Deck 1: Collecting Data in Reasonable Ways

Question 1

If the sample size is small relative to the population size, there is little
practical difference in the results of sampling with replacement and
sampling without replacement.

Answer 1

True

Question 2

If the subjects as well as the person measuring the response are aware of
the treatment assigned to the subject, only single-blinding is being used.

Answer 2

False

Question 3

In a well-designed experiment the treatments are confounded with other
variables whenever possible.

Answer 3

False

Question 4

A placebo is designed to be identical in appearance to the treatment of
interest, but contains no active ingredients.

Question 5

The method of control wherein an extraneous variable is held constant is
called blocking.

Question 6

A control group provides a baseline for comparison with a treatment
group.

Question 7

Selection bias occurs if only volunteers are used in a study.

Question 8

Variables are extraneous if their effects on the response variable cannot be
distinguished from one another.

Question 9

A treatment is a particular combination of values for the explanatory
variables.

Question 10

A study is an observational study if the investigator observes the behavior
of a response variable after one or more factors have been manipulated.

Question 11

Random assignment to treatments will guarantee that treatment groups are
exactly alike for experimental purposes.

Question 12

Response bias occurs when responses are not actually obtained from all
individuals selected for inclusion in the sample.

Question 13

A simple random sample of size n is by definition a sample that is selected
in a manner to guarantee each individual in the population an equal chance
of selection.

Question 14

Increasing sample size will eliminate bias in a sample.

Question 15

Blocking is used to filter out the effects of some extraneous variables.

Question 16

Random assignment of volunteers to treatments will, on average, result in
comparable experimental groups.

Question 17

Clusters are non-overlapping subgroups of a population that have been
identified as homogeneous.

Question 18

Stratified sampling does not involve simple random sampling.

Question 19

A friend who is not taking statistics wonders why anyone would choose to take a
sample. "Obviously," she says, "you would get better information from a census."
In a short paragraph, explain why statisticians might use a sample rather than a
census.

Question 20

Random subpopulations of a population are called strata.

Question 21

After reading the description below, determine whether the study is an observational
or experimental study. Justify your answer with specific references to the
information in the study.
"We compared paired daytime and night counts of wild brook trout, brown
trout, and rainbow trout made by the same snorkelers in five streams
during August. Overall, we counted 109 trout in the daytime and 333
trout at night. We speculate that trout counted at night were present
during the daytime but were hidden from view. Biologists should consider
that trout behavior and visibility might vary between daytime and night,
even during summer. In some streams, the majority of trout may not be
seen during the daytime."

Question 22

We have distinguished two types of studies: observational and experimental. Briefly
explain the difference between these two types of study. You may use an example to
support your answer but not as a substitute for an explanation.

Question 23

The ZZZ chain of motels has a standard method of constructing their buildings to
maximize the ease of parking for its customers. The rooms are arranged in adjacent
buildings, A and B, so that customers can park close to their rooms. The layout for
the 48-room motels is diagrammed below: The manager wishes to assess customer satisfaction with the motel services. His plan
is to survey the adults in each of 12 rooms. The cleaning staff will place surveys on
the customers' beds before they check in to the motel. In order to make the directions
easy for the cleaning staff to follow, he elects to use systematic sampling.
a) Describe carefully how you would use random numbers to set up the systematic
sampling process. (In your description you may assume you have a random
number table, but do NOT carry out the procedure you describe.)
b) Write a short paragraph for the cleaning staff that explains how to carry out your
method in part (a). The members of the cleaning staff have not taken statistics, so
the use of statistical terminology will not be helpful.

Question 24

Bias is a potentially serious problem that can arise in surveys.
a) In a few sentences, explain the concept of bias.
b) What is the distinction between response bias and non-response bias?

Question 25

A consumer group is performing an experiment to evaluate the tartar-fighting
properties of different brands of toothpaste. Three brands of toothpaste are being
compared in a randomized comparative experiment. (There is no "do-not-brush"
control group.) 300 adult volunteers of varying ages (100 for each toothpaste brand)
have been randomly assigned to the treatments. The toothpaste for each brand is
delivered in containers that are the same except for the letters, X, Y, and Z
prominently displayed. A team of dentists, blind to the identities of the toothpaste
brands, will evaluate the levels of tartar on the subjects' teeth after 2 months of use.
The subjects have been instructed to brush their teeth as they normally do during the
course of the experiment.
(a) What is the explanatory variable (factor) for this experiment?
(b) What is the response variable for this experiment?
(c) After the onset of the experiment, it was discovered that a significant number of
volunteers using Brand Y toothpaste recently enrolled in a short class on health
practices, and one of the lessons involved instruction in effective brushing techniques.
If none of the volunteers using Brands X and Z enrolled in the class, how would this
affect the consumer group's interpretation of the results of the experiment?

Question 26

Two of the basic sampling methods studied in statistics are the simple random sample
and the stratified random sample. How do these methods of sampling differ?

Question 27

An anthropologist is studying the strength of fragments of pottery ("sherds") found in
three archeological sites in the Phoenix Basin area of Arizona. Her study involves
applying force to the sherds until they break, so she plans to use only a small sample
of available artifacts. Her data contains the location of the sherd (site), and the
weight and thickness of the sherd. A partial list of the data is shown below. a) Briefly describe a process to select a simple random sample of size n = 20 from
this list of sherds. You may assume that you have a random number table to work
with, but do NOT carry out the process you describe.
b) Briefly describe how a stratified random sample could be selected with strata
corresponding to archeological sites.

Question 28

Bias is a potentially serious problem that can arise in surveys.
a) In a few sentences, explain the concept of bias.
b) What is the distinction between selection bias and non-response bias?

Question 29

Six species of wood-pecking birds are known to damage homes. Woodpeckers are
protected by the Federal Migratory Bird Treaty Act, and homeowners must control
them by nonlethal methods. Over a three-month period, investigators evaluated the
use of mirrors, artificial snakes, and artificial owls as woodpecker deterrents.
Homeowners' yards were classified into 4 categories: (1) no trees; (2) lightly wooded
yards; (3) wooded yards; and (4) heavily wooded yards. The homes were visited at
least 4 times to establish baseline damage rates (number of new holes per day) before
using any deterrent. Deterrents were randomly assigned to the homes in each
category and changes in the damage rate were recorded at the end of the experimental
time period. The design used was a randomized block design.
(a) What is the explanatory variable (factor) for this experiment?
(b) What is the response variable for this experiment?
(c) After completing the study, someone suggested that amount of rainfall might
affect woodpecker activity and that homes in areas that receive more rainfall
might show greater damage. Is this something that the investigator should be
worried about? If yes, explain why; if no, explain what aspect of the design of the
experiment eliminates this worry.

Question 30

The ZZZ chain of motels has a standard method of constructing their buildings to
maximize the ease of parking for its customers. The rooms are arranged in adjacent
buildings, A and B, so that customers can park close to their rooms. The layout for
the 48-room motels is diagrammed below: The manager wishes to assess customer satisfaction with the motel services. His plan
is to survey the adults in each of 12 rooms. The cleaning staff will place surveys on
the customers' beds before they check in to the motel. As she tries to decide on an
appropriate sampling strategy, the manager realizes the rooms in Building A might be
noisier than Building B, and this should be taken into account.
a) What sampling strategy should she use in this situation? Provide appropriate
statistical justification.
b) Write a short paragraph for the cleaning staff that explains how to carry out your
method in part (a). The members of the cleaning staff have not taken statistics.

Question 31

A friend who is not taking statistics wonders why anyone would choose to take a
sample. "Obviously," she says, "you would get better information from a census."
In a short paragraph, explain why statisticians might use a sample rather than a
census.

Question 32

What is the defining characteristic of a simple random sample?

Question 33

Explain how you would determine if a variable is an explanatory variable or an
extraneous variable? Again, you may use an example to support your answer but not
as a substitute for an explanation.

Question 34

River City is seeking to compare the effects of two mosquito sprays, A and B, to be
used in the insect control plan for their park system. Consider the following two
plans for a statistical study:
• In Plan #1, a simple random sample of plots of park land would be taken from the
population of River City parks. Either treatments A or B would be randomly
assigned to each of the plots.
• In Plan #2, simple random samples of plots of park land would be taken from
each of four geographic areas in River City. (River City has 4 geographic areas of
town, the NE, NW, SE, and SW quadrants.) Either treatments A or B would be
randomly assigned to each of the plots within each geographic area.
a) Consider study plan #1:
i) Would it be appropriate to infer a cause-and-effect relationship if the results of
the two treatments differ? Why or why not?
ii) Could the results be generalized to all areas of the park land? Why or why
not?
b) Consider study plan #2:
i) Would it be appropriate to infer a cause-and-effect relationship if the results of
the two treatments differ? Why or why not?
ii) Could the results be generalized to all areas of the park land? Why or why
not?

Question 35

In competitive sports coaches may record athletes' practice sessions to provide more
effective feedback to the athlete. Some coaches believe video recording may make the
athletes more nervous and actually decrease their performance. You have been asked to
design an experiment to address this issue for competitive high school tennis players. The
proportion of successful first serves will be the response variable. The subjects for the
experiment are 60 high school male competitive tennis players of varying ability who
have volunteered for the experiment.
a) Describe the treatment(s) in your experiment
b) The experience levels of the players is one possible confounding variable. In a few
sentences, explain how you would control this variable.
c) Can the results of this experiment be generalized to all male tennis players?
Why or why not?

Question 36

Explain how you would determine if a variable is an explanatory variable or a
response variable? Again, you may use an example to support your answer but not as
a substitute for an explanation.

Question 37

River City is seeking to compare the effects of two mosquito sprays, A and B, to be
used in the insect control plan for their park system. Consider the following two
plans for a statistical study:
• In Plan #1, a simple random sample of plots of park land would be taken from the
population of River City parks. Either treatment A or B would be randomly
assigned to each of the plots.
• In Plan #2, a simple random sample of plots of park land would be taken from the
population of River City park areas that are rarely visited. Either treatment A or
B would be randomly assigned to each of the plots.
a) Consider study plan #1:
i) Would it be appropriate to infer a cause-and-effect relationship if the results of
the two treatments differ? Why or why not?
ii) Could the results be generalized to all areas of the park land? Why or why
not?
b) Consider study plan #2:
i) Would it be appropriate to infer a cause-and-effect relationship if the results of
the two treatments differ? Why or why not?
ii) Could the results be generalized to all areas of the park land? Why or why
not?

Question 38

We have distinguished two types of studies: observational and experimental. Briefly
explain the difference between these two types of study. You may use an example to
support your answer but not as a substitute for an explanation.

Question 39

Bias is the tendency for samples to differ from the corresponding population in some
systematic way. Some types of bias are: (a) selection bias, (b) response bias, and/or
(c) nonresponse bias. In a few sentences, discuss the differences among these
different types of bias. Examples may illustrate, but not substitute for, a discussion.

Question 40

Consider the following three methods for random sampling: (a) simple random
sampling, (b) stratified random sampling, and (c) cluster sampling. In a few
sentences, discuss the similarities and differences among these sampling methods.
What aspects of the population would lead you to choose each of these methods?
The paragraphs below in questions 2 and 3 present information about a health study.
Each gives a hint about possible bias. Decide whether the possible bias is (i) selection
bias, (ii) response bias, or (iii) nonresponse bias, and explain why you chose your answer.

Question 41

A common classroom practice is to have students exchange their quizzes for grading.
This practice is hypothesized to reduce time between quiz and feedback to students,
thus resulting in higher achievement. Your history teacher, aware of your statistical
prowess, has asked you to design an experiment to test this theory. You have decided
to use the final exam (not graded by students) as your response measure. Your
history teacher has three classes, one early in the morning, one at noon, and one late
in the afternoon. Each class contains 30 students.
(a) Describe the treatments you will use in your experiment
(b) One possible confounding variable is the time of day; students may be more alert
at certain times of the day than at other times. Describe a method that could be
used to control this variable. Students have already been assigned their schedules,
and these cannot be changed.
(c) Do you feel the results of your experiment could be generalized to math classes?
Explain why or why not.

Question 42

After reading the description below, determine whether the study is an observational
or experimental study. Justify your answer with specific references to the
information in the study.
"Before expanding the regional airport, children living nearby were determined
to be in one of two aircraft-noise groups (i) aircraft noise at present or (ii)
aircraft noise would come with the expansion. Three hundred twenty-six
children (mean age = 10.4 years) took part in three data-collection waves, one
before and two after the expansion of the airports. After the expansion, long-
term memory and reading were found to be impaired in the group newly
exposed to aircraft noise."

Question 43

One part of the Nurses Health Study focuses on possible causes of skin cancer.
Nurses were asked about different behaviors and aspects of their health when they
entered the study. Those nurses subsequently diagnosed with cancer were given the
questionnaires again. Investigators discovered that after the diagnosis the nurses
tended to report a reduced ability to tan. The investigators concluded that the shift in
reporting might be caused by an awareness of their diagnosis.

Question 44

One part of the Demographic and Health Surveys Program is concerned with
measures of malnutrition. Investigators measure physical characteristics of children,
at different ages. Sadly, in some countries, many children die early, and thus a bias is
introduced in the study because the investigators cannot collect data from the
deceased children.