Section 1.2 Exercises

CLARIFYING THE CONCEPTS

Question 1.9

1. Write a sentence describing in your own words the field of statistics. (p. 5)

1.2.1

Answers will vary.

Question 1.10

2. What do we call the entities from which the data are collected? (p. 7)

Question 1.11

3. Describe the difference between a qualitative and a quantitative variable. (p. 9)

1.2.3

A qualitative variable is usually classified into categories; a quantitative variable takes on numerical values.

Question 1.12

4. What is another term for a qualitative variable? (p. 9)

Question 1.13

5. True or false: The actual value of a population parameter is usually unknown. (p. 12)

1.2.5

True

Question 1.14

6. What is the difference between a sample and a population? (p. 12)

Question 1.15

7. Explain what a statistic is. (p. 12)

1.2.7

A statistic is a characteristic of a sample.

Question 1.16

8. Describe one difference between a statistic and a parameter. (p. 12)

Question 1.17

9. What is a census? (p. 13)

1.2.9

Collections of data from every element in the population

Question 1.18

10. True or false: Statistical inference refers to methods for summarizing and organizing the information in a data set. (p. 14)

PRACTICING THE TECHNIQUES

image CHECK IT OUT!

To do Check out Topic
Exercises 11–13,
17–19, and 23–25		 Example 5 Elements, variables,
and observations
Exercises 14, 20,
and 26		 Example 6 Qualitative and
quantitative variables
Exercises 15, 21,
and 27		 Example 7 Discrete and
continuous variables
Exercises 16, 22,
and 28		 Example 8 Levels of measurement
Exercises 29–42 Examples 6,
7, and 8 		Types of variables and
levels of measurement
Exercises 43–45 Example 9 Population and sample
Exercises 46–48 Example 10 Parameter and statistic
Exercises 49–51 Example 11 Statistical inference
Exercises 52–57 Example 9 Population and sample
Exercises 58–64 Example 11 Statistical inference

For Exercises 11–16, answer the following questions about the data in Table 6.

Table 1.9: TABLE 6 Information about four sports teams in a dormitory intramural league
Team Captain's
gender		 Wins Rank Winning
percentage
Dragonborn Male 10 1 0.667
Sprites Female 9 2 0.600
Enchanters Female 7 3 0.467
Trolls Male 4 4 0.267

Question 1.19

11. What are the elements?

1.2.11

Teams: Dragonborn, Sprites, Enchanters, Trolls

Question 1.20

12. List the variables.

Question 1.21

13. Do the following.

  1. List the values that the variable Captain's gender takes.
  2. Provide the observation for the Sprites.

1.2.13

(a) Male, female (b) Female, 9, 2, 0.600

Question 1.22

14. List the quantitative variables and the qualitative variables.

Question 1.23

15. Which variables are discrete and which variables are continuous?

1.2.15

Discrete: wins; Continuous: winning percentage

Question 1.24

16. For each variable, determine whether it represents nominal, ordinal, interval, or ratio data.

For Exercises 17–22, answer the following questions about the data in Table 7.

Table 1.10: TABLE 7 Major League Baseball batting leaders, 2013
Player Team Batting
average		 Hits Rank Year of
birth
Miguel
Cabrera		 Detroit
Tigers		 0.348 193 1 1983
Michael
Cuddyer		 Colorado
Rockies		 0.331 162 2 1979
Joe
Mauer		 Minnesota
Twins		 0.324 144 3 1991
Michael
Trout		 Los Angeles
Angels		 0.323 190 4 1983
Chris
Johnson		 Atlanta
Braves		 0.321 165 5 1984
Table 1.10: Source: www.baseball-reference.com.

17

Question 1.25

17. What are the elements?

1.2.17

The players: Miguel Cabrera, Michael Cuddyer, Joe Mauer, Michael Trout, Chris Johnson

Question 1.26

18. List the variables.

Question 1.27

19. Do the following.

  1. List the values that the variable Team takes.
  2. Provide the observation for Miguel Cabrera.

1.2.19

(a) Detroit Tigers, Colorado Rockies, Minnesota Twins, Los Angeles Angels, Atlanta Braves (b) Detroit Tigers, 0.348, 193, 1, 1983

Question 1.28

20. List the quantitative variables and the qualitative variables.

Question 1.29

21. Which variables are discrete and which variables are continuous?

1.2.21

Discrete: hits, year of birth; Continuous: batting average

Question 1.30

22. For each variable, determine whether it represents nominal, ordinal, interval, or ratio data.

For Exercises 23–28, answer the following questions regarding the data in Table 8, which contains the five universities with the most federal student loan recipients for the 2013–2014 academic year.

Question 1.31

23. What are the elements?

1.2.23

Schools: University of Phoenix, Devry University, ITT Technical Institute, Penn State University, Kaplan University

Question 1.32

24. List the variables.

Question 1.33

25. Do the following.

  1. List the values that the variable School type takes.
  2. Provide the observation for Penn State University.

1.2.25

(a) Proprietary and public (b) PA, Public, 42,011, $151 million

Question 1.34

26. List the quantitative variables and the qualitative variables.

Question 1.35

27. Which variables are discrete and which variables are continuous?

1.2.27

Discrete: recipients, total loan amount ($ millions)

Question 1.36

28. For each variable, determine whether it represents nominal, ordinal, interval, or ratio data.

Table 1.11: TABLE 8 Federal student loan data4
School State School type Recipients Total loan
amount
($ millions)
University
of Phoenix		 AZ Proprietary 123,583 453
Devry
University		 IL Proprietary 45,361 215
ITT
Technical
Institute		 IN Proprietary 43,671 155
Penn State
University		 PA Public 42,011 151
Kaplan
University		 IA Proprietary 36,001 140

For Exercises 29–42:

  1. State whether the variable is qualitative or quantitative. If the variable is quantitative, state whether it is discrete or continuous.
  2. Identify the level of measurement represented by the data.

Question 1.37

29. The year you were born

1.2.29

(a) Quantitative, discrete (b) Interval

Question 1.38

30. Whether you own a cell phone or not

Question 1.39

31. The price of tea in China

1.2.31

(a) Quantitative, discrete (b) Ratio

Question 1.40

32. The SAT Math score of the person sitting next to you (scores range from 200 to 800)

Question 1.41

33. The winning score in next year's Super Bowl

1.2.33

(a) Quantitative, discrete (b) Ratio

Question 1.42

34. The winning team in next year's Super Bowl

Question 1.43

35. The rank of the winning Super Bowl team in its division

1.2.35

(a) Qualitative (b) Ordinal

Question 1.44

36. The number of friends on a student's Facebook page

Question 1.45

37. Your favorite television show

1.2.37

(a) Qualitative (b) Nominal

Question 1.46

38. How many contacts you have on your cell phone

Question 1.47

39. Your favorite ice cream

1.2.39

(a) Qualitative (b) Nominal

Question 1.48

40. Your credit card balance

Question 1.49

41. How old your car is

1.2.41

(a) Quantitative, continuous (b) Ratio

Question 1.50

42. What model your car is

For Exercises 43–45, state whether the data in the indicated table represent a sample or a population.

Question 1.51

43. Table 6: Note that the four teams represent all the teams in the intramural league.

1.2.43

Population

Question 1.52

44. Table 7

Question 1.53

45. Table 8

1.2.45

Sample

For Exercises 46–48, state whether the indicated measure represents a statistic or a parameter.

Question 1.54

46. Refer to Table 6 and Exercise 43. The most wins in the league is 10.

Question 1.55

47. Refer to Table 7 and Exercise 44. The oldest player was born in 1979.

1.2.47

Statistic

Question 1.56

48. Refer to Table 8 and Exercise 45. Four out of five (80%) of the universities in Table 8 are proprietary.

For Exercises 49–51, state whether descriptive statistics or statistical inference is indicated.

Question 1.57

49. Refer to Table 6. Half of the teams in the league have female team captains.

1.2.49

Descriptive statistics

Question 1.58

50. Refer to Table 7. Suppose we find the average number of hits of the players in Table 7, and infer this value to represent the average number of hits for all players in the league.

Question 1.59

51. Refer to Table 8. Suppose we infer from Exercise 48 that 80% of all universities are proprietary.

1.2.51

Statistical inference

For Exercises 52–57, identify the population and the sample.

Question 1.60

52. A researcher is interested in the median home sales price in Tarrant County, Texas. He collects sales data on 100 home sales.

Question 1.61

53. A psychologist is concerned about the health of veterans returning from war. She examines 20 veterans and assesses whether they show signs of post-traumatic stress disorder.

1.2.53

Population: all veterans returning from war; Sample: the 20 veterans selected.

Question 1.62

54. A sociologist wants to learn about the number of meetings per year of the 4-H clubs in Maricopa County, Arizona. He collects information from 10 different 4-H clubs in various parts of the county.

Question 1.63

55. A physical therapist would like to determine whether a new exercise method can delay the onset of osteoporosis in older women. She chooses 10 of her patients to use the new method.

1.2.55

Population: all older women; Sample: the physical therapist's 10 selected patients.

Question 1.64

56. An educator asks a sample of students at Portland Community College whether they would be interested in taking a course online.

Question 1.65

57. A financial adviser would like to assess the effect of mergers on price/earnings ratio. She collects data on 50 companies that recently underwent a merger.

1.2.57

Population: all companies that recently underwent a merger; Sample: the 50 selected companies that recently underwent a merger.

18

For Exercises 58–64, state whether descriptive statistics or statistical inference was used, and explain why.

Question 1.66

58. The average price in a sample of 15 homes sold in Jacksonville, Florida, for the week of April 21 was $253,200.

Question 1.67

59. According to the Department of Transportation, 60% of all automobile passengers wear seat belts. This is based on a survey of 1000 automobile passengers, of whom 600 wore seat belts.

1.2.59

Inferential statistics; the sample was used to draw a conclusion about the entire population.

Question 1.68

60. In a sample of 500 subjects, it was found that daily exercise lowered the average cholesterol level by 10%. A medical spokesperson then stated that daily exercise can lower everyone's cholesterol level by 10%.

Question 1.69

61. In a sample of 140 traffic fatalities in New York, 75 involved alcohol.

1.2.61

Descriptive statistics; the variable describes a sample.

Question 1.70

62. The goals-against average for the Charlestown Chiefs hockey team in a sample of 20 games was 3.57 goals per game.

Question 1.71

63. The Department of Health and Human Services conducted a survey, in which it was found that the percentage of 15- to 18-year-olds using illicit drugs has dropped in the last two years. The department concluded that illicit drug use has fallen among all 15- to 18-year-olds.

1.2.63

Inferential statistics; the sample was used to draw a conclusion about the entire population.

Question 1.72

64. The average on the first statistics exam for a sample of 10 students in Ms. Reynolds' class was 70.

APPLYING THE CONCEPTS

For Exercises 65–71, do the following.

  1. List the elements and the variables.
  2. Identify the qualitative variables and the quantitative variables.
  3. For each quantitative variable, indicate whether it is discrete or continuous.
  4. For each variable, identify the level of measurement.
  5. Provide the observation for the indicated element.

Question 1.73

65. Endangered Species. Refer to the following table, which lists four of the endangered animal species in the United States, as listed by www.earthsendangered.com. Do (a)–(d) and then provide the observation for the Florida panther.

Endangered
species		 Year listed as
endangered		 Estimated
number
remaining		 Range
Pygmy rabbit 2001 20 Washington
State
Florida panther 1973 50 Florida
Red wolf 1967 200 North
Carolina
West Indian
manatee		 1967 2500 Florida

1.2.65

(a) Elements: Endangered species pygmy rabbit, Florida panther, red wolf, and West Indian manatee; Variables: year listed as endangered, estimated number remaining, and range. (b) Qualitative variables: range; Quantitative variables: year listed as endangered and estimated number remaining. (c) Year listed as endangered—discrete, estimated number remaining—discrete. (d) Year listed as endangered—interval; estimated number remaining—ratio, range—nominal. (e) 1973, 50, Florida.

Question 1.74

66. Top Five Employers in Santa Monica, CA. Refer to the following table. Do (a)–(d), and then provide the observation for the city of Santa Monica.

Company Employees Industry
City of Santa Monica 1892 Government
St. John's Health Center 1755 Health services
The Macerich Company 1605 Real estate
Fremont General Corp 1600 Insurance
Entravision Corp 1206 Media company
Table 1.13: Source: Santa Monica Chamber of Commerce.

Question 1.75

67. Genetically Engineered Crops. Genetically engineered (GE) crops are now planted on the majority of acreage in many states around the country. GE corn comes in three varieties: insect-resistant, herbicide-tolerant, and stacked genes. The following table contains the proportion of the corn grown in each of five states that is GE, along with the GE type most prevalent in each state, for 2013.5 Do (a)–(d), and then provide the observation for the state of Texas.

State Proportion
of GE corn		 Most prevalent type
Texas 89% Herbicide-tolerant
Missouri 92% Insect-resistant
Minnesota 91% Herbicide-tolerant
Ohio 85% Herbicide-tolerant
South Dakota 96% Herbicide-tolerant

1.2.67

(a) Elements: States Texas, Missouri, Minnesota, Ohio, and South Dakota; Variables: proportion of GE corn and most prevalent type.

(b) Qualitative variables: most prevalent type; quantitative variables: proportion of GE corn (c) proportion of GE corn—ratio; most prevalent type—nominal (d) proportion of GE corn—continuous (e) 89%, herbicide-tolerant

Question 1.76

68. Hospitals Near Jackson, MS. Refer to the following table. Do (a)–(d). What is the observation for Rankin Medical Center?

Hospital Beds City Zip
Hardy Wilson 49 Hazlehurst 39083
Humphreys County 34 Belzoni 39038
Jefferson County 30 Fayette 39069
Lackey Memorial 15 Forest 39074
Leake Memorial 25 Carthage 39051
Madison County 67 Canton 39046
Montfort Jones 72 Kosciusko 39090
Rankin Medical Center 134 Brandon 39042

Question 1.77

69. Births and Maternal Age in Westchester County, NY. The following table represents the number of births and the average maternal age in 10 hospitals in northwest Westchester County, New York. Do (a)–(d). What is the observation for Sleepy Hollow?

19

Hospital Births Average maternal age
Briarcliff Manor 71 34.1
Buchanan 25 31.6
Cortlandt 348 32.2
Croton-on-Hudson 93 33.5
Mount Pleasant 277 32.8
Ossining 1 80 32.1
Ossining 2 371 29.2
Peekskill 365 29.0
Pleasantville 79 32.9
Sleepy Hollow 134 29.2

1.2.69

(a) Elements: Hospitals Briarcliff Manor, Buchanan, Cortlandt, Croton-on-Hudson, Mount Pleasant, Ossining 1, Ossining 2, Peekskill, Pleasantville, and Sleepy Hollow; Variables: births and average maternal age (b) Qualitative variables: There are no qualitative variables; Quantitative variables: births and average maternal age (c) Births—discrete; average maternal age— continuous (d) Births—ratio; average maternal age—ratio (e) 134, 29.2

Question 1.78

70. Commodity Prices. The financial company Bloomberg (www.bloomberg.com) reported that, on June 4, 2014, the prices in dollars for the following commodities were oil ($102.79, +0.13%), gold ($1243.62, −0.110%), and wheat ($616.25, +0.61%). Do (a)–(d). What is the observation for gold?

Question 1.79

71. Worst Tornadoes. CNN.com reports6 that the five worst tornadoes in American history in terms of death toll are as shown in the following table. Do (a)–(d). What is the observation for the St. Louis Tornado?

Tornado name Deaths Year
Tri-State 695 1925
Natchez 317 1840
St. Louis 255 1896
Tupelo 216 1936
Gainesville 203 1936

1.2.71

(a) Elements are the tornado names: Tri-State, Natchez, St. Louis, Tupelo, Gainesville; Variables: deaths, year (b) Quantitative variables: deaths, year (c) Discrete: deaths, year (d) Deaths is ratio, year is interval (e) 255, 1896

Question 1.80

72. Top Five Employers in Santa Monica, CA. Refer to Exercise 66 to answer the following questions.

  1. Do these five employers represent a sample or a population?
  2. Could these five companies be considered a representative sample of the number of employees per company for all companies in Santa Monica? Explain.

Question 1.81

73. Worst Tornadoes. Refer to Exercise 71 to answer the following questions.

  1. Do the data in the table represent a sample or a population?
  2. Could these data be considered a representative sample of the number of annual tornado deaths for all years? Explain.

1.2.73

(a) Sample (b) No, only the five tornadoes with the highest death toll are included.

Light Bulb Lifetime. Use the following information for Exercises 74 and 75. An electrical company has developed a new form of light bulb that it claims lasts longer than current models. The company has 1 million bulbs in its inventory.

Question 1.82

74. How do you think the company found evidence for its claim?

Question 1.83

75. Suppose you take a representative sample of 100 of the new light bulbs and find the average lifetime to be 2000 hours.

  1. Is this a statistic or a parameter?
  2. Write a sentence that estimates the average lifetime of all the new light bulbs.

1.2.75

(a) Statistic (b) An estimate of the average lifetime of all new light bulbs is the average lifetime of the sample of 100 light bulbs, which is 2000 hours.

Largest University Campuses. The National Center for Education Statistics reported that the colleges or university campuses with the largest enrollment in 2014 are as shown in the table. Use this information for Exercises 76 and 77.

Institution State Enrollment Rank
Ashford University Iowa 74,596 1
Arizona State University Arizona 72,254 2
Liberty University Virginia 64,096 3
Miami Dade College Florida 63,736 4
Lone Star College
System		 Texas 63,029 5

Question 1.84

76. Do the following.

  1. List the elements.
  2. List the variables.
  3. Identify the qualitative variables.
  4. Identify the quantitative variables.
  5. For each variable, identify the level of measurement.

Question 1.85

77. Answer the following.

  1. Do these five campuses represent a sample or a population?
  2. Could these five campuses be considered a representative sample of the enrollment for all university campuses in the United States? Explain.
  3. Provide the observation for Arizona State University.

1.2.77

(a) Sample (b) No, only the five campuses with the largest enrollment are included. (c) Arizona, 72,254, 2

BRINGING IT ALL TOGETHER

Chapter 1 Case Study: Video Game Sales.

Use Table 3 (page 8) to answer Exercises 78–88.

Question 1.86

videogamesales

78. Which of the variables are qualitative?

Question 1.87

videogamesales

79. List the quantitative variables.

1.2.79

Sales for week, sales total, weeks on list

Question 1.88

videogamesales

80. Is Weeks on list a discrete variable or a continuous variable?

Question 1.89

videogamesales

81. Does the list in Table 3 represent a sample or a population? Explain.

1.2.81

Sample, only the 30 best-selling video games are included.

Question 1.90

videogamesales

82. The number for highest sales for the week is 36,732. Does this represent a parameter or a statistic?

Question 1.91

videogamesales

83. State the nominal variables.

1.2.83

Platform, studio, type, weeks on list

Question 1.92

videogamesales

84. Are there any ordinal variables?

Question 1.93

videogamesales

85. Which variables represent ratio data?

1.2.85

Sales for week, sales total

Question 1.94

videogamesales

86. Is there a variable that can be viewed as interval data? Explain.

Question 1.95

videogamesales

87. The Xbox 360 version of Grand Theft Auto V outsold the PS3 version of the game for the week of May 14, 2014. Is this considered descriptive statistics or statistical inference?

1.2.87

Descriptive statistics

Question 1.96

videogamesales

88. Refer to the previous question. Suppose we then predict that the Xbox 360 version of Grand Theft Auto V will outsell the PS3 version of the game for the following week. Does this represent descriptive statistics or statistical inference?