of students working out at the gymnasium on Monday night.

Question 1.123

27. Identify the target population and the potential population.

1.3.27

Target population: All college students; Potential population: All students working out at the gymnasium on the Monday night Brandon was there.

Question 1.124

28. Does selection bias exist? Explain why or why not.

Use the following information for Exercises 29 and 30. Michelle would like to determine the proportion of small businesses that employ at least one college student parttime. She obtains a sample of businesses near the state university.

Question 1.125

29. Identify the target population and the potential population.

1.3.29

Target population: All small businesses; Potential population: Small businesses near the state university.

Question 1.126

30. Does selection bias exist? Explain why or why not.

For Exercises 31–34, identify which of the five factors for good questionnaire design is violated, if any.

Question 1.127

31. Do you sometimes feel anxiety about your health?

1.3.31

Vague terminology

Question 1.128

32. Do you support the valiant efforts of our mayor to dispel the lies spread by the corrupt opposition?

Question 1.129

33. Do you espouse the diminution of the graduated income tax?

1.3.33

Neither simple nor clear

Question 1.130

34. Do you support laws restricting invasion of privacy and locking up those responsible for doing so?

For Exercises 35–38, do the following: (a) State which type of study is involved: experimental or observational. (b) Identify the response variable and the predictor variable.

Question 1.131

35. A sociologist is interested in whether large families (at least four children) attend religious services more often than smaller families do.

1.3.35

(a) Observational (b) response variable: how often they attend religious services; predictor variable: whether or not the family is large (at least four children)

Question 1.132

36. A financial researcher is interested in whether companies that give large bonuses to their chief executive officers (at least $1 million per year) have a higher stock price.

Question 1.133

37. A manufacturer is interested in whether a new computer processor will improve the performance of its electronics equipment.

1.3.37

(a) Experimental (b) response variable: performance of the electronics equipment; predictor variable: whether or not a piece of equipment has a new computer processor

Question 1.134

38. A pharmaceutical company wants to see if its new drug will lower high blood pressure.

Use the following information for Exercises 39–42. Agricultural researchers are investigating whether a new form of pesticide will lead to lower levels of insect damage to crops than the traditional pesticide.

Question 1.135

39. Identify the response variable.

1.3.39

Level of insect damage to crops

Question 1.136

40. Identify the predictor variable.

Question 1.137

41. What is the treatment?

1.3.41

The new pesticide

Question 1.138

42. What is the control?

Use the following information for Exercises 43–46.

Cholesterol researchers are investigating whether any difference exists between a new medication and a placebo (inactive pill) in lowering LDL cholesterol levels in the bloodstream.

Question 1.139

43. Identify the response variable.

1.3.43

LDL cholesterol level in the bloodstream

Question 1.140

44. Identify the predictor variable.

Question 1.141

45. What is the treatment?

1.3.45

New medication

Question 1.142

46. What is the control?

For each of the following scenarios in Exercises 47 and 48, indicate (a) whether randomization is present, and (b) whether sufficient replication has been made.

Question 1.143

47. A total of 100 subjects with high LDL cholesterol levels are randomly assigned to receive a new medication or the traditional medication.

1.3.47

(a) Randomization is present for the 100 randomly assigned subjects but not for the subject with high LDL cholesterol levels. (b) The sample of 100 people is probably enough replication.

Question 1.144

48. Four subjects, two each, are randomly assigned to receive either a new Alzheimer's-resistant drug or a control.

Examine the following scenarios in Exercises 49 and 50, and state whether each represents an experiment or an observational study.

Question 1.145

49. Patients with heart conditions were randomly assigned to receive either a dose of aspirin or a placebo. Occurrences of myocardial infarctions were measured.

1.3.49

Experiment

Question 1.146

50. Groups of Democrats, Independents, and Republicans were surveyed, and their opinions regarding Second Amendment rights were compared.

APPLYING THE CONCEPTS

Case Study: Video Game Sales.

Use the 30 top-selling video games in Table 3 (page 8) for Exercises 51–54.

Use the Simple Random Sample applet for Exercise 51.

Question 1.147

51. Random Sampling.

  1. Generate a random sample of size 5 video games.
  2. Before you generate another random sample of 5 video games, is it likely that it will be the same as in (a)? Why or why not?
  3. Think of your favorite video game from Table 3. Before we generate another random sample, is there any way of foretelling whether your game will be in the random sample? Explain.
  4. Go ahead and generate another random sample of 5 video games. Was it the same as the first sample? Was your game in the sample?

1.3.51

(a) Answers will vary (b) No. Every possible sample of 5 video games has the same chance of being selected. (c) No. Every possible sample of 5 video games has the same chance of being selected. Some of the samples will contain the video game and some won't. (d) Answers will vary; answers will vary

Question 1.148

52. Obtain a systematic sample of every 4th video game. Start with the first video game.

Question 1.149

53. Obtain a stratified sample of two video games from each platform (omit the PSV platform).

1.3.53

Answers will vary

Question 1.150

54. Obtain a cluster sample of all the video games from two randomly selected platforms.

35

Question 1.151

55. Contradicting Ann Landers. “If you had to do it over again, would you have children?” This is the question that advice columnist Ann Landers once asked her readers. It turns out that nearly 70% of the 10,000 responses she received were “No.” A professional poll by Newsday found that 91% of respondents would have children again. Explain the apparent contradiction between these two surveys using what you have learned in this section.

1.3.55

Answers will vary. For instance, the poll by Ann Landers was extremely biased. Only people who read the Ann Landers column and felt strongly about the poll responded to this poll. The Newsday poll was done professionally, and therefore the sample used was more likely to be representative of the population.

Question 1.152

56. High School Dropouts. For the following survey, describe the target population and the potential population, and discuss the potential for selection bias. Researchers are interested in the proportion of high school students in New England who drop out (leave school before graduating). A survey is made of 15 high schools in Greater Boston.

Question 1.153

57. Living Below the Poverty Level. For the following survey, describe the target population and the potential population, and discuss the potential for selection bias. A sociologist is interested in the proportion of people living below the poverty level in Chicago. He takes a random sample of phone numbers from the Chicago phone directory and asks each respondent his or her annual household income.

1.3.57

Target population: all the people living in Chicago; potential population: people who have phones and who have their phone number listed in the Chicago phone directory. Reasons for potential selection bias vary; for instance, many of the people living below the poverty level in Chicago may not have phones.

Question 1.154

58. Rap or Hip-Hop? Describe what is wrong, if anything, with the following survey question. “Do you enjoy listening to rap or hip-hop music?”

Question 1.155

59. Financial Ruin. Describe what is wrong, if anything, with the following survey question: “Do you think that we should tax and spend our way into financial ruin?”

1.3.59

The survey question is a leading question.

Question 1.156

60. Abortion. Suppose 67% of female respondents respond affirmatively to the question “Do you support the right of a woman to terminate a pregnancy when her life is in danger?” Would the researcher be justified in reporting, “Two-thirds of women support abortion”?

Question 1.157

61. Most Active Stocks. Here is a list of the five most active stocks on the NYSE on June 5, 2014.

Stock Price
Rite Aid $7.87
Bank of America $15.43
Twitter $33.89
Sprint $9.02
Ford Motors $16.68
  1. We are about to select a random sample and determine the lowest price in the sample. Do we know what this price will be before we select the sample? Why or why not?
  2. Select a random sample of size 2 from the table.
  3. If you take another sample of size 2, is it likely to comprise the same two companies? Why or why not?
  4. Which stock in your sample has the lowest price? What is that price?

1.3.61

(a) No, different random samples may contain different lowest stock prices. (b) Answers will vary. (c) No; see answer (a). (d) Answers will vary.

Question 1.158

62. Most Active Stocks. Refer to the list of stocks from the previous exercise.

  1. We are about to select another random sample and determine the lowest price in the sample. Do we know what this price will be before we select the sample? Do we know whether it will be the same as in the previous exercise? Why or why not?
  2. Select another random sample of size 2.
  3. Which stock in your new sample has the lowest price? What is that price?

Question 1.159

63. Challenge Exercise. Compare your answers in Exercise 61(d) with those in Exercise 62(c). What can we say about a quantity like “the lowest price in a random sample of stocks”?

1.3.63

It is a variable that may vary from sample to sample.

Question 1.160

64. Mediterranean Diet. The American Heart Association reported the following results of an experimental study.7 Patients who ate a Mediterranean diet had a significantly lower risk of having a second heart attack than patients who ate a Western diet. Identify the response variable and the predictor variable in this experimental study.

Question 1.161

65. Secondhand Smoking and Illness in Children. A Surgeon General's report found that “the evidence is sufficient to infer a causal relationship” between secondhand tobacco smoke exposure from parental smoking and respiratory illnesses in infants and children.8

  1. Given the health risks associated with tobacco use, discuss the ethics of forcing the parents of a treatment group to smoke tobacco.
  2. State whether this report was based on an experimental study or an observational study.

1.3.65

(a) Forcing the parents of a treatment group to smoke tobacco will increase the occurrence of respiratory illnesses of their children. This is not very ethical. (b) Observational study

Question 1.162

66. Ethics, Experiments, and Observational Studies. According to the British medical journal The Lancet, experimental studies performed on animals (nonhuman primates, squirrel monkeys, and rodents) have revealed that large doses of the drug Ecstasy (methylene-dioxymethamphetamine, or MDMA) produce “large and possibly permanent damage” to neural axons in the brain.9 Explain why the researchers did not perform their experiment on humans.

BRINGING IT ALL TOGETHER

Evidence for an Alternative Therapy? Use the following information for Exercises 67–69. A company called QT, Inc. sells “ionized bracelets,” called Q-Ray Bracelets, that it claims help to ease pain by balancing the body's flow of “electromagnetic energy.” QT, Inc. claims that Q-Ray Bracelets can ease pain caused by cancer, restore wellbeing, and provide many other health benefits. The Mayo Clinic decided to conduct a statistical study to determine whether the extravagant claims for Q-Ray Bracelets were justified.10 In the study, 305 subjects wore the Q-Ray “ionized” bracelet and 305 wore a placebo bracelet (identical to the ionized bracelet except for the ionization) for four weeks, at the end of which certain measures of pain were evaluated and compared between the treatments. The subjects, upon entry to the study, were randomly assigned to receive either the ionized bracelet or the placebo bracelet.

36

Question 1.163

67. Identify the following aspects of this study.

  1. The control
  2. The randomization
  3. The replication

1.3.67

(a) The 305 subjects that wore the placebo bracelet (b) The subjects were randomly assigned to wear either the placebo bracelet or the ionized bracelet. (c) There are 305 subjects in both the treatment and the control groups.

Question 1.164

68. Identify the following aspects of this study.

  1. The predictor variable
  2. The treatment
  3. The response variable

Question 1.165

69. Does this statistical study represent an experimental study or an observational study? Write a sentence explaining why.

1.3.69

This study is an experimental study because the subjects were randomly assigned to either a treatment or a control.