Solution Manual for Statistics, Updated Edition, 13th Edition

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Statistics, Data, and Statistical Thinking 1
Statistics, Data,
and Statistical Thinking
1.2 Descriptive statistics utilizes numerical and graphical methods to look for patterns, to
summarize, and to present the information in a set of data. Inferential statistics utilizes
sample data to make estimates, decisions, predictions, or other generalizations about a larger
set of data.
1.4 The first major method of collecting data is from a published source. These data have already
been collected by someone else and is available in a published source. The second method of
collecting data is from a designed experiment. These data are collected by a researcher who
exerts strict control over the experimental units in a study. These data are measured directly
from the experimental units. The third method of collecting data is from a survey. These
data are collected by a researcher asking a group of people one or more questions. Again,
these data are collected directly from the experimental units or people. The final method of
collecting data is observationally. These data are collected directly from experimental units
by simply observing the experimental units in their natural environment and recording the
values of the desired characteristics.
1.6 A population is a set of existing units such as people, objects, transactions, or events. A
variable is a characteristic or property of an individual population unit such as height of a
person, time of a reflex, amount of a transaction, etc.
1.8 A representative sample is a sample that exhibits characteristics similar to those possessed by
the target population. A representative sample is essential if inferential statistics is to be
applied. If a sample does not possess the same characteristics as the target population, then
any inferences made using the sample will be unreliable.
1.10 Statistical thinking involves applying rational thought processes to critically assess data and
inferences made from the data. It involves not taking all data and inferences presented at face
value, but rather making sure the inferences and data are valid.
1.12 a. High school GPA is a number usually between 0.0 and 4.0. Therefore, it is quantitative.
b. High school class rank is a number: 1st, 2nd, 3rd, etc. Therefore, it is quantitative.
c. The scores on the SAT's are numbers between 200 and 800. Therefore, it is
quantitative.
d. Gender is either male or female. Therefore, it is qualitative.
e. Parent's income is a number: $25,000, $45,000, etc. Therefore, it is quantitative.
f. Age is a number: 17, 18, etc. Therefore, it is quantitative.
1.14 a. The experimental unit for this experiment is a drafted NFL quarterback.
b. Draft position is one of three categories. Therefore, it is a qualitative variable. NFL
winning ratio is a number. Therefore, it is a quantitative variable. QB production score
is a number. Therefore, it is a quantitative variable.
Chapter
1

2 Chapter 1
c. Because all quarterbacks drafted over a 38-year period were used, the application of this
study is descriptive statistics.
1.16 a. The variable “difference between before and after sprint times” is measured in seconds.
Thus, it is quantitative. The variable “improvement” is measured as one of three
categories. Thus, it is qualitative.
b. The data set is a sample. It contains observations from only 14 of all high school football
players.
1.18 a. The population of interest is all the students in the class. The variable of interest is the
GPA of a student in the class.
b. Since GPA is measured on a numerical scale, it is quantitative.
c. Since the population of interest is all the students in the class and you obtained the GPA
of every member of the class, this set of data would be a census.
d. Assuming the class had more than 10 students in it, the set of 10 GPAs would represent
a sample. The set of ten students is only a subset of the entire class.
e. This average would have 100% reliability as an "estimate" of the class average, since it
is the average of interest.
f. The average GPA of 10 members of the class will not necessarily be the same as the
average GPA of the entire class. The reliability of the estimate will depend on how
large the class is and how representative the sample is of the entire population.
g. In order for the sample to be a random sample, every member of the class must have an
equal
1.20 a. Flight capability can have only 2 possible outcomes: volant or flightless. Thus, it is
qualitative.
b. Habitat type can have only 3 possible outcomes: aquatic, ground terrestrial, or aerial
terrestrial. Thus, it is qualitative.
c. Nesting site can have only 4 possible outcomes: ground, cavity within ground, tree, or
cavity above ground. Thus, it is qualitative.
d. Nest density can have only 2 possible outcomes: high or low. Thus, it is qualitative.
e. Diet can have only 4 possible outcomes: fish, vertebrates, vegetables, or invertebrates.
Thus, it is qualitative.
f. Body mass is measured in grams, a meaningful number. Thus, it is quantitative.
g. Egg length is measured in millimeters, a meaningful number. Thus, it is quantitative.
h. Extinct status can have only 3 possible outcomes: extinct, absent from island, or present.
Thus, it is qualitative.

Statistics, Data, and Statistical Thinking 3
1.22 a. The population of interest to CSI is all computer security personnel at all U.S.
corporations and government agencies.
b. The data collection method is a survey. A survey was sent to 5,412 firms with 351 firms
responding.
c. The variable collected was whether or not the respondents admitted unauthorized use of
computer systems at their firms during the year. Since the response to the questions was
either “yes” or “no”, this variable is qualitative.
d. In the sample 41% of the respondents admitted unauthorized use of computer systems at
their firms during the year. If there is no nonresponse bias, then we can conclude that
41% of all firms would admit to unauthorized use of computer systems at their firms
during the year.
1.24 The following variables would be qualitative because the response would be a category:
country of operator/owner, primary use, and class of orbit. The following variables would be
quantitative because the response would be a number: Longitudinal position, apogee, launch
mass, usable electric power, and expected lifetime.
1.26 a. The population of interest is all senior managers at CPA firms.
b. The data collection method used is a survey.
c. Because only 992 of the 23,500 surveys sent out were returned and useable, there may be
a problem with selection bias and/or nonresponse bias.
d. The validity of the inferences drawn from the study would be suspect. The inferences
would only be valid if the 992 returned surveys were indeed, representative of the entire
population. This is very unlikely.
1.28 a. The experimental unit for this study is a single-family residential property in Arlington,
Texas.
b. The variables measured were the Zillow estimated value and the actual sale price. Both
are quantitative variables.
c. If the population was described as all single-family residential properties in Arlington,
Texas that sold within a given time period, then these 2,045 single-family residential
properties could be the population if these were the only single-family residential
property sales in Arlington, Texas in that time period.
d. The population could be all single-family residential properties sold in Arlington, Texas
in a given time period and these 2,045 single-family residential properties did not include
all the properties sold.
e. No. The single-family residential properties sold in Arlington, Texas probably are not
similar to all single-family residential properties sold in the United States. Single-family
residential properties sold in Arlington, Texas are not similar to single-family residential
properties sold in places like New York City or San Francisco, California.

4 Chapter 1
1.30 a. The population of interest is the set of all adults living in Tennessee. The sample of
interest is the set of 575 people selected from Tennessee.
b. The data collection method used was a survey. A random-digit telephone dialing
procedure was used to collect the sample. Since some people do not own phones, this
would not be a random sample. Everyone in the state of Tennessee would not have an
equal chance of being selected. Those without telephones would tend to be the
undereducated. Thus, there could be potential biases in the data.
c. The two variables identified in this problem are the number of years of education and the
insomnia status of each subject. The number of years of education is quantitative and the
insomnia status is qualitative.
d. The researchers inferred that the fewer the years of education, the more likely the person
was to have chronic insomnia.
1.32 a. The experimental units of this study were people who used a popular website for engaged
couples.
b. The variables of interest are the engagement ring price and the level of appreciation of
the recipient.
c. The population of interest were all those people on the popular website for engaged
couples with “average” American names.
d. This sample of 33 respondents is probably not representative of the population. Those
who decided to respond to the online survey self-selected themselves. They were not
randomly selected. Generally speaking, those people who choose to respond to a survey
have very strong feelings and are not representative of the entire population.
e. Answers will vary. Enter the numbers 1-50 in the first column of Minitab. Now, apply
the random number generator of Minitab, requesting that 25 individuals be selected
without replacement. The sample generated include individuals 1, 3, 6, 7, 9, 10, 11, 12,
13, 17, 18, 22, 24, 25, 27, 28, 30, 31, 32, 36, 37, 46, 47, 48, 50. These individuals would
be placed in the gift-receiver role and the remaining individuals would be placed in the
gift-giver role.
1.34 a. In Method 1, the researchers controlled which hot spots received the new program
(through random assignment) and which did not. Therefore, a designed experiment was
used to collect data in Method 1.
b. In Method 2, the researchers first divided the 56 hot spots into 4 groups based on the
level of drug crimes. The researchers then controlled which hot spots received the new
program (through random assignment) and which did not in each of the 4 groups.
Therefore, a designed experiment was also used to collect data in Method 2.
c. This would be an application of inferential statistics because not all hot spots in Jersey
City were used in the study. Only a sample of 56 hot spots was used.

Statistics, Data, and Statistical Thinking 5
d. Method 2 would be recommended. By creating 4 groups where the crime rate within
each group is similar, we can control for a known source of variation. Within each
group, we can then see how the new program compares to no program.
1.36 a. Although eating oat bran can reduce cholesterol, oat bran must be the only thing eaten.
Reporting that eating oat bran is an easy and cheap way to lower your cholesterol implies
that if you add oat bran to your diet, you can reduce your cholesterol, which may not be
the case at all.
b. One would need to collect data on a sample of women who gave birth to babies with birth
defects. Then, each woman in the study would also be asked whether she was a victim of
domestic violence while pregnant or not. The data collection method for this study
would be an observational study. Specifically, one would use a survey to collect the data.
c. In this study, only the results of the most positive response were reported. Not that many
high school girls would ‘Always’ be happy with the way they were. To be more
representative of those who are happy with the way they were, one should combine the
results of those who responded ‘Always true’, ‘Sort of true’, and ‘Sometimes true’.

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6 Chapter 2
Methods for Describing
Sets of Data
2.2 In a bar graph, a bar or rectangle is drawn above each class of the qualitative variable
corresponding to the class frequency or class relative frequency. In a pie chart, each slice of
the pie corresponds to the relative frequency of a class of the qualitative variable.
2.4 First, we find the frequency of the grade A. The sum of the frequencies for all 5 grades must
be 200. Therefore, subtract the sum of the frequencies of the other 4 grades from 200. The
frequency for grade A is:
200  (36 + 90 + 30 + 28) = 200  184 = 16
To find the relative frequency for each grade, divide the frequency by the total sample size,
200. The relative frequency for the grade B is 36/200 = .18. The rest of the relative
frequencies are found in a similar manner and appear in the table:
Grade on Statistics Exam Frequency Relative Frequency
A: 90100 16 .08
B: 80 89 36 .18
C: 65 79 90 .45
D: 50 64 30 .15
F: Below 50 28 .14
Total 200 1.00
2.6 a. The graph shown is a pie chart.
b. The qualitative variable described in the graph is opinion on library importance.
c. The most common opinion is more important, with 46.0% of the responders indicating
that they think libraries have become more important.
d. Using MINITAB, the Pareto diagram is:
Of those who responded to the question, almost half (46%) believe that libraries have
become more important to their community. Only 18% believe that libraries have
become less important.
Chapter
2
LessSameMore
50
40
30
20
10
0
Importance
Percent
Chart of Percent

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Methods for Describing Sets of Data 7
2.8 a. From the pie chart, 50.4% or 0.504 of adults living in the U.S. use the internet and pay
to download music. From the data, 506 out of 1,003 adults or 506/1,003 = 0.504 of
adults in the U.S. use the internet and pay to download music. These two results agree.
b. Using MINITAB, a pie chart of the data is:
33.0%
No Pay
67.0%
Pay
Category
Pay
No Pay
Pie Chart of Download-Music
2.10 a. Data were collected on 3 questions. For questions 1 and 2, the responses were either
‘yes’ or ‘no’. Since these are not numbers, the data are qualitative. For question 3, the
responses include ‘character counts’, ‘roots of empathy’, ‘teacher designed’, other’, and
‘none’. Since these responses are not numbers, the data are qualitative.
b. Using MINITAB, bar charts for the 3 questions are:
NoYes
60
50
40
30
20
10
0
Classroom Pets
Count
Chart of Classroom Pets

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8 Chapter 2
c. Many different things can be written. Possible answers might be: Most of the classroom
teachers surveyed (61 / 75 0.813) keep classroom pets. A little less than half of the
surveyed classroom teachers (35 / 75 0.467) allow visits by pets.
2.12 Using MINITAB, the pie chart is:
NoYes
40
30
20
10
0
Pet Visits
Count
Chart of Pet Visits
NoneOtherTeacher designedRoots of EmpathyCharacter Counts
30
25
20
15
10
5
0
Education
Count
Chart of Education
Urban
Suburban
Rural
Category
Rural
5.7%
Suburban
32.8%
Urban
61.5%
Pie Chart of Loc

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Methods for Describing Sets of Data 9
2.14 a. The two qualitative variables graphed in the bar charts are the occupational titles of clan
individuals in the continued line and the occupational titles of clan individuals in the
dropout line.
b. In the Continued Line, about 63% were in either the high or the middle grade. Only
about 20% were in the nonofficial category. In the Dropout Line, only about 22% were
in either the high or middle grade while about 64% were in the nonofficial category.
The percentages in the low grade and provincial official categories were about the same
for the two lines.
2.16 Using MINITAB, the Pareto chart is:
From the graph, it appears that tracks #5 and #8 were over-utilized and track #1 is under-
utilized.
2.18 a. Using MINITAB, the Pareto chart of the total annual shootings involving the Boston
street gang is:
#1#9#4#3#2#11#10#7#6#8#5
.14
.12
.10
.08
.06
.04
.02
0
Track
Relative frequency
Proportion within all data.
Chart of Allocation
20102008200920072006
.5
.4
.3
.2
.1
0
Year
Proportion of Total Shootings
Chart of Total Shootings
Proportion within all data.

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10 Chapter 2
b. Using MINITAB, the Pareto chart of the annual shootings of the Boston gang members
is:
c. Because the proportion of shootings per year dropped drastically after 2007 for both the
total annual shootings and annual shootings of the Boston street gang members, it
appears that Operation Ceasefire was effective.
2.20 Using MINITAB, the side-by-side bar graphs showing the distribution of dives for the three
match situations are:
From the graphs, it appears that when a team is tied or ahead, there is no difference in the
proportion of times the goal-keeper dives right or left. However, if the team is behind, the
goal-keeper tends to dive right much more frequently than left.
20102008200920072006
.5
.4
.3
.2
.1
0
Year
Proportion of Gang Members
Chart of Gang Member Shootings
Proportion within all data.
RightMiddleLeft
.8
.6
.4
.2
0
RightMiddleLeft
.8
.6
.4
.2
0
Team behind
Dive
Proportion
Tied
Team ahead
Chart of Team behind, Tied, Team ahead
Proportion within all data.

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Methods for Describing Sets of Data 11
2.22 Using MINITAB, a bar graph of the data is:
The researcher concluded that “there is a large amount of variation within the museum
community with regards to . . . performance measurement and evaluation”. From the data,
there are only 5 different performance measures. I would not say that this is a large amount.
Within these 5 categories, the number of times each is used does not vary that much. I would
disagree with the researcher. There is not much variation.
2.24 Using MINITAB a bar chart for the Extinct status versus flight capability is:
It appears that extinct status is related to flight capability. For birds that do have flight
capability, most of them are present. For those birds that do not have flight capability, most
are extinct.
MembersFunds raisedBig showsPaying visitorsTotal Visitors
9
8
7
6
5
4
3
2
1
0
Measure
Freq
Chart of Measure
Extinct
Flight
YesNoAbsent
YesNoYesNoYesNo
80
70
60
50
40
30
20
10
0
Count
Chart of Extinct, Flight

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12 Chapter 2
The bar chart for Extinct status versus Nest Density is:
It appears that extinct status is not related to nest density. The proportion of birds present,
absent, and extinct appears to be very similar for nest density high and nest density low.
The bar chart for Extinct status versus Habitat is:
It appears that the extinct status is related to habitat. For those in aerial terrestrial (TA), most
species are present. For those in ground terrestrial (TG), most species are extinct. For those
in aquatic, most species are present.
2.26 The difference between a bar chart and a histogram is that a bar chart is used for qualitative
data and a histogram is used for quantitative data. For a bar chart, the categories of the
qualitative variable usually appear on the horizontal axis. The frequency or relative
frequency for each category usually appears on the vertical axis. For a histogram, values of
the quantitative variable usually appear on the horizontal axis and either frequency or relative
frequency usually appears on the vertical axis. The quantitative data are grouped into
intervals which appear on the horizontal axis. The number of observations appearing in each
interval is then graphed. Bar charts usually leave spaces between the bars while histograms
do not.
2.28 In a histogram, a class interval is a range of numbers above which the frequency of the
measurements or relative frequency of the measurements is plotted.
Extinct
Nest Density
YesNoAbsent
LHLHLH
60
50
40
30
20
10
0
Count
Chart of Extinct, Nest Density
Extinct
Habitat
YesNoAbsent
TGTAATGTAATGTAA
40
30
20
10
0
Count
Chart of Extinct, Habitat

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Methods for Describing Sets of Data 13
2.30 a. This is a frequency histogram because the number of observations is displayed rather
than the relative frequencies.
b. There are 14 class intervals used in this histogram.
c. The total number of measurements in the data set is 49.
2.32 Using MINITAB, the relative frequency histogram is:
Class Interval
Relative frequency
16.514.512.510.58.56.54.52.50.5
.25
.20
.15
.10
.05
0
2.34 a. Using MINITAB, the relative frequency histogram is:
b. From the graph, the proportion of subjects with RDER values between 75 and 105 is
about 0.18. The exact proportion is 13 / 71 0.183 .
b. From the graph, the proportion of subjects with RDER values below 15 is about
0.01 0.08 0.09  . The exact proportion is  1 6 / 71 0.099  .
2.36 a. Because the label on the vertical axis is ‘Percent’ , this is a relative frequency histogram.
255225195165135105754515-15-45
0.25
0.20
0.15
0.10
0.05
0
RDER Value
Relative Frequency
Histogram of RDER

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14 Chapter 2
b. From the graph, the percentage of the 992 senior managers who reported a high level of
support for corporate sustainability is about
3.8 2.4 2.1 1.2 1.2 0.5 0.7 0.2 0.1 0 0.1 12.3%           .
2.38 Using MINITAB, the stem-and-leaf display is:
Stem-and-Leaf Display: Depth
Stem-and-leaf of Depth N = 18
Leaf Unit = 0.10
2 13 29
4 14 00
8 15 7789
(3) 16 125
7 17 08
5 18 11
3 19 347
The data in the stem-and-leaf display are displayed to 1 decimal place while the actual data is
displayed to 2 decimal places. To 1 decimal place, there are 3 numbers that appear twice –
14.0, 15.7, and 18.1. However, to 2 decimal places, none of these numbers are the same.
Thus, no molar depth occurs more frequently in the data.
2.40 a. Using MINITAB, the dot plot of the honey dosage data is:
b. Both 10 and 12 occurred 6 times in the honey dosage group.
c. From the graph in part c, 8 of the top 11 scores (72.7%) are from the honey dosage
group. Of the top 30 scores, 18 (60%) are from the honey dosage group. This supports
the conclusions of the researchers that honey may be a preferable treatment for the
cough and sleep difficulty associated with childhood upper respiratory tract infection.
16141210864
Improvement Score
Dotplot of Honey Dosage Group

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Methods for Describing Sets of Data 15
2.42 a. Using MINITAB, the stem-and-leaf display is:
Stem-and-Leaf Display: Spider
Stem-and-leaf of Spider N = 10
Leaf Unit = 10
1 0 0
3 0 33
(3) 0 455
4 0 67
2 0 9
1 1 1
b. The spiders with a contrast value of 70 or higher are in bold type in the stem-and-leaf
display in part a. There are 3 spiders in this group.
c. The sample proportion of spiders that a bird could detect is 3 / 10 0.3 . Thus, we could
infer that a bird could detect a crab-spider sitting on the yellow central part of a daisy
about 30% of the time.
2.44 a. A stem-and-leaf display of the data using MINITAB is:
Stem-and-Leaf Display: FNE
Stem-and-leaf of FNE N = 25
Leaf Unit = 1.0
2 0 67
3 0 8
6 1 001
10 1 3333
12 1 45
(2) 1 66
11 1 8999
7 2 0011
3 2 3
2 2 45
b. The numbers in bold in the stem-and-leaf display represent the bulimic students. Those
numbers tend to be the larger numbers. The larger numbers indicate a greater fear of
negative evaluation. Thus, the bulimic students tend to have a greater fear of negative
evaluation.
c. A measure of reliability indicates how certain one is that the conclusion drawn is
correct. Without a measure of reliability, anyone could just guess at a conclusion.

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