b The experimental unit on which the number of errors is measured is the exam.

NEL Copyright © 2014 Nelson Education Limited 1-1

Chapter 1: Describing Data with Graphs

1.1 a The experimental unit, the individual or object on which a variable is measured, is the student.b The experimental unit on which the number of errors is measured is the exam.c The experimental unit is the patient.d The experimental unit is the azalea plant.e The experimental unit is the car.

1.2 a “Time to assemble” is a quantitative variable because a numerical quantity (1 hour, 1.5 hours, etc.) is measured.b “Number of students” is a quantitative variable because a numerical quantity (1, 2, etc.) is measured.c “Rating of a politician” is a qualitative variable since a quality (excellent, good, fair, poor) is measured.d “Province or territory of residence” is a qualitative variable since a quality (ON, AB, BC, etc. ) is measured.

1.3 a “Population” is a discrete variable because it can take on only integer values.b “Weight” is a continuous variable, taking on any values associated with an interval on the real line.c “Time” is a continuous variable.d “Number of consumers” is integer-valued and hence discrete.

1.4 a “Number of boating accidents” is integer-valued and hence discrete.b “Time” is a continuous variable.c “Choice of colour” is a qualitative variable since a quality (white, cream, black, etc.) is measured.d “Number of brothers and sisters” is integer-valued and hence discrete.e “Yield in kilograms” is a continuous variable, taking on any values associated with an interval on the real line.

1.5 a The experimental unit, the item or object on which variables are measured, is the vehicle.b Type (qualitative); make (qualitative); carpool (qualitative); one-way commute distance (quantitative continuous); age of vehicle (quantitative continuous) c Since five variables have been measured, the data is multivariate.

1.6 a The set of ages at death represents a population, because there have only been 15 different prime ministers in Canadian history.b The variable being measured is the continuous variable “age.” c “Age” is a quantitative variable.

1.7 The population of interest consists of voter opinions (for or against the candidate) at the time of the election for all persons voting in the election. Note that when a sample is taken (at some time prior or the election), we are not actually sampling from the population of interest. As time passes, voter opinions change. Hence, the population of voter opinions changes with time, and the sample may not be representative of the population of interest.

1.8 a–b The variable “survival times” is a quantitative continuous variable.c The population of interest is the population of survival times for all patients having a particular type of cancer and having undergone a particular type of radiotherapy.d–e Note that there is a problem with sampling in this situation. If we sample from all patients having cancer and radiotherapy, some may still be living and their survival time will not be measurable.Hence, we cannot sample directly from the population of interest, but must arrive at some reasonable alternate population from which to sample.

(Introduction to Probability and Statistics, 3rd Canadian Edition 3e William Mendenhall, Robert Beaver, Ejaz Ahmed) (Solution Manual all Chapters) 1 / 4

Instructor’s Solutions Manual to Accompany Introduction to Probability and Statistics, 3CE 1-2 Copyright © 2014 Nelson Education Limited NEL 1.9 a The variable “reading score” is a quantitative variable, which is usually integer-valued and hence discrete.b The individual on which the variable is measured is the student.c The population is hypothetical—it does not exist in fact—but consists of the reading scores for all students who could possibly be taught by this method.

1.10 a–b The variable “category” is a qualitative variable measured for each of 50 people who constitute the experimental units.c The pie chart is constructed by partitioning the circle into four parts according to the total contributed by each part. Since the total number of people is 50, the total number in category A represents 11/50 = 0.22 or 22% of the total. Thus, this category will be represented by a sector angle of 0.22(360) = 79.2°. The other sector angles are shown below. The pie chart is shown in the figure below.

Category Frequency Fraction of Total Sector Angle

A 11 0.22 79.2

B 14 0.28 100.8

C 20 0.40 144.0

D 5 0.10 36.0

d The bar chart represents each category as a bar with height equal to the frequency of occurrence of that category and is shown in the figure below.

Ca t e gor y Fr e q u e n c y DCBA 20 15 10 5

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Instructor’s Solutions Manual to Accompany Introduction to Probability and Statistics, 3CE NEL Copyright © 2014 Nelson Education Limited 1-3 e Yes, the shape will change depending on the order of presentation. The order is unimportant.f The proportion of people in categories B, C, or D is found by summing the frequencies in those three categories, and dividing by n = 50. That is, (14 + 20 + 5)/50 = 0.78.g Since there are 14 people in category B, there are 50 − 14 = 36 who are not, and the percentage is calculated as (36/50)100 = 72%.

1.11 a–b The experimental unit is the pair of jeans, on which the qualitative variable “province” is measured.c–d First, construct a statistical table to summarize the data. The pie and bar charts are shown in the figures below.

Province Frequency Fraction of Total Sector Angle

ON 9 0.36 129.6

QC 8 0.32 115.2

MB 8 0.32 115.2

MBQCON

9 8 7 6 5 4 3 2 1

Province Frequency

e From the table or the chart, Quebec produced 825 0.32 of the jeans.f The highest bar represents Ontario, which produced the most pairs of jeans.g Since the bars and the sectors are almost equal in size, the three provinces produced roughly the same number of pairs of jeans.

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Instructor’s Solutions Manual to Accompany Introduction to Probability and Statistics, 3CE 1-4 Copyright © 2014 Nelson Education Limited NEL 1.12 a The population of interest consists of voter opinions (political or religious) on the conflict between Islam and the West.b The population from which the pollsters have sampled is the population of all adults from 27 countries (no further details available).c The percentages given in the exercise only add to 85%. We should add another category called “Other,” which will account for the other 15% of the responses.d Answers will vary.

1.13 a No, a few more Islamic countries (Iraq, Pakistan, Afghanistan, Syria, etc.) can be added in the table.b A bar chart is appropriate.c

TurkeyIndonesiaEgyptLebanon 80 70 60 50 40 30 20 10

Islamic Countries Percentage

d Answers will vary.

1.14 a–b The variable being measured is a qualitative variable, which would be described as “educational attainment.” c The numbers represent the percentages of Aboriginal and non-Aboriginal population who fall in each of the five educational attainment categories.d–e The percentages falling in each of the five categories have already been calculated, and the pie chart (Aboriginal) and bar chart (non-Aboriginal) are shown in the figures below and on the next page.

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