Answer Section

1. ANS: B

2. ANS: D

3. ANS: D

4. ANS: C

5. ANS: A

6. ANS: C

7. ANS: B

8. ANS: A

9. ANS: B

10. ANS: D

11. ANS: D

12. ANS: D

13. ANS: A

14. ANS: A

15. ANS: C

16. ANS: B

17. ANS: C

18. ANS: C

19. ANS: B

COMPLETION

20. ANS: the sampling frame

21. ANS: a deviation

22. ANS: the variance

23. ANS: z-score

24. ANS: the population

25. ANS: outliers

26. ANS: measures of spread or measures of dispersion

27. ANS: median

28. ANS: mode

29. ANS: Percentiles

30. ANS: response

31. ANS: mean

32. ANS: discrete

33. ANS: sampling

34. ANS: non-response

35. ANS: measurement

36. ANS: continuous

37. ANS: Quartiles

38. ANS: the standard deviation

39. ANS: The interquartile range

MATCHING

40. ANS: F

41. ANS: D

42. ANS: C

43. ANS: B

44. ANS: E

45. ANS: A

46. ANS: A

47. ANS: A

48. ANS: C

49. ANS: A

50. ANS: B

51. ANS: C

52. ANS: C

53. ANS: B

54. ANS: D

55. ANS: A

SHORT ANSWER

56. ANS: range $110, interquartile range $30

57. ANS: a) 1.13 b) –0.24

58. ANS: a) –0.33 b) –0.0082 c) 3.85

59. ANS: The 39 scales in the survey can be considered a sample of the population of all the different bathroom scales on the market. Therefore, use the formulas for calculating statistics for a sample.

= $35.18, s = $22.02, = 485

60. ANS: median $30, first quartile $20, third quartile $50

61. ANS: loaded questions a) Do small dogs make good pets? b) Should logging be restricted in Canada?

62. ANS:

A bar graph is any graph in which values are represented by the height or area of a bar. A histogram is a special type of bar graph in which the areas of the bars are proportional to the frequencies of the values in a set of data. Histograms are used for variables whose values can be arranged in numerical order, while bar graphs can represent frequencies of either numerical or categorical variables.

63. ANS:

a) either all people who own TVs or just those who are watching TV at the time the program is on

b) all members of the party

c) people who are teenagers now

d) adult Ontario residents who use toothbrushes

64. ANS: mean 22, median 25, mode, 28

65. ANS: mean 16, median 15, mode, 22

66. ANS: a) current and potential readers of the sports section b) sampling bias

67. ANS: loaded questions

a) Which is less damaging to the environment: nuclear power or hydro-electric power?

b) Can fast food be nutritious?

68. ANS:

a) systematic sample

b) simple random sample

c) cluster sample

d) stratified sample

69. ANS: mean 12, median 14.5, mode 16

70. ANS: Convenience sample

71. ANS:

You and your financial planner have interpreted the word typical differently. The planner was referring to the mode of the minimum investment amounts, while you calculated the mean.

72. ANS: voluntary-response within a cluster sample

73. ANS: Yes. Examples may vary. Half-sizes for shirts and shoes are two everyday examples.

74. ANS:

leading questions

a) Which tastes better, cola A or cola B? Why?

b) Why is skiing Canada’s favourite winter sport?

75. ANS:

Since the study is trying to determine the characteristics of the population of all autistic children, use the formulas for calculating statistics for a sample.

= 45.7, s = 15.1, s2 = 229

76. ANS:

Answers will vary. Here are two simple examples:

a) A survey conducted by e-mail will miss households that do not have computers.

b) If a telephone survey is conducted only in English, people who do not speak it fluently might choose not to participate.

77. ANS:

leading questions

a) What is the best way to start the day?

b) What are the effects of loud music on the human body?

78. ANS:

a) mean 44.1, median 49, mode 53

b) The mean indicates that the arithmetic average of the group’s ages is about 44. The median indicates that half of the friends are under 49 and the other half are over 49. The mode indicates that 53 is the most common age in the group, but this information is not significant since the group is so small.

c) Since the median is higher than the mean, the group’s ages must be unevenly distributed.

79. ANS:

A continuous variable can have any value within a given range, while a discrete variable can have only certain separate values.

80. ANS:

The last two intervals overlap. Also, the intervals have three different widths, so it is not possible to make direct comparisons of the frequencies.

81. ANS:

a) The 25–34 age group had the most accidents.

b) Make all the intervals the same width by combining the data for drivers from 16 to 24.

c) The combined 16–24 interval had more accidents than any other interval with the same width.

d) You do not know how many drivers are in each age group.

82. ANS:

Response bias occurs when respondents give false answers; non-response bias occurs when particular groups in the population tend not to participate in the survey.

83. ANS: 23

PROBLEM

84. ANS:

a)

Students in this course missed an average of about six classes each.

b) The total number of students is 7 + 12 + 5 + 3 + 2 = 29, so the median interval is the one that includes the 15th largest value. Thus, the interval for 4–6 classes missed is the median interval.

85. ANS:

a) Sampling bias could be a problem in this survey. Although members of arts groups will generally be happy to help the magazine improve its arts coverage, they will tend to favour reviews of the arts in which they are active. As a result, the survey results may not be representative of the magazine’s readership.

b) Answers may vary. One possibility is a telephone survey of a random sample chosen from the magazine’s subscriber list.

86. ANS:

Sampling bias: The traffic through the major intersection may not be representative of that throughout the city core. Also, traffic volumes in the early afternoon may not be representative of those throughout the day, especially since the measurements do not include either morning or afternoon rush-hour periods.

87. ANS:

a) Since there are 21 cities listed, the median is simply the 11th highest value in the set of data: 193 600. The first quartile is the midpoint between the fifth and sixth lowest values, so Q1 = 97 500. Similarly, the third quartile is the midpoint between the fifth and sixth highest values, so Q3 = 350 900.

The median and quartiles can be calculated with a graphing calculator by entering the data into a list and then using the 1-Var Stats function from the STAT CALC menu. In a spreadsheet, you can use the MEDIAN and QUARTILE functions.

b) The range is the highest value minus the lowest one: 2 571 700 – 60 300 = 2 511 400. The interquartile range is Q3 – Q1 = 253 400.

c) The 21 cities can be considered a sample of all the cities in Canada. Therefore, use the sample version of the formulas for the mean, standard deviation, and variance. On a graphing calculator, the 1-VAR Stats function will calculate both and s. In Microsoft® Excel, you can use the AVERAGE, STDEV, and VAR functions to calculate , s, and s2, respectively. In Corel® Quattro® Pro, use @AVG, @STDS, and @VARS. The resulting values are  = 381 114, s = 552 863, and  = 2.6335  1010.

d) For Windsor,

e) For Toronto,

88. ANS:

Answers may vary. Students might suggest giving a questionnaire to every tenth student on the school’s roll.

89. ANS:

a) 12

b) Answers may vary. Two of the better choices are five 3-h intervals or seven 2-h intervals.

c) Answers may vary.

90. ANS:

Sampling and non-response bias: People using the recreation centre may not be representative of the population; also, people who are not interested in volunteer work are less likely than active volunteers to answer the questionnaire.

91. ANS:

Sampling bias: The people who visit the Internet site may not be representative of either the radio station’s present listeners or the potential audience for the new format.

Response bias: Fans of either format might deliberately overstate their opinions in the hopes of influencing the station’s decision.

Non-response bias: The fans of one format might be less inclined to answer on-line surveys than the fans of the other format are.

92. ANS:

Measurement bias caused by a loaded question: The survey question prompts the respondent by implying that it is unjust to restrict cigarette advertising.

93. ANS:

Sampling bias: Users of the department store’s credit cards may not be representative of the general public.

94. ANS:

a)

Students in this course missed an average of about seven classes each.

b) The numbers of students is 9 + 6 + 13 + 9 + 1 = 38. Since the 7–9 interval includes both the 19th and the 20th largest values, it is the median interval for this set of data.

95. ANS:

a) 44

b) Answers may vary. Possible choices include five 10-h intervals, six 8-h intervals, and eight 6-h intervals.

c) Answers may vary.

96. ANS:

a) Yes, although the probability is quite low.

b) Answers will vary. Since male students could well have different interests than female students do, such a sample probably would not be representative.

97. ANS:

a) The median has a value halfway between the fifth and sixth highest gross earnings. Thus, the median is million dollars. The first quartile is the median of the lower half of the data and the third quartile is the median of the upper half, so Q1 = 767 million dollars and Q3 = 924 million dollars.

b) The range is 1836 – 680 = 1156 million dollars. The interquartile range is

Q3 – Q1 = 924 – 767

= 157 million dollars

c) The ten top-grossing films are a separate population of unusually successful movies rather than a representative sample of all movies. Therefore, use the population formulas to calculate the mean, standard deviation, and variance:

and

d) For The Lion King,

e) For Titanic,

98. ANS:

These trucks were driven about 13 000 km a year.

99. ANS:

Measurement bias caused by a loaded question: The wording of the survey question could influence respondents to favour province-wide examinations.

100. ANS:

Computers Sold	Frequency
3	3
4	6
5	2
6	7
7	9
8	8
9	9
10	5
11	0
12	1

101. ANS:

Answers may vary. Students could suggest randomly selecting several classes and then surveying some or all members of each class.

102. ANS:

Answers may vary. Students might divide the school population by grade, gender, or neighbourhood. Students should indicate that the sample must include an equal proportion of each group in the population.

103. ANS:

Answers may vary. Students should outline a method for randomly selecting 36 students from grade 9, 33 from grade 10, 31 from grade 11, and either 28 or 29 from grade 12.

104. ANS:

a)

Next, arrange the data in ascending order: 3, 9, 10, 12, 13, 13, 13, 21, 23

Clearly, the middle value and the most common value are both 13, so this value is both the median and the mode.

b) The machine could have been shut down for maintenance or repair for most of the day on which it was used for only 3 h. If so, the hours of use on that day would not reflect the demand for the machine.

105. ANS:

106. ANS: