Chapter: 1 Basic Ideas
SECTION 1.1 EXERCISES
21. Answers will vary.
Understanding the Concepts
22. Answers will vary. Stratified
Exercises 1-6 are the Check Your
Understanding exercises located within the
section. Their answers are found on page
12.
23. Answers will vary. Cluster
7.
population
26. Cluster
8.
sample
27. Sample of convenience
9.
simple random sample
28. Systematic
24. Answers will vary. Systematic
25. Stratified
10. sample of convenience
29. Voluntary response
11. cluster
30. Cluster
12. stratified
31. Sample of convenience
13. False. A sample of convenience is
acceptable when it is difficult or
impossible to draw a sample in a truly
random way.
32. Simple random sample
33. Stratified
34. Cluster
14. False. In a cluster sample, a simple
random sample of clusters is selected,
and every individual in each selected
cluster is part of the sample.
35. Simple random sample
36. Stratified
15. True.
Working with the Concepts
16. True.
37. Sample of convenience. In order to
choose a simple random sample, every
individual in the population has to have
the same chance of being selected.
Since presumably every person in the
world suffers from headaches, this
means that the pharmaceutical company
would have to randomly select persons
from every state and every country,
which is not feasible.
Practicing the Skills
17. Statistic
18. Parameter
19. Parameter
20. Statistic
1
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Chapter: 1 Basic Ideas
38. Simple random sample. It would not be
difficult to randomly select 100
students from all of the student body at
a university. Each student has a student
ID number and 100 students could be
randomly selected from them via a
lottery type generator.
39. Obtain a list of all registered voters in
the town, and randomly select out 500 of
them.
be an example of voluntary response
sampling. If we have the school’s
admission’s office draw a simple
random sample of 50 males at the
school, as well as a simple random
sample of 50 females at the school, and
we interview all subjects within these
two strata, this would be stratified
sampling. If we choose three different
one-half hour time intervals, and
interview all students at the library as to
their opinion on the issue, this would be
an example of cluster sampling. Finally,
if we interview every 8th student that
walks into the library over a certain
amount of time, this would be an
example of systematic sampling.
40. Randomly choose items off of the
assembly line. For instance, take an
item. Then maybe let 10 go by, then
take another item. Let 10 more go by,
then select another item. Let 10 more go
by, select another item. Continue
selecting items in this fashion.
44. In cluster sampling, the population is
divided into clusters, then a simple
random sample of these clusters is
selected, and every unit within the
selected clusters is sampled. This is a
two-stage sampling plan. In systematic
sampling, we first select a random
starting point in the population, and then
sample every kth item beginning at that
starting point. This is also a two-stage
sampling plan, where we employ a
simple random sample of size 1 from
the list of potential starting points, and
then census the sampling units at
multiples of k units from the initial unit.
41. Draw a stratified sample. That is,
separate the employees by gender, then
randomly choose equal number of men
and women from their respective strata.
42. Using a computer, the IRS can
randomly select 1000 W2 tax forms
from the population of all tax forms.
Extending the Concepts
43. To get a simple random sample,
we could have the school’s admission’s
office randomly choose 75 names from
the entire student enrollment, then we
would interview these subjects. To get a
sample of convenience, we could go to
the school’s student center and randomly
ask students about their opinions. We
could put an advertisement in the
school’s newspaper, or hand out flyers
on campus, asking students to go to a
particular Facebook page and express
their opinions on the issue. This would
SECTION 1-2 EXERCISES
Understanding the Concepts
Exercises 1-4 are the Check Your
Understanding exercises located within the
section. Their answers are found on page
18.
2
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distributed, or posted on a website, in whole or part.
Chapter: 1 Basic Ideas
5.
variables
28. ordinal
6.
qualitative
29. nominal
7.
Quantitative
30. nominal
8.
nominal; ordinal
31. nominal
9.
discrete
32. ordinal
10. Continuous
33. continuous
11. False. Quantitative variables do.
34. continuous
12. True
35. discrete
13. True
36. discrete
14. True
37. continuous
Practicing the Skills
38. discrete
15. qualitative
Working with the Concepts
16. quantitative
39. ordinal
17. quantitative
40. discrete
18. qualitative
41. ordinal
19. quantitative
42. quantitative
20. quantitative
43. nominal
21. qualitative
44. ordinal
22. qualitative
45 (A) Game Title and Publisher
(B) % of Gaming Audience and
Average Minutes Played per Week
(C) Publisher
(D) Game Title
23. qualitative
24. quantitative
25. ordinal
46 (A) Movie Title, Creative Type,
and MPAA Rating
(B) Year, Ticket Sales, and Tickets Sold
(C) Movie Title and Creative Type
26. nominal
27. ordinal
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distributed, or posted on a website, in whole or part.
Chapter: 1 Basic Ideas
(D) MPAA Rating
14. False. Observational studies are
generally less reliable than randomized
experiments.
Extending the Concepts
47 (A)
(B)
(C)
(D)
(E)
(F)
(G)
15. True
ordinal
yes
no
quantitative
yes; yes
nominal
no; no
16. True
Practicing the Skills
17 (A) It is a randomized experiment.
(B) Yes. In a randomized experiment, if
there are large differences in
outcomes among the treatment
groups, we may conclude that the
differences are due to the treatments.
SECTION 1-3 EXERCISES
18 (A) It is an observational study.
Understanding the Concepts
(B) No. In an observational
study, when there are differences in
the outcomes among the treatment
groups, it is often difficult to
determine whether the differences
are due to the treatments or to
confounding.
Exercises 1-4 are the Check Your
Understanding exercises located within the
section. Their answers are found on page
26.
5.
randomized
6.
double-blind
7.
observational
8.
confounder
9.
prospective
19 (A) It is a randomized experiment.
(B) Yes. In a randomized experiment, if
there are large differences in
outcomes among the treatment
groups, we may conclude that the
differences are due to the treatments.
10. cohort
20 (A) The four types of fertilizer.
11. True
(B) It is a randomized experiment.
12. False. A confounder makes it harder to
draw conclusions from a study.
(C) Yes. In a randomized experiment, if
there are large differences in
outcomes among the treatment
groups, we may conclude that the
differences are due to the treatments.
13. False. In an observational study,
subjects choose their own treatments.
4
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for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded,
distributed, or posted on a website, in whole or part.
Chapter: 1 Basic Ideas
(D) cross-sectional
Working with the Concepts
(E) it is unlikely
21. An observational study will be
necessary, this is because the subjects
themselves decide where they live.
Extending the Concepts
29 (A) yes
22. It is possible to design a
randomized experiment, since the
scientists may assign the subjects at
random to the two treatments.
23. It could be due to confounding.
(B) It was important for the doctors in
the study not to know which children
were getting the vaccine because a
doctor’s diagnosis may be influenced
by the knowledge of which particular
treatment a patient received.
24. It could be due to confounding.
(C) It could be due to confounding of
one’s socio-economic status.
25 (A) False
30 (A) no
(B) True
(B) no
26. Age is a likely confounder.
Older children tend to be taller and also
tend to know more words.
(C) It could still be due to confounding
of one’s socio-economic status.
Again, the children who did not
participate in the study were more
likely to come from lower-income
families, who tended to have lower
rates of polio.
27 (A) heart rate
(B) maternal smoking
(C) cohort
SECTION 1-4 EXERCISES
(D) prospective
Understanding the Concepts
(E) Yes. Smoking mothers may be in
worse shape than nonsmoking
mothers, and the conditioning (or
lack thereof) may be a confounder.
Exercises 1 and 2 are the Check Your
Understanding exercises located within the
section. Their answers are found on page
29.
28 (A) respiratory problems
3. voluntary response surveys
(B) formaldehyde level
4. nonresponders
(C) cohort
5. population
5
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for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded,
distributed, or posted on a website, in whole or part.
Chapter: 1 Basic Ideas
gone completely cellular, and such a
sampling method misses this entire large
group of people.
6. False. The way that a question in a
survey is worded has a huge effect on the
responses.
7. True
20. Yes, many people pick the first of
something when they are not sure.
8. False. The fact that a sample is large,
does not make it any better or more
reliable.
Extending the Concepts
21 (A) In essence, the poll surveyed
the rich, and a majority of the rich
are Republicans. That is why, the
digest had the Republican candidate
incorrectly winning in a landslide.
Practicing the Skills
9.
nonresponse
10. sampling bias
(B) Only about one-fifth of the
surveys were returned. This creates
nonresponse bias.
11. self-interest
12. nonresponse
(C) A big sample size does not
offset bias.
13. voluntary response
14. social acceptability
Chapter Quiz
15. nonresponse
16. social acceptability
Working with the Concepts
17 (A) No.
(B) No. The first survey has self-interest
bias, and the second one has social
acceptability as well as leading question
bias.
18. Yes, because many people do
not pick up the phones when they do not
recognize the number on their caller ID.
This creates nonresponse bias.
19. Yes, because many people have
1.
Answers will vary.
2.
qualitative
3.
True
4.
5.
Continuous
False. It should represent the
population as much as possible.
6.
stratified sample
7.
acceptable
8.
sample of convenience
9.
True
10. observational study
6
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for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded,
distributed, or posted on a website, in whole or part.
Chapter: 1 Basic Ideas
(B) It is unlikely, because in a
randomized experiment, if there are
large differences in outcomes among
the treatment groups, we may
conclude that the differences are due
to the treatments.
11. randomized experiment
12. differences in the treatments
13. Seniors are older and maybe better
prepared and more experienced.
11 (A) observational study
14. True
(B) Yes, because in an
observational study, when there are
differences in the outcomes among
the treatment groups, it is often
difficult to determine whether the
differences are due to the treatments
or to confounding.
15. Not reliable at all.
Review Exercises
1. quantitative
2. nominal
12 (A) randomized experiment
3. continuous
(B) It is unlikely, because in a
randomized experiment, if there are
large differences in outcomes among
the treatment groups, we may
conclude that the differences are due
to the treatments.
4 (A) True
(B) True
(C) False. It is discrete.
5. stratified sample
13. It is a voluntary response
sample.
6. voluntary response sample
14. It has nonresponse bias.
7. cluster sample
15. It has nonresponse bias.
8. simple random sample
9. (A) observational study
(B) Yes, people in countries with
the fluoridation of water are
probably wealthier than people in
countries without it, and therefore
probably have better overall dental
care.
Write About It
1. A stratified sample is one in
which the population is divided into
groups and a random sample is drawn
from each group. In a cluster sample, a
simple random sample of clusters is
selected, and every individual in each
selected cluster is part of the sample.
10 (A) randomized experiment
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for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded,
distributed, or posted on a website, in whole or part.
Chapter: 1 Basic Ideas
2. The most basic, and in many
cases the best, sampling method is the
method of simple random sampling. In
simple random sampling, the sample
represents the population very closely.
This is very desirable. However, in a
sample of convenience, the sample may
differ systematically in some way from
the population.
selected for the sample. Any method of
selecting the subjects (like randomly
generating a list of names from a
computer random number generator) that
is analogous to lottery selection, works
fine.
4. An example of an ordinal random
variable is X = the letter grade on exam
#1 for each student in the statistics class
3. A circumstance under which a
sample of convenience might be used is
when an engineer wishes to study the
crushing strength of a hugh shipment of
concrete blocks that are very heavy. In
such an instance, sampling blocks in the
center or on the bottom might not be
possible.
An example of a nominal random
variable is X = the political part
affiliations of all the students in the class
An example of a discrete random variable
is X = the number of people who went to
the mall today
A cluster sample would be used to
estimate the unemployment rate in a
county. In this instance, a simple
random sample of households in the
county would be selected, and every
member of each household would be
interviewed.
An example of a continuous random
variable is X = the weights (in pounds)
of all the students in the class
5. Qualitative variables are not
numeric. They are variables that classify
subjects into categories.
A stratified sample would be used if we
wanted to poll the opinions on a certain
issue by gender. The population would
be divided into the two genders, and a
random sample would be selected out of
each sex.
6. The major difference between a
randomized experiment and an
observational study has to do with the
nature of assigning the subjects to
respective treatment groups. If the
assignment is made by the investigator it
is randomized. If however, the
assignment is not made by the
investigator, it is observational. As
such, if there are large differences in
outcomes among the treatment groups in
a randomized study, we may conclude
that the differences are attributed to the
treatments. This is not necessarily true
for an observational study because of the
effects of confounding.
A systematic sample is employed
when police pull over every 10th car or
so at a sobriety check point.
Whenever possible, we prefer to use a
simple random sample selected from a
population of interest.
The governing principle here is that each
subject has the same likelihood of being
8
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for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded,
distributed, or posted on a website, in whole or part.
Chapter: 1 Basic Ideas
7. In a double-blind study, neither
the investigators nor the subjects know
who has been assigned to which
treatment. The major advantage to this
is that no biases of the doctors or
subjects can interfere with the results.
There really is no disadvantage, other
than it is not always possible to do such
a study. However, whenever possible,
double-blind studies should be
performed.
8. If a major pharmaceutical
company pays a statistician a lot of
money to perform statistical analyses as
to the utility of a certain drug, the
statistician has a paid vested interest in
the outcome, as does the company. It
might be tempting to “fudge” the results
to obtain a positive outcome.
9 (A) This question has very
leading question bias. It is hinting
that people are doing something
wrong and really should change. A
better question would be, “If you had
more money, do you think you
would spend it or save it?”
2.
41
4.
43
5.
2
6.
4.7%
7.
Yes, there is a significant difference
between the two.
8.
Because every person who
returned the questionnaire via school
return did so on a day that corresponded
to a high exposure PM level.
9.
Because every person who
returned the questionnaire via mail
return did so on a day that corresponded
to a low exposure PM level.
11. The people who had symptoms all
returned their questionnaires via school
return, with the exception of two who
mailed it in. Everyone else who mailed
in their responses did not have any
symptoms. This is indeed evidence that
people who have symptoms are eager to
participate, while those who are
unaffected are less interested.
Therefore, the mode of response is
related to the outcomes.
Case Study: Air Pollution and
Respiratory Symptoms
450
9.1%
10. The people who did not return
their questionnaires via school return,
had to be mailed another questionnaire.
This time delay caused the researchers to
get these questionnaires later, well into
April when it was warmer. Since less
wood burning stoves are being used than
they were in March, this definitely
affects the PM level and wheezing
percentages.
(B) This question has social
acceptability bias. A much better
question would be, “What is your
opinion on funding for charitable
organizations?” Chose from the
following: they have enough, they
need more, or they have too much
1.
3.
9
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Chapter: 1 Basic Ideas
12. By telephoning the subjects over
a few days or weeks, the confounding
would have been drastically reduced
because then they would not have had
the striking change in weather affecting
the outcomes. Notice how the actual
study went from March 5 until April 22.
10
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for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded,
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