Solution Manual for Statistical Reasoning for Everyday Life, 5th Edition
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SOLUTIONS MANUAL
S TATISTICAL R EASONING
FOR E VERYDAY L IFE
F IFTH EDITION
Jeffrey Bennett
University of Colorado at Boulder
William L. Briggs
University of Colorado at Denver
Mario F. Triola
Dutchess Community College
S TATISTICAL R EASONING
FOR E VERYDAY L IFE
F IFTH EDITION
Jeffrey Bennett
University of Colorado at Boulder
William L. Briggs
University of Colorado at Denver
Mario F. Triola
Dutchess Community College
iii
Contents
Chapter 1 Speaking of Statistics .................................................................................................................. 1
Chapter 2 Measurement in Statistics ......................................................................................................... 9
Chapter 3 Visual Displays of Data .......................................................................................................... 17
Chapter 4 Describing Data .......................................................................................................................... 27
Chapter 5 A Normal World ......................................................................................................................... 37
Chapter 6 Probability in Statistics ........................................................................................................... 45
Chapter 7 Correlation and Causality ...................................................................................................... 53
Chapter 8 Inferences from Samples to Populations ........................................................................ 61
Chapter 9 Hypothesis Testing .................................................................................................................... 67
Chapter 10 t Tests, Two-Way Tables, and ANOVA ...................................................................... 73
Contents
Chapter 1 Speaking of Statistics .................................................................................................................. 1
Chapter 2 Measurement in Statistics ......................................................................................................... 9
Chapter 3 Visual Displays of Data .......................................................................................................... 17
Chapter 4 Describing Data .......................................................................................................................... 27
Chapter 5 A Normal World ......................................................................................................................... 37
Chapter 6 Probability in Statistics ........................................................................................................... 45
Chapter 7 Correlation and Causality ...................................................................................................... 53
Chapter 8 Inferences from Samples to Populations ........................................................................ 61
Chapter 9 Hypothesis Testing .................................................................................................................... 67
Chapter 10 t Tests, Two-Way Tables, and ANOVA ...................................................................... 73
1
CHAPTER 1
Section 1.1
Statistical Literacy and Critical Thinking
1 The two meanings are: (1) statistics is the science of collecting,
organizing, and interpreting data; and (2) statistics are the data (numbers
or other pieces of information) that describe or summarize some
characteristic from a sample. Note that for the first meaning, the word
“statistics” is singular and for the second it is plural.
2 A population is the complete set of people or things being studied, while a
sample is a subset of a population. In other words, the sample is only a
part of the complete population. A population parameter is a characteristic
of a population. A sample statistic is a characteristic of a sample found by
consolidating or summarizing raw data. Raw data are all measurements or
observations collected. It is usually impractical to directly measure
population parameters for large populations, so we usually infer likely
values of the population parameters from the measured sample statistics.
3 The margin of error is used to describe the range of values in a confidence
interval. We add and subtract the margin of error from a sample statistic to
find the confidence interval, or the range of values that is likely to
contain some population parameter. The confidence interval is used to
estimate the population parameter, and the confidence level (e.g. 95%) tells
us how confident we should be that the population parameter lies within the
quoted range.
4 The basic steps, summarized in Figure 1.1, are: (1) identify the goals; (2)
choose a representative sample from the population; (3) collect raw data
from the sample and summarize them with sample statistics; (4) use the
sample statistics to make inferences about the population; (5) draw
conclusions from your results. Students should come up with their own
example.
5 This statement does not make sense. The statement is drawing a conclusion
about all American adults, which means it is identifying the exact value of
a population parameter. But the pollster only surveyed a sample of 1009
adults, so it is not possible to know with certainty the value of the
population parameter.
6 This statement does make sense. The margin of error suggests a (presumably
95%) confidence interval from 52% to 58%. However, there is always some
chance that the actual population proportion is outside the confidence
interval, and in this case it would not need to be far outside for the
candidate to lose. Moreover, the poll was taken 2 months before the
election, and voters may change their minds by election time.
7 This statement does not make sense. A margin of error of zero would imply
that there is no uncertainty in a survey result, and that could happen only
if the entire population was surveyed, rather than just a sample.
8 This statement does not make sense. The confidence interval tells us that
we can have 95% confidence that the values from 55% to 60% contain the
population parameter, but we cannot be absolutely certain that the true
population parameter isn’t significantly lower or higher.
9 This statement does not make sense. Inferences about one population (males)
do not necessarily apply to a different population (females).
10 This statement does make sense. The purpose of statistics is to help with
decision making, and if the survey was conducted well, it is possible to
draw conclusions with high confidence from a survey of a 1000-person sample.
If the survey results indicate that most people like the song, then it makes
sense to promote it, even though there is no guarantee that the promotion
will be successful.
CHAPTER 1
Section 1.1
Statistical Literacy and Critical Thinking
1 The two meanings are: (1) statistics is the science of collecting,
organizing, and interpreting data; and (2) statistics are the data (numbers
or other pieces of information) that describe or summarize some
characteristic from a sample. Note that for the first meaning, the word
“statistics” is singular and for the second it is plural.
2 A population is the complete set of people or things being studied, while a
sample is a subset of a population. In other words, the sample is only a
part of the complete population. A population parameter is a characteristic
of a population. A sample statistic is a characteristic of a sample found by
consolidating or summarizing raw data. Raw data are all measurements or
observations collected. It is usually impractical to directly measure
population parameters for large populations, so we usually infer likely
values of the population parameters from the measured sample statistics.
3 The margin of error is used to describe the range of values in a confidence
interval. We add and subtract the margin of error from a sample statistic to
find the confidence interval, or the range of values that is likely to
contain some population parameter. The confidence interval is used to
estimate the population parameter, and the confidence level (e.g. 95%) tells
us how confident we should be that the population parameter lies within the
quoted range.
4 The basic steps, summarized in Figure 1.1, are: (1) identify the goals; (2)
choose a representative sample from the population; (3) collect raw data
from the sample and summarize them with sample statistics; (4) use the
sample statistics to make inferences about the population; (5) draw
conclusions from your results. Students should come up with their own
example.
5 This statement does not make sense. The statement is drawing a conclusion
about all American adults, which means it is identifying the exact value of
a population parameter. But the pollster only surveyed a sample of 1009
adults, so it is not possible to know with certainty the value of the
population parameter.
6 This statement does make sense. The margin of error suggests a (presumably
95%) confidence interval from 52% to 58%. However, there is always some
chance that the actual population proportion is outside the confidence
interval, and in this case it would not need to be far outside for the
candidate to lose. Moreover, the poll was taken 2 months before the
election, and voters may change their minds by election time.
7 This statement does not make sense. A margin of error of zero would imply
that there is no uncertainty in a survey result, and that could happen only
if the entire population was surveyed, rather than just a sample.
8 This statement does not make sense. The confidence interval tells us that
we can have 95% confidence that the values from 55% to 60% contain the
population parameter, but we cannot be absolutely certain that the true
population parameter isn’t significantly lower or higher.
9 This statement does not make sense. Inferences about one population (males)
do not necessarily apply to a different population (females).
10 This statement does make sense. The purpose of statistics is to help with
decision making, and if the survey was conducted well, it is possible to
draw conclusions with high confidence from a survey of a 1000-person sample.
If the survey results indicate that most people like the song, then it makes
sense to promote it, even though there is no guarantee that the promotion
will be successful.
2 CHAPTER 1, SPEAKING OF STATISTICS
Concepts and Applications
11 Sample: the 1018 adults selected. Population: the complete set of all
adults (presumably in the United States). Sample statistic: 22%. The
value of the population parameter is not known, but it is the
percentage of all adults (presumably in the United States) who smoked
cigarettes in the past week.
12 Sample: the 186 babies selected. Population: the complete set of all
babies. Sample statistic: 3103 g. The value of the population
parameter is not known, but it is the average (mean) birth weight of
all babies.
13 Sample: the 47 subjects treated with Garlicin. Population: the
complete set of all adults. Sample statistic: 3.2 mg/dL. The value of
the population parameter is not known, but it is the average (mean)
change in LDL cholesterol.
14 Sample: the 150 senior executives who were surveyed. Population: the
complete set of all senior executives. Sample statistic: 47%. The
value of the population parameter is not known, but it is the
percentage of all senior executives who say that the most common job
interview mistake is to have little or no knowledge of the company
where the applicant is being interviewed.
15 The range of values likely to contain the true value of the population
parameter is from 77% - 2% to 77% + 2% or from 75% to 79%.
16 The range of values likely to contain the true value of the population
parameter is from 85% - 1% to 85% + 1% or from 84% to 86%.
17 The range of values likely to contain the true value of the population
parameter is from 96% – 3% to 96% + 3% or from 93% to 99%.
18 The range of values likely to contain the true value of the population
parameter (mean body temperature) is 98.2º F – 0.1º F to 98.2º F +
0.1º F or from 98.1º F to 98.3º F degrees.
19 The range of values likely to contain the true value of the population
parameter is from 57% – 4% to 57% + 4% or from 53% to 61%.
20 The range of values likely to contain the true value of the population
parameter is from 0.032% – 0.006% to 0.032% + 0.006% or from 0.026% to
0.038%.
21 Based on the survey, the actual percentage of voters is expected to be
between 67% and 73%, which does not include the 61% value from actual
voting records. If the survey was conducted well, then it is unlikely
that its result would be so different from the actual voter turnout,
implying either that respondents intentionally lied to appear
favorable to the pollsters or that their memories may have been
faulty.
22 It appears that the men who were surveyed may have been influenced by
the gender of the interviewer. When they were interviewed by women,
they may have been more inclined to respond in a way that they thought
was more favorable to the female interviewers.
23 Yes, we can safely conclude that fewer than half of all students say
they are tired on most days. Based on the confidence interval and
margin of error, it is likely that the actual population parameter is
fairly close to the 39% sample statistic, and very unlikely that the
true value could be above 50%.
24 No, the results do not contradict Mendel’s theory. Using the margin of
error, it appears that the percentage of yellow peas is likely to be
between 22% and 30%, and that range of values includes Mendel’s
claimed value of 25%, so the results do not contradict his theory.
Concepts and Applications
11 Sample: the 1018 adults selected. Population: the complete set of all
adults (presumably in the United States). Sample statistic: 22%. The
value of the population parameter is not known, but it is the
percentage of all adults (presumably in the United States) who smoked
cigarettes in the past week.
12 Sample: the 186 babies selected. Population: the complete set of all
babies. Sample statistic: 3103 g. The value of the population
parameter is not known, but it is the average (mean) birth weight of
all babies.
13 Sample: the 47 subjects treated with Garlicin. Population: the
complete set of all adults. Sample statistic: 3.2 mg/dL. The value of
the population parameter is not known, but it is the average (mean)
change in LDL cholesterol.
14 Sample: the 150 senior executives who were surveyed. Population: the
complete set of all senior executives. Sample statistic: 47%. The
value of the population parameter is not known, but it is the
percentage of all senior executives who say that the most common job
interview mistake is to have little or no knowledge of the company
where the applicant is being interviewed.
15 The range of values likely to contain the true value of the population
parameter is from 77% - 2% to 77% + 2% or from 75% to 79%.
16 The range of values likely to contain the true value of the population
parameter is from 85% - 1% to 85% + 1% or from 84% to 86%.
17 The range of values likely to contain the true value of the population
parameter is from 96% – 3% to 96% + 3% or from 93% to 99%.
18 The range of values likely to contain the true value of the population
parameter (mean body temperature) is 98.2º F – 0.1º F to 98.2º F +
0.1º F or from 98.1º F to 98.3º F degrees.
19 The range of values likely to contain the true value of the population
parameter is from 57% – 4% to 57% + 4% or from 53% to 61%.
20 The range of values likely to contain the true value of the population
parameter is from 0.032% – 0.006% to 0.032% + 0.006% or from 0.026% to
0.038%.
21 Based on the survey, the actual percentage of voters is expected to be
between 67% and 73%, which does not include the 61% value from actual
voting records. If the survey was conducted well, then it is unlikely
that its result would be so different from the actual voter turnout,
implying either that respondents intentionally lied to appear
favorable to the pollsters or that their memories may have been
faulty.
22 It appears that the men who were surveyed may have been influenced by
the gender of the interviewer. When they were interviewed by women,
they may have been more inclined to respond in a way that they thought
was more favorable to the female interviewers.
23 Yes, we can safely conclude that fewer than half of all students say
they are tired on most days. Based on the confidence interval and
margin of error, it is likely that the actual population parameter is
fairly close to the 39% sample statistic, and very unlikely that the
true value could be above 50%.
24 No, the results do not contradict Mendel’s theory. Using the margin of
error, it appears that the percentage of yellow peas is likely to be
between 22% and 30%, and that range of values includes Mendel’s
claimed value of 25%, so the results do not contradict his theory.
SECTION 1.1, WHAT IS/ARE STATISTICS? 3
25 a) Goal: determine the percentage of employees who would like to have
their boss’s job. Population: the complete set of all employees.
Population parameter: the percentage of all employees who would like
to have their boss’s job.
b) Sample: the 144 employees selected for the survey. Raw data:
individual responses to the question. Sample statistic: 21%.
c) The range of values likely to contain the population parameter is from
21% - 7% to 21% + % (or from 14% to 28%).
26 a) Goal: determine the percentage of older adults (aged 57 to 85 years)
who use at least one prescription drug. Population: the complete set
of all older adults. Population parameter: the percentage of all older
adults who use at least one prescription drug.
b) Sample: the 3005 older adults selected for the survey. Raw data:
individual responses to the question. Sample statistic: 82%.
c) The range of values likely to contain the population parameter is from
82% - 2% to 82% + 2% (or from 80% to 84%).
27 a) Goal: determine the percentage of adults who say that they are
underpaid. Population: the complete set of all adults. Population
parameter: the percentage of all adults who say that they are
underpaid.
b) Sample: the 557 adults randomly selected and surveyed. Raw data:
individual responses to the survey question. Sample statistic: 51%.
c) The range of values likely to contain the population parameter is 51%
- 4% to 51% + 4% (or from 47% to 55%).
28 a) Goal: determine the percentage of human resource professionals who say
that piercings or tattoos are big grooming red flags. Population: the
complete set of all human resource professionals. Population
parameter: the percentage of all human resource professionals who say
that piercings or tattoos are big grooming red flags.
b) Sample: the 514 human resource professionals selected for the survey.
Raw data: individual responses to the question. Sample statistic: 46%.
c) The range of values likely to contain the population parameter is 46%
- 4% to 46% + 4% (or from 42% to 50%).
29 Step 1: Goal: identify the percentage of all drivers who text while they
are driving.
Step 2: Choose a representative sample of drivers.
Step 3: Somehow collect data on whether the drivers in the sample text
while driving. Find the percentage who do.
Step 4: Use the sample statistic to make an inference about the
percentage of all drivers who text while they are driving.
Step 5: Based on the likely value of the population parameter, form a
conclusion about the percentage of drivers who text while they
are driving.
30 Step 1: Goal: identify the average (mean) FICO score of all adults in
the United States.
Step 2: Choose a sample of adult consumers.
Step 3:
25 a) Goal: determine the percentage of employees who would like to have
their boss’s job. Population: the complete set of all employees.
Population parameter: the percentage of all employees who would like
to have their boss’s job.
b) Sample: the 144 employees selected for the survey. Raw data:
individual responses to the question. Sample statistic: 21%.
c) The range of values likely to contain the population parameter is from
21% - 7% to 21% + % (or from 14% to 28%).
26 a) Goal: determine the percentage of older adults (aged 57 to 85 years)
who use at least one prescription drug. Population: the complete set
of all older adults. Population parameter: the percentage of all older
adults who use at least one prescription drug.
b) Sample: the 3005 older adults selected for the survey. Raw data:
individual responses to the question. Sample statistic: 82%.
c) The range of values likely to contain the population parameter is from
82% - 2% to 82% + 2% (or from 80% to 84%).
27 a) Goal: determine the percentage of adults who say that they are
underpaid. Population: the complete set of all adults. Population
parameter: the percentage of all adults who say that they are
underpaid.
b) Sample: the 557 adults randomly selected and surveyed. Raw data:
individual responses to the survey question. Sample statistic: 51%.
c) The range of values likely to contain the population parameter is 51%
- 4% to 51% + 4% (or from 47% to 55%).
28 a) Goal: determine the percentage of human resource professionals who say
that piercings or tattoos are big grooming red flags. Population: the
complete set of all human resource professionals. Population
parameter: the percentage of all human resource professionals who say
that piercings or tattoos are big grooming red flags.
b) Sample: the 514 human resource professionals selected for the survey.
Raw data: individual responses to the question. Sample statistic: 46%.
c) The range of values likely to contain the population parameter is 46%
- 4% to 46% + 4% (or from 42% to 50%).
29 Step 1: Goal: identify the percentage of all drivers who text while they
are driving.
Step 2: Choose a representative sample of drivers.
Step 3: Somehow collect data on whether the drivers in the sample text
while driving. Find the percentage who do.
Step 4: Use the sample statistic to make an inference about the
percentage of all drivers who text while they are driving.
Step 5: Based on the likely value of the population parameter, form a
conclusion about the percentage of drivers who text while they
are driving.
30 Step 1: Goal: identify the average (mean) FICO score of all adults in
the United States.
Step 2: Choose a sample of adult consumers.
Step 3:
Loading page 6...
4 CHAPTER 1, SPEAKING OF STATISTICS
Step 4: Use the sample statistic to make an inference about the
average weight of all airline passengers.
Step 5: Based on the likely value of the population parameter, form
a conclusion about the average weight of all airline
passengers.
32 Step 1: Goal: identify the average (mean) length of time that
pacemaker batteries last before failure.
Step 2: Choose a sample of pacemaker batteries.
Step 3: Record the length of time that each battery in the sample
lasts before failure. Find the average of those times.
Step 4: Use the sample statistic to make an inference about the
average length of time that all pacemaker batteries last
before failure.
Step 5: Based on the likely value of the population parameter, form
a conclusion about the average length of time that all
pacemaker batteries last before failure.
Section 1.2
Statistical Literacy and Critical Thinking
1 A census is a collection of data from every member of a population, but a
sample is a collection of data from only part of a population.
2 A representative sample is a sample in which the relevant characteristics of
the sample members are generally the same as the characteristics of the
population. It is critically important to collect a sample that is
representative of the population for which you intend to make inferences
about. Failure to obtain a representative sample is a major contributor to
misleading statistics.
3 A biased sample is a sample that somehow tends to favor certain results.
Because a biased sample is not representative of the population, results
obtained from a biased sample are likely to be misleading. Preventing bias
is one of the greatest challenges in statistical research.
4 The five common sampling methods described in the text are:
Simple random sampling: A sample of items is collected in such a way
that every sample of the same size has an equal chance of being
selected.
Systematic sampling: A simple system is used to choose the sample,
such as selecting every 10th or every 50th member of the population.
Convenience sampling: A sample is collected that happens to be
convenient to select.
Step 4: Use the sample statistic to make an inference about the
average weight of all airline passengers.
Step 5: Based on the likely value of the population parameter, form
a conclusion about the average weight of all airline
passengers.
32 Step 1: Goal: identify the average (mean) length of time that
pacemaker batteries last before failure.
Step 2: Choose a sample of pacemaker batteries.
Step 3: Record the length of time that each battery in the sample
lasts before failure. Find the average of those times.
Step 4: Use the sample statistic to make an inference about the
average length of time that all pacemaker batteries last
before failure.
Step 5: Based on the likely value of the population parameter, form
a conclusion about the average length of time that all
pacemaker batteries last before failure.
Section 1.2
Statistical Literacy and Critical Thinking
1 A census is a collection of data from every member of a population, but a
sample is a collection of data from only part of a population.
2 A representative sample is a sample in which the relevant characteristics of
the sample members are generally the same as the characteristics of the
population. It is critically important to collect a sample that is
representative of the population for which you intend to make inferences
about. Failure to obtain a representative sample is a major contributor to
misleading statistics.
3 A biased sample is a sample that somehow tends to favor certain results.
Because a biased sample is not representative of the population, results
obtained from a biased sample are likely to be misleading. Preventing bias
is one of the greatest challenges in statistical research.
4 The five common sampling methods described in the text are:
Simple random sampling: A sample of items is collected in such a way
that every sample of the same size has an equal chance of being
selected.
Systematic sampling: A simple system is used to choose the sample,
such as selecting every 10th or every 50th member of the population.
Convenience sampling: A sample is collected that happens to be
convenient to select.
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SECTION 1.3, TYPES OF STATISTICAL STUDIES 5
7 This statement does make sense. The gender makeup of the sample should
reflect the gender makeup of the movie-going population. While that
population might not have precisely equal proportions of males and females,
it certainly is not so male-dominated as this sample, so the study used a
biased sample.
8 This statement does make sense. The procedure described does result in a
simple random sample, and it is a procedure that is commonly used.
Concepts and Applications
9 A census is practical. Even though NFL team rosters include about 1700
players, it is easy to find their weights on the Internet.
10 A census is not practical because the number of high school football players
in California is too large and their weights are not readily available.
11 A census is not practical. The number of statistics students in the United
States is too large (hundreds of thousands), and it would probably be
difficult to find their ages.
12 A census is practical. The number of members of Congress is not large (535),
and their annual salaries are available on the Internet.
13 Sample: the 1002 surveyed subjects. Population: all adults. Sampling method:
simple random sampling. The sample is likely to be representative of the
population.
14 Sample: the 4500 mailed responses from women. Population: all women.
Sampling method: convenience sampling. The sample is not likely to be
representative of the population.
15 Sample: the 47 responses from the website. Population: all adult Americans.
Sampling method: convenience sampling. Because the sample is very small and
is limited to Internet users, it is not likely to be representative of the
population.
16 Sample: the 1,059 selected adults. Population: the complete set of all
adults. Sampling method: simple random sampling. Because the sample is
fairly large and was obtained by a reputable firm, it is likely to be
representative of the population.
17 Sample 3 is the most representative, because the list is a random sample
that is not likely to be biased. Sample 1 is a convenience sample limited to
readers of the newspaper and is therefore likely to be biased. Sample 2 is
likely to be biased because it is limited to the geographic region of
Anchorage. Sample 4 is biased because it includes only car owners and does
not include those who cannot afford a car or choose not to own a car.
18 Sample 4 is the most representative and is a good use of systematic
sampling. Sample 1 is biased because it consists of people from one
geographic region located at the extreme southern part of the state. Sample
2 is biased because it consists of people from one specific geographic urban
region. Sample 3 is likely to be biased because it is a self-selected
sample.
19 There is no bias. The U.S. Department of Labor and its employees have
nothing to gain by distorting the results, and they typically use very sound
sampling methods.
20 There is no bias. Because the magazine does not accept free products or run
advertisements, it is not influenced by the manufacturers of the cars that
it reviews.
21 Yes, there is a possibility of bias. The university scientists receive
funding from Monsanto, so they might be inclined to please the company in
the hope of getting further funding in the future. Thus, there may be an
inclination to provide favorable results. To determine whether this bias is
a problem, you would need to explore the methods and conclusions very
carefully.
7 This statement does make sense. The gender makeup of the sample should
reflect the gender makeup of the movie-going population. While that
population might not have precisely equal proportions of males and females,
it certainly is not so male-dominated as this sample, so the study used a
biased sample.
8 This statement does make sense. The procedure described does result in a
simple random sample, and it is a procedure that is commonly used.
Concepts and Applications
9 A census is practical. Even though NFL team rosters include about 1700
players, it is easy to find their weights on the Internet.
10 A census is not practical because the number of high school football players
in California is too large and their weights are not readily available.
11 A census is not practical. The number of statistics students in the United
States is too large (hundreds of thousands), and it would probably be
difficult to find their ages.
12 A census is practical. The number of members of Congress is not large (535),
and their annual salaries are available on the Internet.
13 Sample: the 1002 surveyed subjects. Population: all adults. Sampling method:
simple random sampling. The sample is likely to be representative of the
population.
14 Sample: the 4500 mailed responses from women. Population: all women.
Sampling method: convenience sampling. The sample is not likely to be
representative of the population.
15 Sample: the 47 responses from the website. Population: all adult Americans.
Sampling method: convenience sampling. Because the sample is very small and
is limited to Internet users, it is not likely to be representative of the
population.
16 Sample: the 1,059 selected adults. Population: the complete set of all
adults. Sampling method: simple random sampling. Because the sample is
fairly large and was obtained by a reputable firm, it is likely to be
representative of the population.
17 Sample 3 is the most representative, because the list is a random sample
that is not likely to be biased. Sample 1 is a convenience sample limited to
readers of the newspaper and is therefore likely to be biased. Sample 2 is
likely to be biased because it is limited to the geographic region of
Anchorage. Sample 4 is biased because it includes only car owners and does
not include those who cannot afford a car or choose not to own a car.
18 Sample 4 is the most representative and is a good use of systematic
sampling. Sample 1 is biased because it consists of people from one
geographic region located at the extreme southern part of the state. Sample
2 is biased because it consists of people from one specific geographic urban
region. Sample 3 is likely to be biased because it is a self-selected
sample.
19 There is no bias. The U.S. Department of Labor and its employees have
nothing to gain by distorting the results, and they typically use very sound
sampling methods.
20 There is no bias. Because the magazine does not accept free products or run
advertisements, it is not influenced by the manufacturers of the cars that
it reviews.
21 Yes, there is a possibility of bias. The university scientists receive
funding from Monsanto, so they might be inclined to please the company in
the hope of getting further funding in the future. Thus, there may be an
inclination to provide favorable results. To determine whether this bias is
a problem, you would need to explore the methods and conclusions very
carefully.
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6 CHAPTER 1, SPEAKING OF STATISTICS
22 Yes, there is a possibility of bias. Because the physicians receive funding
from the pharmaceutical company, they might be more inclined to provide
favorable results so that they can get additional funding in the future.
(The magazine now requires that all such physician authors disclose funding
sources, and those disclosures are included in the articles.)
23 The sample is a simple random sample that is likely to be representative
because there is no bias in the selection process.
24 The sample is systematic and is likely to be representative because there is
no inherent bias in the way that it was selected.
25 The sample is a cluster sample. It is likely to be representative, although
the exact method of selecting the polling stations could affect whether the
sample is biased.
26 The sample is stratified. It is likely to be representative because it has
about the same proportion of males and females as is found in the
population.
27 The sample is a convenience sample. It is likely to be biased, because it
consists of family members likely to have similar physical characteristics
and exercise habits.
28 The sample is a cluster sample. It is likely to be biased for several
reasons. The servers are not likely to give accurate responses. Also, the
small number of restaurants could easily result in a sample that is not
representative.
29 The sample is a stratified sample. It is likely to be biased because people
from those age groups are not evenly distributed throughout the population.
However, the results could be weighted to reflect the age distribution of
the population.
30 The sample is a convenience sample. The sample is likely to be biased
because the customers are all shopping at one upscale store, so they not
likely to be representative of all consumers.
31 The sample is a systematic sample. The sample is likely to be representative
of students at the college, but not representative of all college students
in the United States.
32 The sample is a simple random sample. Because it is a simple random sample
and the sample size is fairly large, it is likely to be representative.
33 The sample is a stratified sample. It is likely to be biased because the
population does not have equal numbers of people in each of the 50 states.
However, the results could be weighted to reflect the actual distribution of
the population.
34 The sample is a cluster sample. It is likely to be representative of
students at the college but not representative of all college students in
the United States.
35 The sample is a convenience sample. It is likely to be biased because it is
a self-selected sample and consists of those with strong feelings about the
topic.
36 The sample is a simple random sample. Because it is a simple random sample,
it is likely to be representative, although a larger sample size would be
better.
37 The sampling plan results in a simple random sample, which is likely to be
representative.
38 The sample is a systematic sample. The sample is likely to be
representative, unless there are special factors, such as a manufacturing
22 Yes, there is a possibility of bias. Because the physicians receive funding
from the pharmaceutical company, they might be more inclined to provide
favorable results so that they can get additional funding in the future.
(The magazine now requires that all such physician authors disclose funding
sources, and those disclosures are included in the articles.)
23 The sample is a simple random sample that is likely to be representative
because there is no bias in the selection process.
24 The sample is systematic and is likely to be representative because there is
no inherent bias in the way that it was selected.
25 The sample is a cluster sample. It is likely to be representative, although
the exact method of selecting the polling stations could affect whether the
sample is biased.
26 The sample is stratified. It is likely to be representative because it has
about the same proportion of males and females as is found in the
population.
27 The sample is a convenience sample. It is likely to be biased, because it
consists of family members likely to have similar physical characteristics
and exercise habits.
28 The sample is a cluster sample. It is likely to be biased for several
reasons. The servers are not likely to give accurate responses. Also, the
small number of restaurants could easily result in a sample that is not
representative.
29 The sample is a stratified sample. It is likely to be biased because people
from those age groups are not evenly distributed throughout the population.
However, the results could be weighted to reflect the age distribution of
the population.
30 The sample is a convenience sample. The sample is likely to be biased
because the customers are all shopping at one upscale store, so they not
likely to be representative of all consumers.
31 The sample is a systematic sample. The sample is likely to be representative
of students at the college, but not representative of all college students
in the United States.
32 The sample is a simple random sample. Because it is a simple random sample
and the sample size is fairly large, it is likely to be representative.
33 The sample is a stratified sample. It is likely to be biased because the
population does not have equal numbers of people in each of the 50 states.
However, the results could be weighted to reflect the actual distribution of
the population.
34 The sample is a cluster sample. It is likely to be representative of
students at the college but not representative of all college students in
the United States.
35 The sample is a convenience sample. It is likely to be biased because it is
a self-selected sample and consists of those with strong feelings about the
topic.
36 The sample is a simple random sample. Because it is a simple random sample,
it is likely to be representative, although a larger sample size would be
better.
37 The sampling plan results in a simple random sample, which is likely to be
representative.
38 The sample is a systematic sample. The sample is likely to be
representative, unless there are special factors, such as a manufacturing
Loading page 9...
SECTION 1.3, TYPES OF STATISTICAL STUDIES 7
c. First, select a random sample of farms. Next, at each farm, randomly
select a sample of rice to be tested.
40 Simple random sampling may be adequate. Better, however, would be stratified
sampling with the different ethnic groups as the strata, since there may be
differences in blood type distribution among these groups.
41 A stratified sample in which you choose a few parents at each school would
be effective.
42 a. A serious manufacturing problem could potentially be missed. As one
example, if the end of a production run is affected by worn machinery,
systematic sampling might be too slow to allow for recognition of the
problem.
b. A potential problem of a simple random sample of only 5 altimeters is
that it is probably too small to represent the population.
Section 1.3
Statistical Literacy and Critical Thinking
1 A variable is any item or quantity that can vary or take on different
values. The variables of interest in a statistical study are the items or
quantities that the study seeks to measure. When cause and effect may be
involved, an explanatory variable is a variable that may explain or cause
the effect, while a response variable is a variable that responds to changes
in the explanatory variable.
2 Confounding is the mixing of effects from different factors so that we
cannot determine the effects from the specific factors being studied. If
males are given the treatment and females are given placebos, we would not
know whether effects are due to the treatment or the gender of the
participant.
3 A placebo is physically similar to a treatment, but it lacks any active
ingredients, so it should not by itself produce any effects. Use of a
placebo is important so that results from subjects given the real treatment
can be compared with results from subjects given the placebo.
4 Blinding is the practice whereby participants and/or experimenters do not
know who belongs to the treatment group and who belongs to the control
group. It is important to use blinding for participants so that they are not
affected by the knowledge that they are receiving the real treatment, and it
is important to use it for experimenters so that they can evaluate results
objectively instead of being influenced by knowledge about who is getting
the real treatment.
5 This statement does not make sense. The subjects who exercise obviously know
that they are exercising. Those who evaluate results should not know whether
a subject is in the treatment group of those exercising or a control group
of those not exercising. In this case, a single-blind experiment is
practical, but a double-blind experiment is not.
6
c. First, select a random sample of farms. Next, at each farm, randomly
select a sample of rice to be tested.
40 Simple random sampling may be adequate. Better, however, would be stratified
sampling with the different ethnic groups as the strata, since there may be
differences in blood type distribution among these groups.
41 A stratified sample in which you choose a few parents at each school would
be effective.
42 a. A serious manufacturing problem could potentially be missed. As one
example, if the end of a production run is affected by worn machinery,
systematic sampling might be too slow to allow for recognition of the
problem.
b. A potential problem of a simple random sample of only 5 altimeters is
that it is probably too small to represent the population.
Section 1.3
Statistical Literacy and Critical Thinking
1 A variable is any item or quantity that can vary or take on different
values. The variables of interest in a statistical study are the items or
quantities that the study seeks to measure. When cause and effect may be
involved, an explanatory variable is a variable that may explain or cause
the effect, while a response variable is a variable that responds to changes
in the explanatory variable.
2 Confounding is the mixing of effects from different factors so that we
cannot determine the effects from the specific factors being studied. If
males are given the treatment and females are given placebos, we would not
know whether effects are due to the treatment or the gender of the
participant.
3 A placebo is physically similar to a treatment, but it lacks any active
ingredients, so it should not by itself produce any effects. Use of a
placebo is important so that results from subjects given the real treatment
can be compared with results from subjects given the placebo.
4 Blinding is the practice whereby participants and/or experimenters do not
know who belongs to the treatment group and who belongs to the control
group. It is important to use blinding for participants so that they are not
affected by the knowledge that they are receiving the real treatment, and it
is important to use it for experimenters so that they can evaluate results
objectively instead of being influenced by knowledge about who is getting
the real treatment.
5 This statement does not make sense. The subjects who exercise obviously know
that they are exercising. Those who evaluate results should not know whether
a subject is in the treatment group of those exercising or a control group
of those not exercising. In this case, a single-blind experiment is
practical, but a double-blind experiment is not.
6
Loading page 10...
8 CHAPTER 1, SPEAKING OF STATISTICS
Concepts and Applications
9 This is an observational study because the TV viewers are being measured,
but they are not treated.
10 This is an experiment because the samples of glass are treated.
11 This is an experiment. The treatment group consists of those treated with
magnets. The control group consists of those given the non-magnetic devices.
12 This is an observational study because the subjects were tested, but they
were not given any treatment.
13 This is an observational study. The subjects were tested, but they were not
given any treatment.
14 This is a retrospective observational study comparing those who were texting
and those who were not.
15 This is an experiment because the subjects were given a treatment. The
treatment group consists of the 945 couples given the XSORT treatment. The
control group consists of others not given any treatment.
16 This is an observational study since no treatment was given.
17 This is an experiment. The treatment group consists of the genetically
modified corn, and the control group consists of corn not genetically
modified.
18 This is an observational study because the subjects were surveyed, but they
were not given any treatment.
19 This is a meta-analysis in which all of the individual studies are
observational.
20 This is meta-analysis in which all of the individual studies are
observational.
21 Confounding is likely to occur. If there are differences in tree growth in
the two groups, it will be impossible to tell if those differences are due
to the treatment (fertilizer or irrigation) or to the type of region (moist
or dry). This confounding can be avoided by using blocks of fertilized
trees in both regions and blocks of irrigated trees in both regions.
Concepts and Applications
9 This is an observational study because the TV viewers are being measured,
but they are not treated.
10 This is an experiment because the samples of glass are treated.
11 This is an experiment. The treatment group consists of those treated with
magnets. The control group consists of those given the non-magnetic devices.
12 This is an observational study because the subjects were tested, but they
were not given any treatment.
13 This is an observational study. The subjects were tested, but they were not
given any treatment.
14 This is a retrospective observational study comparing those who were texting
and those who were not.
15 This is an experiment because the subjects were given a treatment. The
treatment group consists of the 945 couples given the XSORT treatment. The
control group consists of others not given any treatment.
16 This is an observational study since no treatment was given.
17 This is an experiment. The treatment group consists of the genetically
modified corn, and the control group consists of corn not genetically
modified.
18 This is an observational study because the subjects were surveyed, but they
were not given any treatment.
19 This is a meta-analysis in which all of the individual studies are
observational.
20 This is meta-analysis in which all of the individual studies are
observational.
21 Confounding is likely to occur. If there are differences in tree growth in
the two groups, it will be impossible to tell if those differences are due
to the treatment (fertilizer or irrigation) or to the type of region (moist
or dry). This confounding can be avoided by using blocks of fertilized
trees in both regions and blocks of irrigated trees in both regions.
Loading page 11...
SECTION 1.4, SHOULD YOU BELIEVE A STATISTICAL STUDY? 9
27 In this case, the tennis balls play the role of placebos. Confounding can
occur because of a placebo effect and/or an experimenter effect, because it
will be obvious to both subjects and experimenters whether they are lifting
heavy weights. It would be better to use the heavy weights and the tennis
balls with the same subjects at different times, to see if the different
regimens affect blood pressure.
28 Confounding is very possible. It is not possible to disguise the car models
and they have different reputations and very different prices that could
affect the evaluations made by the driver.
29 The control group consists of those who do not listen to Beethoven’s music,
and the treatment group consists of those who do listen to it. This should
be a single-blind experiment. Subjects know whether they are listening to
Beethoven, but blinding should be used so that those who measure
intelligence are not influenced by their knowledge about whether there was
exposure to Beethoven’s music. The blinding could be accomplished by
assigning code numbers to subjects, with only the researchers knowing which
code numbers belonged to the treatment group and which belonged to the
control group.
30 This should be a double-blind experiment with a control group consisting of
subjects given placebos and a treatment group consisting of those treated
with Echinacea. Participants should be randomly assigned to the two groups.
31 The control group consists of smartphones with the current battery, and the
treatment group consists of smartphones with the new battery. Blinding is
not necessary for the smartphones because they are not that smart, and it is
probably unnecessary for the researchers because the longevity of the
batteries will likely be measured with objective tools.
32 It is sufficient to use the three different groups of homes with aluminum
siding, vinyl siding, and wood siding. It isn’t necessary to identify one of
the groups as a control group. Blinding is not necessary for the houses, and
it is unnecessary for the researchers if the longevity is measured with
objective tools. Blinding would be difficult to implement because whether a
home has aluminum siding or vinyl siding or wood siding would be obvious to
those who evaluate the results.
Section 1.4
Statistical Literacy and Critical Thinking
1 The eight guidelines are as follows:
1. Get a big picture view of the study.
2. Consider the source.
3. Look for bias in the sample.
4. Look for problems in defining or measuring the variables of interest.
5. Beware of confounding variables.
6. Consider the setting and wording in surveys.
7. Check that results are presented fairly.
8. Consider the conclusions.
2 Peer review is a process in which experts in a field evaluate a research
report before the report is published. It is useful in lending credibility
to the research because it implies that other experts agree that it was
carried out properly.
3 Selection bias occurs when researchers select their sample in a way that
tends to make it unrepresentative of the population, and participation bias
occurs when the participants themselves choose to be included in the study.
4 When participants select themselves for a survey, those with strong opinions
about the topic being surveyed are more likely to participate, and this
group is typically not representative of the general population.
27 In this case, the tennis balls play the role of placebos. Confounding can
occur because of a placebo effect and/or an experimenter effect, because it
will be obvious to both subjects and experimenters whether they are lifting
heavy weights. It would be better to use the heavy weights and the tennis
balls with the same subjects at different times, to see if the different
regimens affect blood pressure.
28 Confounding is very possible. It is not possible to disguise the car models
and they have different reputations and very different prices that could
affect the evaluations made by the driver.
29 The control group consists of those who do not listen to Beethoven’s music,
and the treatment group consists of those who do listen to it. This should
be a single-blind experiment. Subjects know whether they are listening to
Beethoven, but blinding should be used so that those who measure
intelligence are not influenced by their knowledge about whether there was
exposure to Beethoven’s music. The blinding could be accomplished by
assigning code numbers to subjects, with only the researchers knowing which
code numbers belonged to the treatment group and which belonged to the
control group.
30 This should be a double-blind experiment with a control group consisting of
subjects given placebos and a treatment group consisting of those treated
with Echinacea. Participants should be randomly assigned to the two groups.
31 The control group consists of smartphones with the current battery, and the
treatment group consists of smartphones with the new battery. Blinding is
not necessary for the smartphones because they are not that smart, and it is
probably unnecessary for the researchers because the longevity of the
batteries will likely be measured with objective tools.
32 It is sufficient to use the three different groups of homes with aluminum
siding, vinyl siding, and wood siding. It isn’t necessary to identify one of
the groups as a control group. Blinding is not necessary for the houses, and
it is unnecessary for the researchers if the longevity is measured with
objective tools. Blinding would be difficult to implement because whether a
home has aluminum siding or vinyl siding or wood siding would be obvious to
those who evaluate the results.
Section 1.4
Statistical Literacy and Critical Thinking
1 The eight guidelines are as follows:
1. Get a big picture view of the study.
2. Consider the source.
3. Look for bias in the sample.
4. Look for problems in defining or measuring the variables of interest.
5. Beware of confounding variables.
6. Consider the setting and wording in surveys.
7. Check that results are presented fairly.
8. Consider the conclusions.
2 Peer review is a process in which experts in a field evaluate a research
report before the report is published. It is useful in lending credibility
to the research because it implies that other experts agree that it was
carried out properly.
3 Selection bias occurs when researchers select their sample in a way that
tends to make it unrepresentative of the population, and participation bias
occurs when the participants themselves choose to be included in the study.
4 When participants select themselves for a survey, those with strong opinions
about the topic being surveyed are more likely to participate, and this
group is typically not representative of the general population.
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