A P P E N D I X C
Solutions to End-of-Chapter Problems
CHAPTER 1 must be reliable, but a reliable measure is not necessarily a
valid one.
1.1 Descriptive statistics organize, summarize, and communicate a
group of numerical observations. Inferential statistics use sample 1.9 An operational definition specifies the operations or procedures
data to make general estimates about the larger population. used to measure or manipulate an independent or dependent
variable.
1.2 A sample is a set of observations drawn from the population of
interest that, it is hoped, shares the same characteristics as the 1.10 In everyday language, people often use the word experiment to
population of interest. A population includes all possible refer to something they are trying out to see what will happen.
observations about which we’d like to know something. Researchers use the term to refer to a type of study in which
participants are randomly assigned to levels of the independent
1.3 The four types of variables are nominal, ordinal, interval, and variable.
ratio. A nominal variable is used for observations that have
categories, or names, as their values. An ordinal variable is used
1.11 When conducting experiments, the researcher randomly assigns
participants to conditions or levels of the independent variable.
for observations that have rankings (i.e., 1st, 2nd, 3rd, . . .) as
When random assignment is not possible, such as when
their values. An interval variable has numbers as its values; the
studying something like gender or marital status, correlational
distance (or interval) between pairs of consecutive numbers is
research is used. Correlational research allows us to examine
assumed to be equal. Finally, a ratio variable meets the criteria
how variables are related to each other; experimental research
for interval variables but also has a meaningful zero point.
allows us to make assertions about how an independent
Interval and ratio variables are both often referred to as scale
variable causes an effect in a dependent variable.
variables.
1.12 In a between-groups research design, participants experience
1.4 Statisticians use scale as another term for an interval or ratio
one, and only one, level of the independent variable. In a
measure. They also use scale as a word for many measurement
within-groups research design, all levels of the independent
tools, particularly those that involve a series of items that test-
variable are experienced by all participants in the study.
takers must complete.
1.13 a. “This was an experiment.” (not “This was a correlational
1.5 Discrete variables can only be represented by specific numbers,
study.”)
usually whole numbers; continuous variables can take on any
values, including those with great decimal precision (e.g., b. “. . . the independent variable of caffeine . . .” (not “ . . . the
1.597). dependent variable of caffeine . . . ”)
c. “A university assessed the validity . . .” (not “A university
1.6 An independent variable is a variable that we either manipulate assessed the reliability . . . ”)
or observe to determine its effects on the dependent variable; a d. “In a between-groups experiment . . .” (not “In a within-
dependent variable is the outcome variable that we hypothesize groups experiment . . . ”)
to be related to, or caused by, changes in the independent
variable. e. “A researcher studied a sample of 20 rats . . .” (not “A
researcher studied a population of 20 rats . . . ”)
1.7 A confounding variable (also called a confound) is any variable
that systematically varies with the independent variable so that
1.14 An outlier is a participant or observation that is very different
from other observations in the study.
we cannot logically determine which variable affects the
dependent variable. Researchers attempt to control 1.15 When identifying why a particular observation is so different
confounding variables in experiments by randomly assigning from the other observations in the study (i.e., outlier analysis),
participants to conditions. The hope with random assignment is the researcher may gain insight into other factors that influence
that the confounding variable will be spread equally across the the dependent variable.
different conditions of the study, thus neutralizing its effects.
1.16 a. 130 people
1.8 Reliability refers to the consistency of a measure. Validity b. All people living in urban areas in the United States
refers to the extent to which a test actually measures what it
was intended to measure. A measure that is valid absolutely 1.17 a. 73 people
C-1
,C-2 APPENDIX C
b. All people who shop in grocery stores similar to the one 1.32 a. Ordinal
where data were collected b. Scale
1.18 Descriptive statistic c. Scale
d. Nominal
1.19 Inferential statistic
e. Nominal
1.20 a. Answers may vary, but one way is to sort people into
groups such as “long distance walked,” “medium distance
1.33 a. Discrete
walked,” and “short distance walked.” b. Continuous
b. Answers may vary, but pedometers could be used to c. Discrete
measure steps taken and miles walked, both of which are d. Discrete
scale measures. e. Continuous
1.21 a. Answers may vary, but people could be labeled as having a 1.34 a. They relate more to validity because they suggest that the
“healthy diet” or an “unhealthy diet.” Rorschach test is not really measuring what it intends to
b. Answers may vary, but there could be groupings such as “no measure.
items,” “minimal items,” “some items,” and “many items.” b. A Rorschach test might be consistent; for example, five
c. Answers may vary, but the number of items could be clinicians might interpret the responses in one Rorschach in
counted or weighed. the same way. Yet the interpretation might not be accurate—
it might not be a valid measure of a person’s personality.
1.22 Answers may vary, but on a national level, one could look at
the rate of houses in foreclosure or the amount of government 1.35 a. The independent variables are temperature and rainfall.
debt. Both are continuous, scale variables.
b. The dependent variable is experts’ ratings. These are
1.23 The independent variables are physical distance and emotional discrete, scale variables.
distance. The dependent variable is accuracy of memory.
c. The researchers wanted to know if the wine experts are
1.24 There are two levels of physical distance (within 100 miles and consistent in their ratings—that is, if they’re reliable.
100 miles or farther) and three levels of emotional distance d. This observation would suggest that Robert Parker’s
(knowing no one who was affected, knowing people who were judgments are valid. His ratings seem to be measuring what
affected but lived, and knowing someone who died). they intend to measure—wine quality.
1.25 Answers may vary, but accuracy of memory could be 1.36 a. A reliable test is one that provides consistent results. If you
operationalized as the number of facts correctly recalled. take the test twice, you should get the same results, an
indication of reliability.
1.26 a. Skin tone
b. A valid test is one that measures what it intends to measure.
b. Severity of facial wrinkles
This test has the stated intention of measuring personality. If
c. Three levels (light, medium, and dark) in fact it is measuring personality accurately, then it is a
1.27 Both Miguel Induráin and Lance Armstrong could be valid test.
considered outliers because their scores (number of wins) are 1.37 a. There are several possible answers to this question. The
extreme compared to the typical number of wins experienced developers of this Web site might, for example, hypothesize
by Tour de France winners. that the region of the world in which one grew up predicts
1.28 An outlier analysis of Miguel Induráin and Lance Armstrong different personality profiles based on region.
might lead a researcher to identify factors that are critical to b. The independent variable would be region and the
superior cycling performance. dependent variable would be personality profile.
1.29 a. The average weight for a 10-year-old girl was 77.4 pounds 1.38 Answers may vary, but the following are possible answers.
in 1963 and nearly 88 pounds in 2002. a. Final score on a video game; average reaction time on a
b. No; the CDC would not be able to weigh every single girl video game task
in the United States because it would be too expensive and b. Parental measure of child aggression; number of aggressive
time-consuming. acts observed in an hour of play
c. It is a descriptive statistic because it is a numerical summary c. Weight loss measured in pounds or kilograms; weight loss
of a sample. It is an inferential statistic because the measured by change in waist size
researchers drew conclusions about the population’s average d. Average test score for the semester; overall grade for the
weight based on this information from a sample. semester
1.30 a. The sample is the 60,000 people they studied. e. Minutes to fall asleep from when the participant goes to
b. The researchers would like to generalize their findings to bed; actual time at which the participant falls asleep
the population of all Norwegians, or perhaps even more 1.39 a. Age: teenagers and adults in their 30s
broadly. b. Spanking: spanking and not spanking
1.31 a. Ordinal c. Meetings: go to meetings and participate online
b. Scale d. Studying: with others and alone
c. Nominal e. Beverage: caffeinated and decaffeinated
, APPENDIX C C-3
1.40 a. (i) Measured the distance between the well and the homes b. Other unhealthy behaviors have been associated with
on a map; (ii) measuring how many steps it took to walk smoking, such as poor diet and infrequent exercise. These
from a home to the well other unhealthy behaviors might be confounded with
b. (i) Described hair as short, medium, or very long; (ii) smoking.
measuring the length of the hair in inches c. The tobacco industry could claim it was not the smoking
that was harming people, but rather the other activities in
1.41 a. Researchers could have randomly assigned some people which smokers tend to engage or fail to engage.
who are HIV-positive to take the oral vaccine and other
d. One could randomly assign people to either a smoking
people who are HIV-positive not to take the oral vaccine.
group or a nonsmoking group. Confounding variables could
The second group would likely take a placebo.
be controlled through random assignment and by
b. This would have been a between-groups experiment attempting to control the diet and lifestyles of those
because the people who are HIV-positive would have been participating in the research.
in only one group: either vaccine or no vaccine.
c. This limits the researchers’ ability to draw causal conclusions 1.46 a. This research is correlational because participants could not
because the participants who received the vaccine may have be randomly assigned to be high in individualism or
been different in some way from those who did not receive collectivism.
the vaccine. There may have been a confounding variable b. The sample is the 32 people who tested high for
that led to these findings. For example, those who received individualism and the 37 people who tested high for
the vaccine might have had better access to health care and collectivism.
better sanitary conditions to begin with, making them less c. Answers may vary, but one hypothesis could be “On
likely to contract cholera regardless of the vaccine’s average, people high in individualism will experience more
effectiveness. relationship conflict than those high in collectivism.”
d. Answers may vary, but one way to measure relationship
1.42 a. The researchers might not have used random assignment
conflict could be the number of disagreements or fights per
because it would have meant recruiting participants, likely
month.
immunizing half, then following up with all of them. It
would have been difficult to track those who had received 1.47 a. This is experimental because students are randomly assigned
the vaccine and those who had not in order to compare to one of the recycling incentive conditions.
them. b. Answers may vary, but one hypothesis could be “Students
b. The researchers likely did not want to deny the vaccine to fined for not recycling will report lower concerns for the
people who were HIV-positive because they might have environment, on average, than those rewarded for
contracted cholera and died without it. recycling.”
1.43 We could have recruited a sample of people who were HIV- 1.48 a. The person would be considered an outlier because his or her
positive. Half would have been randomly assigned to take the score was far from the scores of all the others in the study.
oral vaccine; half would have been randomly assigned to take b. Outlier analysis might be useful to find out why this person
something that appeared to be an oral vaccine but did not have gained so much despite the exercise program. For example,
the active ingredient. They would have been followed to was the person eating much more because he or she
determine whether they developed cholera. incorrectly assumed the exercise would burn all the extra
calories?
1.44 a. The study could use a between-groups research design by
assigning half the participants to exercise and half not to c. We are looking for any reason that might explain why this
exercise. outlier exists. Is there something about this individual that
provides evidence for our hypothesis, when, on the face of
b. Participants could be followed for several months to
it, the outlier seems to discredit our hypothesis?
determine weight loss, then start the exercise program and
be followed for several months to determine weight loss. 1.49 a. The person who took 3 minutes would be considered an
c. There are several possible confounds. In the within-groups outlier because the person’s response time was much more
design, the participants are having their weight loss tracked, extreme than any of the response times exhibited by the
then starting an exercise program, then having their weight other participants
loss tracked some more. It is possible that the mere act of b. In this case, the researcher might look to see if the
tracking weight loss leads participants to implement weight- participant was slow on other experimental tasks as well or
loss tactics other than exercise and that they start reaping if there was some other independent evidence that the
the benefits of these tactics around the time the exercise participant did not take the experimental task seriously.
program begins. Alternatively, it is possible that the no-
exercise segment occurs in the winter and the exercise
segment occurs in the spring. Many people gain a bit of CHAPTER 2
weight during the winter and lose weight as summer—and
bathing-suit season—approaches. It might be the weather, 2.1 Raw scores are the original data, to which nothing has been
not the exercise program, that leads to weight loss. done.
1.45 a. An experiment requires random assignment to conditions. 2.2 To create a frequency table: (1) Determine the highest and
It would not be ethical to randomly assign some people to lowest scores. (2) Create two columns: the first labeled with the
smoke and some people not to smoke, so this research had variable name and the second labeled “frequency.” (3) List the
to be correlational. full range of values that encompasses all the scores in the data
, C-4 APPENDIX C
set from lowest to highest, even those for which the frequency 2.17 Five
is 0. (4) Count the number of scores at each value, and write
those numbers in the frequency column. 2.18 The intervals would be 0–4, 5–9, 10–14, 15–19, 20–24, and
25–29.
2.3 A frequency table is a visual depiction of data that shows how
often each value occurred; that is, it shows how many scores 2.19 The full range of data is 68 minus 2, plus 1, or 67. The range
are at each value. Values are listed in one column, and the (67) divided by the desired seven intervals gives us an interval
numbers of individuals with scores at that value are listed in the size of 9.57, or 10 with rounding. The seven intervals are: 0–9,
second column. A grouped frequency table is a visual depiction 10–19, 20–29, 30–39, 40–49, 50–59, and 60–69.
of data that reports the frequency within each given interval 2.20 37.5, 52.5, and 67.5
rather than the frequency for each specific value.
2.21 25 shows
2.4 Statisticians might use interval to describe a type of variable.
Interval variables have numbers as their values, and the distance 2.22 Twelve countries had between two and ten first- or second-
(or interval) between numbers is assumed to be equal. place World Cup finishes.
Statisticians might also use interval to refer to the range of values
to be used in a grouped frequency table, histogram, or polygon.
2.23 Serial killers would create positive skew, adding high numbers
of murders to the data that are clustered around 1.
2.5 A histogram looks like a bar graph but is typically used to
depict scale data with the values (or midpoints of intervals) of
2.24 People convicted of murder are assumed to have killed at least
one person, so observations below one are not seen, which
the variable on the x-axis and the frequencies on the y-axis. A
creates a floor effect.
frequency polygon is a line graph with the x-axis representing
values (or midpoints of intervals) and the y-axis representing 2.25 a. For the college population, the range of ages extends farther
frequencies; a point is placed at the frequency for each value to the right (with greater years) than to the left, creating
(or midpoint), and the points are connected. positive skew.
2.6 Visual displays of data often help us see patterns that are not b. The fact that youthful prodigies have limited access to
obvious when we examine a long list of numbers. They help us college creates a sort of floor effect that makes low scores
organize our data in meaningful ways. less possible.
2.7 In everyday conversation, we use the word distribution in a 2.26 a. five
number of different contexts, from the distribution of food to b. six
marketing distribution. In statistics, we use the word distribution c. none
in a very particular way. We are interested in the way that a set
of scores, such as a set of grades, is distributed. That is, we are 2.27 a. The women’s distribution has greater variability, or spread.
interested in the overall pattern of our data—what the shape is, b. The distribution for women is skewed.
where the data tend to cluster, and how they trail off. c. The women’s distribution has a positive skew.
2.8 A normal distribution is a specific frequency distribution that is 2.28 a. The stem-and-leaf plot is depicted below:
a bell-shaped, symmetric, unimodal curve.
4 00055
2.9 With positively skewed data, the distribution’s tail extends to the 3 00005555555
right, in a positive direction, and with negatively skewed data, the
distribution’s tail extends to the left, in a negative direction. 2 00555
b. This stem-and-leaf plot depicts a symmetric distribution.
2.10 A floor effect occurs when scores below a certain value do not
occur; a ceiling effect occurs when scores above a certain value 2.29 a.
do not occur. PERCENTAGE FREQUENCY PERCENTAGE
10 1 5.26
2.11 A stem-and-leaf plot is much like a histogram in that it
conveys how often different values in a data set occur. Also, 9 0 0.0
when a stem-and-leaf plot is turned on its side, it has the same 8 0 0.0
shape as a histogram of the same data set.
7 0 0.0
2.12 A stem-and-leaf plot retains information about every unique 6 0 0.0
data point in a set, whereas a histogram does not. Additionally,
it is easy to create side-by-side stem-and-leaf plots for different 5 2 10.53
groups to compare their distributions. Such a side-by-side 4 2 10.53
comparison of groups is not as easy to do with histograms.
3 4 21.05
2.13 17.95% and 40.67% 2 4 21.05
2.14 3.69% and 18.11% are scale variables both as counts and as 1 5 26.32
percentages. 0 1 5.26
2.15 0.04, 198.22, and 17.89
b. 10.53% of these schools had exactly 4% of their students
2.16 The full range is the maximum (27) minus the minimum (0) report that they wrote between 5 and 10 20-page papers
plus 1, which equals 28. that year.
Solutions to End-of-Chapter Problems
CHAPTER 1 must be reliable, but a reliable measure is not necessarily a
valid one.
1.1 Descriptive statistics organize, summarize, and communicate a
group of numerical observations. Inferential statistics use sample 1.9 An operational definition specifies the operations or procedures
data to make general estimates about the larger population. used to measure or manipulate an independent or dependent
variable.
1.2 A sample is a set of observations drawn from the population of
interest that, it is hoped, shares the same characteristics as the 1.10 In everyday language, people often use the word experiment to
population of interest. A population includes all possible refer to something they are trying out to see what will happen.
observations about which we’d like to know something. Researchers use the term to refer to a type of study in which
participants are randomly assigned to levels of the independent
1.3 The four types of variables are nominal, ordinal, interval, and variable.
ratio. A nominal variable is used for observations that have
categories, or names, as their values. An ordinal variable is used
1.11 When conducting experiments, the researcher randomly assigns
participants to conditions or levels of the independent variable.
for observations that have rankings (i.e., 1st, 2nd, 3rd, . . .) as
When random assignment is not possible, such as when
their values. An interval variable has numbers as its values; the
studying something like gender or marital status, correlational
distance (or interval) between pairs of consecutive numbers is
research is used. Correlational research allows us to examine
assumed to be equal. Finally, a ratio variable meets the criteria
how variables are related to each other; experimental research
for interval variables but also has a meaningful zero point.
allows us to make assertions about how an independent
Interval and ratio variables are both often referred to as scale
variable causes an effect in a dependent variable.
variables.
1.12 In a between-groups research design, participants experience
1.4 Statisticians use scale as another term for an interval or ratio
one, and only one, level of the independent variable. In a
measure. They also use scale as a word for many measurement
within-groups research design, all levels of the independent
tools, particularly those that involve a series of items that test-
variable are experienced by all participants in the study.
takers must complete.
1.13 a. “This was an experiment.” (not “This was a correlational
1.5 Discrete variables can only be represented by specific numbers,
study.”)
usually whole numbers; continuous variables can take on any
values, including those with great decimal precision (e.g., b. “. . . the independent variable of caffeine . . .” (not “ . . . the
1.597). dependent variable of caffeine . . . ”)
c. “A university assessed the validity . . .” (not “A university
1.6 An independent variable is a variable that we either manipulate assessed the reliability . . . ”)
or observe to determine its effects on the dependent variable; a d. “In a between-groups experiment . . .” (not “In a within-
dependent variable is the outcome variable that we hypothesize groups experiment . . . ”)
to be related to, or caused by, changes in the independent
variable. e. “A researcher studied a sample of 20 rats . . .” (not “A
researcher studied a population of 20 rats . . . ”)
1.7 A confounding variable (also called a confound) is any variable
that systematically varies with the independent variable so that
1.14 An outlier is a participant or observation that is very different
from other observations in the study.
we cannot logically determine which variable affects the
dependent variable. Researchers attempt to control 1.15 When identifying why a particular observation is so different
confounding variables in experiments by randomly assigning from the other observations in the study (i.e., outlier analysis),
participants to conditions. The hope with random assignment is the researcher may gain insight into other factors that influence
that the confounding variable will be spread equally across the the dependent variable.
different conditions of the study, thus neutralizing its effects.
1.16 a. 130 people
1.8 Reliability refers to the consistency of a measure. Validity b. All people living in urban areas in the United States
refers to the extent to which a test actually measures what it
was intended to measure. A measure that is valid absolutely 1.17 a. 73 people
C-1
,C-2 APPENDIX C
b. All people who shop in grocery stores similar to the one 1.32 a. Ordinal
where data were collected b. Scale
1.18 Descriptive statistic c. Scale
d. Nominal
1.19 Inferential statistic
e. Nominal
1.20 a. Answers may vary, but one way is to sort people into
groups such as “long distance walked,” “medium distance
1.33 a. Discrete
walked,” and “short distance walked.” b. Continuous
b. Answers may vary, but pedometers could be used to c. Discrete
measure steps taken and miles walked, both of which are d. Discrete
scale measures. e. Continuous
1.21 a. Answers may vary, but people could be labeled as having a 1.34 a. They relate more to validity because they suggest that the
“healthy diet” or an “unhealthy diet.” Rorschach test is not really measuring what it intends to
b. Answers may vary, but there could be groupings such as “no measure.
items,” “minimal items,” “some items,” and “many items.” b. A Rorschach test might be consistent; for example, five
c. Answers may vary, but the number of items could be clinicians might interpret the responses in one Rorschach in
counted or weighed. the same way. Yet the interpretation might not be accurate—
it might not be a valid measure of a person’s personality.
1.22 Answers may vary, but on a national level, one could look at
the rate of houses in foreclosure or the amount of government 1.35 a. The independent variables are temperature and rainfall.
debt. Both are continuous, scale variables.
b. The dependent variable is experts’ ratings. These are
1.23 The independent variables are physical distance and emotional discrete, scale variables.
distance. The dependent variable is accuracy of memory.
c. The researchers wanted to know if the wine experts are
1.24 There are two levels of physical distance (within 100 miles and consistent in their ratings—that is, if they’re reliable.
100 miles or farther) and three levels of emotional distance d. This observation would suggest that Robert Parker’s
(knowing no one who was affected, knowing people who were judgments are valid. His ratings seem to be measuring what
affected but lived, and knowing someone who died). they intend to measure—wine quality.
1.25 Answers may vary, but accuracy of memory could be 1.36 a. A reliable test is one that provides consistent results. If you
operationalized as the number of facts correctly recalled. take the test twice, you should get the same results, an
indication of reliability.
1.26 a. Skin tone
b. A valid test is one that measures what it intends to measure.
b. Severity of facial wrinkles
This test has the stated intention of measuring personality. If
c. Three levels (light, medium, and dark) in fact it is measuring personality accurately, then it is a
1.27 Both Miguel Induráin and Lance Armstrong could be valid test.
considered outliers because their scores (number of wins) are 1.37 a. There are several possible answers to this question. The
extreme compared to the typical number of wins experienced developers of this Web site might, for example, hypothesize
by Tour de France winners. that the region of the world in which one grew up predicts
1.28 An outlier analysis of Miguel Induráin and Lance Armstrong different personality profiles based on region.
might lead a researcher to identify factors that are critical to b. The independent variable would be region and the
superior cycling performance. dependent variable would be personality profile.
1.29 a. The average weight for a 10-year-old girl was 77.4 pounds 1.38 Answers may vary, but the following are possible answers.
in 1963 and nearly 88 pounds in 2002. a. Final score on a video game; average reaction time on a
b. No; the CDC would not be able to weigh every single girl video game task
in the United States because it would be too expensive and b. Parental measure of child aggression; number of aggressive
time-consuming. acts observed in an hour of play
c. It is a descriptive statistic because it is a numerical summary c. Weight loss measured in pounds or kilograms; weight loss
of a sample. It is an inferential statistic because the measured by change in waist size
researchers drew conclusions about the population’s average d. Average test score for the semester; overall grade for the
weight based on this information from a sample. semester
1.30 a. The sample is the 60,000 people they studied. e. Minutes to fall asleep from when the participant goes to
b. The researchers would like to generalize their findings to bed; actual time at which the participant falls asleep
the population of all Norwegians, or perhaps even more 1.39 a. Age: teenagers and adults in their 30s
broadly. b. Spanking: spanking and not spanking
1.31 a. Ordinal c. Meetings: go to meetings and participate online
b. Scale d. Studying: with others and alone
c. Nominal e. Beverage: caffeinated and decaffeinated
, APPENDIX C C-3
1.40 a. (i) Measured the distance between the well and the homes b. Other unhealthy behaviors have been associated with
on a map; (ii) measuring how many steps it took to walk smoking, such as poor diet and infrequent exercise. These
from a home to the well other unhealthy behaviors might be confounded with
b. (i) Described hair as short, medium, or very long; (ii) smoking.
measuring the length of the hair in inches c. The tobacco industry could claim it was not the smoking
that was harming people, but rather the other activities in
1.41 a. Researchers could have randomly assigned some people which smokers tend to engage or fail to engage.
who are HIV-positive to take the oral vaccine and other
d. One could randomly assign people to either a smoking
people who are HIV-positive not to take the oral vaccine.
group or a nonsmoking group. Confounding variables could
The second group would likely take a placebo.
be controlled through random assignment and by
b. This would have been a between-groups experiment attempting to control the diet and lifestyles of those
because the people who are HIV-positive would have been participating in the research.
in only one group: either vaccine or no vaccine.
c. This limits the researchers’ ability to draw causal conclusions 1.46 a. This research is correlational because participants could not
because the participants who received the vaccine may have be randomly assigned to be high in individualism or
been different in some way from those who did not receive collectivism.
the vaccine. There may have been a confounding variable b. The sample is the 32 people who tested high for
that led to these findings. For example, those who received individualism and the 37 people who tested high for
the vaccine might have had better access to health care and collectivism.
better sanitary conditions to begin with, making them less c. Answers may vary, but one hypothesis could be “On
likely to contract cholera regardless of the vaccine’s average, people high in individualism will experience more
effectiveness. relationship conflict than those high in collectivism.”
d. Answers may vary, but one way to measure relationship
1.42 a. The researchers might not have used random assignment
conflict could be the number of disagreements or fights per
because it would have meant recruiting participants, likely
month.
immunizing half, then following up with all of them. It
would have been difficult to track those who had received 1.47 a. This is experimental because students are randomly assigned
the vaccine and those who had not in order to compare to one of the recycling incentive conditions.
them. b. Answers may vary, but one hypothesis could be “Students
b. The researchers likely did not want to deny the vaccine to fined for not recycling will report lower concerns for the
people who were HIV-positive because they might have environment, on average, than those rewarded for
contracted cholera and died without it. recycling.”
1.43 We could have recruited a sample of people who were HIV- 1.48 a. The person would be considered an outlier because his or her
positive. Half would have been randomly assigned to take the score was far from the scores of all the others in the study.
oral vaccine; half would have been randomly assigned to take b. Outlier analysis might be useful to find out why this person
something that appeared to be an oral vaccine but did not have gained so much despite the exercise program. For example,
the active ingredient. They would have been followed to was the person eating much more because he or she
determine whether they developed cholera. incorrectly assumed the exercise would burn all the extra
calories?
1.44 a. The study could use a between-groups research design by
assigning half the participants to exercise and half not to c. We are looking for any reason that might explain why this
exercise. outlier exists. Is there something about this individual that
provides evidence for our hypothesis, when, on the face of
b. Participants could be followed for several months to
it, the outlier seems to discredit our hypothesis?
determine weight loss, then start the exercise program and
be followed for several months to determine weight loss. 1.49 a. The person who took 3 minutes would be considered an
c. There are several possible confounds. In the within-groups outlier because the person’s response time was much more
design, the participants are having their weight loss tracked, extreme than any of the response times exhibited by the
then starting an exercise program, then having their weight other participants
loss tracked some more. It is possible that the mere act of b. In this case, the researcher might look to see if the
tracking weight loss leads participants to implement weight- participant was slow on other experimental tasks as well or
loss tactics other than exercise and that they start reaping if there was some other independent evidence that the
the benefits of these tactics around the time the exercise participant did not take the experimental task seriously.
program begins. Alternatively, it is possible that the no-
exercise segment occurs in the winter and the exercise
segment occurs in the spring. Many people gain a bit of CHAPTER 2
weight during the winter and lose weight as summer—and
bathing-suit season—approaches. It might be the weather, 2.1 Raw scores are the original data, to which nothing has been
not the exercise program, that leads to weight loss. done.
1.45 a. An experiment requires random assignment to conditions. 2.2 To create a frequency table: (1) Determine the highest and
It would not be ethical to randomly assign some people to lowest scores. (2) Create two columns: the first labeled with the
smoke and some people not to smoke, so this research had variable name and the second labeled “frequency.” (3) List the
to be correlational. full range of values that encompasses all the scores in the data
, C-4 APPENDIX C
set from lowest to highest, even those for which the frequency 2.17 Five
is 0. (4) Count the number of scores at each value, and write
those numbers in the frequency column. 2.18 The intervals would be 0–4, 5–9, 10–14, 15–19, 20–24, and
25–29.
2.3 A frequency table is a visual depiction of data that shows how
often each value occurred; that is, it shows how many scores 2.19 The full range of data is 68 minus 2, plus 1, or 67. The range
are at each value. Values are listed in one column, and the (67) divided by the desired seven intervals gives us an interval
numbers of individuals with scores at that value are listed in the size of 9.57, or 10 with rounding. The seven intervals are: 0–9,
second column. A grouped frequency table is a visual depiction 10–19, 20–29, 30–39, 40–49, 50–59, and 60–69.
of data that reports the frequency within each given interval 2.20 37.5, 52.5, and 67.5
rather than the frequency for each specific value.
2.21 25 shows
2.4 Statisticians might use interval to describe a type of variable.
Interval variables have numbers as their values, and the distance 2.22 Twelve countries had between two and ten first- or second-
(or interval) between numbers is assumed to be equal. place World Cup finishes.
Statisticians might also use interval to refer to the range of values
to be used in a grouped frequency table, histogram, or polygon.
2.23 Serial killers would create positive skew, adding high numbers
of murders to the data that are clustered around 1.
2.5 A histogram looks like a bar graph but is typically used to
depict scale data with the values (or midpoints of intervals) of
2.24 People convicted of murder are assumed to have killed at least
one person, so observations below one are not seen, which
the variable on the x-axis and the frequencies on the y-axis. A
creates a floor effect.
frequency polygon is a line graph with the x-axis representing
values (or midpoints of intervals) and the y-axis representing 2.25 a. For the college population, the range of ages extends farther
frequencies; a point is placed at the frequency for each value to the right (with greater years) than to the left, creating
(or midpoint), and the points are connected. positive skew.
2.6 Visual displays of data often help us see patterns that are not b. The fact that youthful prodigies have limited access to
obvious when we examine a long list of numbers. They help us college creates a sort of floor effect that makes low scores
organize our data in meaningful ways. less possible.
2.7 In everyday conversation, we use the word distribution in a 2.26 a. five
number of different contexts, from the distribution of food to b. six
marketing distribution. In statistics, we use the word distribution c. none
in a very particular way. We are interested in the way that a set
of scores, such as a set of grades, is distributed. That is, we are 2.27 a. The women’s distribution has greater variability, or spread.
interested in the overall pattern of our data—what the shape is, b. The distribution for women is skewed.
where the data tend to cluster, and how they trail off. c. The women’s distribution has a positive skew.
2.8 A normal distribution is a specific frequency distribution that is 2.28 a. The stem-and-leaf plot is depicted below:
a bell-shaped, symmetric, unimodal curve.
4 00055
2.9 With positively skewed data, the distribution’s tail extends to the 3 00005555555
right, in a positive direction, and with negatively skewed data, the
distribution’s tail extends to the left, in a negative direction. 2 00555
b. This stem-and-leaf plot depicts a symmetric distribution.
2.10 A floor effect occurs when scores below a certain value do not
occur; a ceiling effect occurs when scores above a certain value 2.29 a.
do not occur. PERCENTAGE FREQUENCY PERCENTAGE
10 1 5.26
2.11 A stem-and-leaf plot is much like a histogram in that it
conveys how often different values in a data set occur. Also, 9 0 0.0
when a stem-and-leaf plot is turned on its side, it has the same 8 0 0.0
shape as a histogram of the same data set.
7 0 0.0
2.12 A stem-and-leaf plot retains information about every unique 6 0 0.0
data point in a set, whereas a histogram does not. Additionally,
it is easy to create side-by-side stem-and-leaf plots for different 5 2 10.53
groups to compare their distributions. Such a side-by-side 4 2 10.53
comparison of groups is not as easy to do with histograms.
3 4 21.05
2.13 17.95% and 40.67% 2 4 21.05
2.14 3.69% and 18.11% are scale variables both as counts and as 1 5 26.32
percentages. 0 1 5.26
2.15 0.04, 198.22, and 17.89
b. 10.53% of these schools had exactly 4% of their students
2.16 The full range is the maximum (27) minus the minimum (0) report that they wrote between 5 and 10 20-page papers
plus 1, which equals 28. that year.
