Chapter 5 Review Watch the following video for a quick review of the sampling methods that we discussed this Chapter http://prezi.com/kibqe-­‐toeunr/13-­‐sampling-­‐techniques/ Also, review the random rectangles activity from this unit. Collecting Data
In order to better understand the characteristics of a population, statisticians and researchers often use a sample from that population and make inferences based on the summery results from the sample. Polling is an example of sampling from the population in order to get a better idea of the characteristics of a population. Because we make inferences about a population from the sample, it is very important that the sample is collected appropriately and that it is representative of the population being studied. The following is a list of possible sample designs and some of the advantages and disadvantages of each: 1) Convenience sampling – Uses subjects that are readily available. This type of sampling will be BIASED (judgmental sample from Random Rectangle activity) Advantage: Easy and less costly to collect Disadvantage: Not representative of the population Example: In order to get an idea of how students think of the new school policy, the principal stands outside the library and asks a few students their opinions. 2) Simple Random Sample (SRS) – consists of n individuals from the population chosen in such a way that every set of n individuals has an equal chance of being the sample actually selected. This is often the best and most appropriate way to collect data for a sample. Advantages – Easy to accomplish using a table of random digits; likely to produce samples that are good representatives of the population. Disadvantage – None (could be cost prohibited) Example: In order to determine how happy students are with their education at DHS, the principal assigns each student a number from 1 to 850 (the number of students at the school) and then uses a random number generator to choose 50 numbers between 1 and 850. He then surveys all the students with the chosen numbers. 3) Stratified random sampling – Divide the population into groups of similar individuals (strata) then select an SRS within each strata. Combine the SRSs from each strata to form your full sample. Advantage: Can produce more exact information (especially in large populations) by taking advantage of the fact that individuals in the same strata are similar to one another. Disadvantage: Not appropriate unless strata are easily defined. Example: In order to get a better idea of what DHS athletes thought about homecoming last year, the director divides all DHS athletes into the teams they play for, and then selects a random sample from each sports team. His full sample consists of aggregating the random samples form each team. Chapter 5 Review 4) Cluster Sampling– Divide the population into sections (clusters) then randomly choose a few of those clusters, and select every member of the clusters chosen. Advantage – Don’t need a list of entire population Disadvantage – More variability between samples depending on how clusters are determined. Example – A psychologist at the University of Pennsylvania collects a sample by first dividing up the students into their respective schools (Wharton, engineering, nursing, arts and sciences) then by the departments that their major is in, and then she selects a few departments at random and surveys every student within those chosen departments. 5) Systematic sampling – randomly select an arbitrary starting point, and then select every kth member of the population Advantage: Every member has an equal probability of being selected Disadvantage: Not every sample of size n has an equal chance of being selected Example: HP Selects every 200th computer off the assembly line and inspects it for quality control. 6) Multi-­‐Stage Sampling refers to a procedure involving two or more steps , each of which could involve any of the various sampling techniques. Example: The Gallup organization often follows a procedure in which nationwide locations are randomly selected, then neighborhoods are randomly selected in each of these locations and finally households are randomly selected in each of these neighborhoods. Identify which type of sampling method is used for questions #1-­‐7 1) 49, 34 and 48 students are selected from the sophomore, junior and senior classes with 496, 348 and 481 students respectively A) convenience B) simple random C) systematic D) stratified E) cluster 2) A sample consists of every 49th students from an ordered list of 496 students A) convenience B) simple random C) systematic D) stratified E) cluster 3) A market researcher randomly selects 500 drivers under 30 years of age and 500 drivers over 30 years of age A) convenience B) simple random C) systematic D) stratified E) cluster 4) A market researcher randomly selects 500 people from each of 10 cities A) convenience B) simple random C) systematic D) stratified E) cluster 5) A tax auditor selects every 1000th income tax return that is received A) convenience B) simple random C) systematic D) stratified E) cluster Chapter 5 Review 6) A pollster uses a computer to generate 500 random numbers, then interviews the voters that correspond to those numbers A) convenience B) simple random C) systematic D) stratified E) cluster 7) A education researcher randomly selects 48 middle schools and interviews all the teachers at each school A) convenience B) simple random C) systematic D) stratified E) cluster 8) An auto analyst is conducting a satisfaction survey, sampling from a list of 10,000 new car buyers. The
list includes 2500 Ford buyers, 2500 GM buyers, 2500 Honda buyers and 2500 Toyota buyers. The
analyst selects a sample of 400 car buyers by randomly selecting 100 buyers of each brand. Is this an
example of a simple random sample?
(A) Yes, because each buyer in the sample was randomly selected
(B) Yes, because each buyer in the sample had an equal chance of being sampled
(C) Yes, because car buyers of every brand were equally represented in the sample
(D) No, because every possible 400 buyer sample did not have an equal chance of being chosen
(E) No, because the population consisted of purchasers of four different brands of cars
9) You want to do a survey of members of the senior class at your school and want to select a simple
random sample. You intend to include 40 students in your sample. Identify the sampling method
described for each of the scenarios below:
(A) Write the names of each students in the senior class on a slip of paper and put the papers in a
container. Then randomly select 40 slips of paper from the container.
(B) Assuming that students are randomly assigned to classes, select two classes at random and include
those students in your sample.
(C) From a list of all seniors, select one of the first 10 names at random. Then select every nth name
on the list until you have 40 people selected.
(D) Select the first 40 seniors to pass through the cafeteria door at lunch
(E) Randomly select 10 students from each of the four senior calculus classes
SOLUTIONS:
1.) D
2.) C
3.) D
4.) D
9.) (A) simple random sample
(B) cluster sample
(C) systematic sample
5.) C
6.) B
7.) E
(D) convenience sample (biased!)
(E) stratified sample
8.) D
Chapter 5 Review Sources of Bias
Samples are biased if they are systematically not representative of the desired population. Under-coverage (Selection Bias): occurs when the way the sample is selected systematically excludes part
of the population .
Literary Digest Example (FDR vs. Alf Landon presidential race polls)
Non-response Bias: Occurs when an individual chosen for a sample can’t be contact or refuses to respond.
Non-response is a big problem in mail surveys.
Example: The DHS administration sends out 100 survey questions to a sample of DHS parents in order to
gage their attitudes toward the school. Only 23 surveys are returned. We have a non-response rate of 77%.
Voluntary Response Bias – samples based on individuals who offer to participate typically give too much emphasis to people with strong opinions. Advantage – Easy to collect Disadvantage – Over represents people with strong opinions. Example: radio call in programs about controversial topics such as gun control and abortion. Online surveys posted to websites are a modern example of voluntary response bias
Response Bias: Caused by the behavior of the respondent or the interviewer
Untruthful answers: people give untruthful answers for several reasons:
1) Sensitive questions
Example: Have you ever cheated on your spouse?
2) Socially acceptable answers
Example: Do you use corporal punishment with your children?
3) Telling the interviewer what he or she wants to hear.
Example: One year after the Detroit race riots of 1967, interviewers asked a sample of
black residents in Detroit if they felt they could trust most white people, some white
people, or none at all. When the interviewer was white, 35% answered "most"; when the
interviewer was black, 7% answered "most”
The fix: secret ballots, anonymous surveys, "sensitive question" techniques.
Chapter 5 Review Lack of memory: giving a wrong answer simply because respondent doesn’t remember the correct answer.
Example: Students were asked to report their grade point averages. Researchers then determined
the actual GPA's. Over 17% of the students reported a GPA that was .4 or more above their actual
average, and about 2% reported a GPA more than .4 below their actual GPA. (more inflated their
GPA's!)
Timing: When a survey is taken can have an impact on the answers.
Example: in January, the National Football League reported a poll that revealed football as the
nation's favorite sport (this is at the time of the Super Bowl)
Phrasing of questions: Subtle differences in phrasing make large differences in the results.
Example:
a) Should the president have the line-item veto to eliminate waste? 97% said “yes”
b) Should the president have the line item veto? 57% said “yes”
Sampling ERROR vs. Sampling BIAS
Sampling Error : The fact that we will get different results from sample to sample, and that no sample
perfectly mirrors the population. Sample to sample variability is expected and unavoidable
Example: Place 50 red and 50 green balls in a bag. Mix the balls thoroughly and randomly sample 30 balls.
In your sample you find that 12 balls are red and 18 are green. Your sample result (12:18 = 2:3) is different
than the true population ratio of 50:50 which is 1 to 1. This difference is due to sampling error. Virtually
any experiment involving a sample will have sampling error. We can minimize sampling error through
various statistical techniques; the most obvious is to increase the sample size.
Sampling Bias: Bias is about center and is a much more serious problem. Bias means that some flaw in
the way you are collecting your data will consistently make your samples off-target.
Example: Place 20 red and 80 green balls in a box. Place the red balls on the bottom and the green balls on
the top. Randomly sample 10 balls from the top without thoroughly mixing the balls. In your sample you
find that 0 balls are red and 10 are green. Your sample result of red to green (0:10) is different than the true
population ratio of 1:4. This difference is due to sampling bias. If we continue to replace the green balls and
sample from the top, we may never get a sample that includes red balls leading us to believe that there are
no green balls in the population.
Chapter 5 Review http://introductorystats.wordpress.com/2011/03/09/design-­‐of-­‐experiments/ Design of experiments
Posted on March 9, 2011 When the goal in a statistical study is to understand cause and effect, experiments are the only way to
obtain convincing evidence for causation. This is an introductory discussion on experimental design,
introducing its vocabulary, its characteristics and its principles. We use a hypothetical example of an
experiment to illustrate the concepts.
An observational study is a study in which the researchers observe individuals and measure variables of
interest but do not attempt to influence the response variable. In an experiment, the researchers deliberately
impose some treatment on individuals and then observe the response variables. When the goal is to
demonstrate cause and effect, experiment is the only source of convincing data.
Terminology
The individuals on which the experiment is performed are called the experimental units. If the experimental
units are human beings, they are called subjects. A treatment is an experimental condition applied to the
experimental units. The goal of an experiment is to determine whether changes in one or more explanatory
variables have any effect on some response variables. For this reason, the distinction between explanatory
variables and response variables is important. The explanatory variables are often called factors. Each
factor may have several values (called levels). Many experiments study the joint effects of several factors.
A treatment is then formed by combining a level of each of the factors.
Introduction of Examples
To illustrate the concepts, we use a hypothetical experiment. Suppose a new medication designed to reduce
fever (and relieve aches and pain) is being tested for efficacy and side effects. For convenience, we call this
new medication Drug X. There are three different dosages: 325 mg, 500 mg and 650 mg. The experiment
enrolls 1200 patients with high fever to test Drug X. Assume that the subjects in this experiment include
600 men and 600 women with age ranging from 18 to 70. The primary outcome measure is the drop in
body temperature three hours after taking the treatment, which is the yardstick by which to measure the
success of Drug X.
The three basic principles of statistical design of experiments are Control, Randomization and
Repetition. When we say the design of an experiment (or experimental design), we refer to the manner in
which these three principles are carried out. There are three main experimental designs: completely
randomized design, randomized block design and matched pairs design. We present several examples
based on the hypothetical experiment to illustrate these ideas.
More Terminology
In all the examples below, the new medication Drug X is compared to a group receiving placebo. A
placebo is a dummy treatment. In this example, it is a medication that has identical look, smell and taste as
Drug X. The experiments described in these examples are double-blind, meaning that both the subjects and
the experimenters do not know which treatment any subject has received.
Example 1a – Completely Randomized Design
The researchers randomly assigns the 1200 subjects into two treatment groups, Group 1 (600 subjects
taking Drug X 325 mg) and Group 2 (600 subjects taking placebo). Three hours after taking the treatments,
the researchers compare the change in body temperature between the treatment groups. In this examples,
there are two treatments, Drug X and placebo.
Chapter 5 Review The treatment of interest (Drug X) is called an intervention and the Drug X group is called the intervention
group. The placebo group is sometimes called the non-intervention group.
This is a one-factor experiment, i.e. only one explanatory variable, namely fever reducing medication. The
one factor has two levels (Drug X 325 mg and placebo). Figure 1 below is an outline of this design.
Example 1b – Completely Randomized Design
The example is similar to Example 1a except that there are four levels in the one factor. The researchers
randomly assign the 1200 subjects into four treatment groups, Group 1 (300 subjects taking Drug X 325
mg), Group 2 (300 subjects taking Drug X 500 mg), Group 3 (300 subjects taking Drug X 650 mg) and
Group 4 (300 subjects taking placebo). As in Example 1a, three hours after taking the treatments, the
researchers compare the change in body temperature between the several treatment groups.
The various Drug X groups are called the intervention groups and the placebo group is called the nonintervention group. Figure 2 below illustrates this design.
The Principles of Experimental Design
Let’s discuss the basic principles outlined in Figures 1 and 2. First, the principle of control. The placebo
group is called the control group, the group of subjects who receive a dummy treatment. Why is the control
group necessary? Why compare different Drug X groups with the placebo group? Why not just apply the
new fever reducing medication to all patients? Without the control group, we do not know whether the
favorable responses from the patients are due to the new medication or to the placebo effect. Some patients
respond well to any treatment, even a placebo. However, with a control group alongside Drug X groups,
both the placebo effect and other influences operate on both the control group and Drug X groups. The only
Chapter 5 Review difference between the groups is the varying levels of Drug X. Thus the purpose of having a control group
is to prevent confounding.
Two variables are confounded when their effect on a response variable (reduction in fever in our
examples) cannot be distinguished from one another. Without the control group as comparison, the effect of
Drug X and the placebo effect on the response variable (reduction in fever) cannot be distinguished from
one another. There could be other variables that may influence the response variable (these variables are
called lurking variables or confounding variables). Without the control group, the effect of Drug X and
these lurking variables may also be confounded.
The first principle of experimental design is control. We just illustrate the simplest form of control, that is,
the comparison of two or more treatments (other forms of control will be discussed below). The purpose of
comparing treatments is to prevent the effect of the explanatory variables (the effect of the new fever
reducing medication in our examples) being confounded with the placebo effect and other lurking
variables.
The second principle of experimental design is randomization. Notice that the patients are assigned to
either the Drug X groups or the placebo group through the use of random chance (conceptually, think
drawing names from a hat). The goal of randomization is to produce treatment groups that are similar
(except for chance variation) before the treatments begin.
The third principle of experimental design is replication, which refers to the practice of applying the
treatments to many experimental units. The goal of repetition is to reduce the role of chance variation on
the results of the experiment. For example, if each treatment group has only one patient, the results would
depend too much on which group gets lucky and is assigned a patient that is less sick (e.g. with milder
fever conditions). If we assign many patients to each group, it will be unlikely that all patients in the Drug
X groups will be less sick.
Prevention of Bias
Control (in particular, comparison of treatments) and randomization together prevent bias (i.e. systematic
favoritism). For example, because of the placebo effect, uncontrolled experiments in medicine can give
new medications or new therapies a higher rate of success. If patients are not assigned to treatment groups
by chance, the subjects in the new medication group and the placebo group may not have similar
characteristics and thus the results may become biased. For example, randomization prevents the possibility
that the researchers try to assign the sicker patients to the new medication groups in an effort to help them.
With randomization, there is no inherent bias resulting from some patients opting to take the new
medication. In a randomized controlled experiment, both the experimenters and the participants do not have
the right to choose the treatments.
In clinical trials involving medication, another way to prevent bias is through the technique of blinding,
which refers to the non-disclosure of the treatment a subject is receiving. There are two types of blinding.
An experiment is single-blind is one in which the subject does not know what treatment he or she is
receiving. A double-blind experiment is one in which both the subject and the medical personnel in contact
with the subject do not know which treatment the subject is receiving.
The double-blind technique avoids unconscious bias. In such an experiment, both the medical personnel
and the subject do not adjust their behavior that may bias the results (e.g. the researcher may think that a
placebo cannot help the patient).
Summary – Completely Randomized Design
The designs described in both Example 1a and Example 1b are called completely randomized designs and
are the simplest statistical designs for experiments. These designs incorporated all three principles of
control, randomization and repetition. A completely randomized design incorporates the simplest form of
control, namely comparison. The goal of comparing different treatments is to prevent the confounding of
Chapter 5 Review the explanatory variables with lurking variables. The element of randomization is to produce treatment
groups that are similar (except for chance variation) before the treatments begin. Comparison and
randomization together prevent bias. The goal of repetition is to reduce the role of chance variation on the
results of the experiment.
However, completely randomized designs are inferior to more elaborate designs. The reason is that it is
possible that not all potential cofounding variables are removed. For example, men and women respond
differently to medication. In the completely randomized designs in Examples 1a and 1b, the random
assignment to treatment groups are done without regard to gender. These two examples ignore the
differences between men and women. Though the patients are assigned by random chance to the treatment
groups, it is possible that one treatment group is assigned more men than women. A better design will look
separately at the responses of men and women. In other words, the researchers will separate out the men
from the women and then randomly assign each gender group to the different treatment groups. This is
called the randomized block design.
Example 2 – Randomized Block Design
The 1200 subjects are assigned to blocks, based on gender. Then subjects within each block are randomly
assigned to the two treatment groups (Drug X 325 mg, and Placebo). The variable of gender is called a
blocking variable. Three hours after taking the treatments, the researchers compare the change in body
temperature between the treatment groups within each block. Figure 3 below outlines this randomized
block design.
The randomized block design in this example is an improvement over the completely randomized design in
Example 1a. In both Example 1a and Example 2, comparison of treatment groups is used to implicitly
prevent confounding. However, the randomized block design in Example 2 explicitly controls the variable
of gender.
We can also create the blocking equivalence of Example 1b by randomly assigning subjects in each block
to four treatments (Drug X 325 mg, Drug X 500 mg, Drug X 650 mg, and Placebo). The outline of this
design is omitted.
Chapter 5 Review Summary – Randomized Block Design
A block is a group of experimental units that are known, prior to the experiment, to be similar according to
some variables and that these variables are expected to affect the response to the treatments. In the
randomized block design, the randomization to treatments is carried out separately winthin each block.
Blocks are another form of control. The block design is to control the variables that are used to form the
blocks (these variables are called the blocking variables). In Example 2, the blocking variable is the gender.
The third main type of design is the matched pairs design, which is a special case of the randomized block
design. This design is only applicable when the experiment has only two treatments and that the
experimental units can be separated into pairs according to some blocking variables. Consider the following
example.
Example 3 – Matched Pairs Design
The 1200 subjects are grouped into 600 matched pairs. The subjects in each pairs have the same gender and
have similar age. Moreover, the subjects in each matched pair are assigned by random chance to the two
treatments (Drug X 325 mg and placebo). The advantage of this design is that it explicitly controls both age
and gender. Each matched pair is like a block (based on age and gender). Randomization is done separately
within each pair. Three hours after taking the treatments, the researchers compare the change in body
temperature within each matched pair.
Summary – The Matched Pairs Design
The matched pairs design is, in some ways, superior to completely randomized design and randomized
block design. The requirements are that this design can only compare two treatments and that the group of
experimental units can be matched in pairs (thus requiring more work on the part of the experimenters).
Because matched subjects are more similar than unmatched subjects, the matched pairs design can
explicitly control the variables that are used to form the pairs.
Randomization remains important in the matched pairs design. For example, which one of the subjects in a
matched pair uses Drug X is decided by a coin toss. In contrast, in a completely randomized design,
random chance is used to assign all the subjects all at once to the treatment groups. In a randomized block
design, the random assignment is done separately within each block.
One common variation of the matched pairs design applies both treatments on the same subject. In such a
design, each subject serves as his or her own control.
Conclusion
One important advantage of experiments over observational studies is that well designed experiments can
provide good evidence for causation. In an experiment, an intervention (Drug X in our examples) is applied
to enough experimental units to ensure that the results of the experiments will not be dependent on chance
variation (the principle of repetition). The experimental units are randomly assigned to an intervention
group and a non-intervention group (placebo group). This refers to the principles of randomization and
control, which help reduce the potential of bias and prevent confounding by increasing the chance that
confounding variables will operate equally on the intervention group and the placebo group. Then the only
difference between the intervention group and the placebo group is the intervention. When the intervention
group experiences favorable results, we can be confident that the intervention makes the difference.
Chapter 5 Review AP Statistics Practice Multiple Choice Questions
1.
Can pleasant aromas help a student learn better? Two researchers believed that the
presence of a floral scent could improve a person’s learning ability in certain
situations. They had 22 people work through a pencil-and- paper maze six times,
three times while wearing a floral-scented mask and three times wearing an
unscented mask. The three trials for each mask closely followed one another. Testers
measured the length of time it took subjects to complete each of the six trials. They
reported that, on average, subjects wearing the floral-scented mask completed the
maze more quickly than those wearing the unscented mask, although the difference
was not statistically significant. This study is
A) a convenience sample
B) an observational study, not an experiment
C) an experiment, but not a double-blind experiment
D) a double-blind experiment
2.
A marketing research firm wishes to determine if the adult men in Laramie, Wyoming,
would be interested in a new upscale men’s clothing store. From a list of all residential
addresses in Laramie, the firm selects a simple random sample of 100 and mails a
brief questionnaire to each. The population of interest is
A) all adult men in Laramie, Wyoming
B) all residential addresses in Laramie, Wyoming
C) the members of the marketing firm that actually conducted the survey
D) the 100 addresses to which the survey was mailed
Twelve people, who suffer from chronic fatigue syndrome, volunteer to take part in an
experiment to see if, shark fin extract will increase one’s energy level. 8 of the volunteers
are men and 4 are women. Half of the volunteers are to be given shark extract twice a
day and the other half a placebo twice a day. We wish to make sure that 4 men and 2
women are assigned each of the treatments, so we decide to use a block design with the
men forming one block and the women the other.
3.
Referring to the information above, a block design is appropriate in this experiment if
A) we believe men and women will respond differently to treatments
B) gender equity is an important legal consideration in this study
C) we want the conclusions to apply equally to men and women
D) all of the above
Chapter 5 Review 4.
Referring to the information above, suppose one of the researchers is responsible for
determining if a subject displays an increase in energy level. In this case, we should
probably
A) use two placebos
B) use stratified sampling to assign subjects to treatments
C) use fewer subjects but observe them more frequently
D) conduct the study as a double-blind experiment
A study of human development showed two types of movies to groups of children.
Crackers were available in a bowl, and the investigators compared the number of
crackers eaten by children watching the different kinds of movies. One kind of movie
was shown at 8 AM (right after the children had breakfast) and another at 11 AM (right
before the children had lunch). It was found that during the movie shown at 11 AM, more
crackers were eaten than during the movie shown at 8 AM. The investigators concluded
that the different types of movies had an effect on appetite. .
5.
The results cannot be trusted because
A) the study was not double-blind. Neither the investigators, nor the children should
have been aware of which movie was being shown
B) the investigators were biased. They knew beforehand what they hoped the study
would show
C) the investigators should have used several bowls, with crackers randomly placed in
each
D) the time the movie was shown is a confounding variable.
6. The response variable in this experiment is
A) the number of crackers eaten
B) the different kinds of movies
C) the time the movie was shown
D) the bowls
Chapter 5 Review 7. In order to select a sample of undergraduate students in the United States, I select a
simple random sample of four states. From each of these states, I select a simple
random sample of two colleges or universities. Finally, from each of these eight
colleges or universities, I select a simple random sample of 20 undergraduates. My
final sample consists of 160 undergraduates. This is an example of
A) simple random sampling
B) stratified random sampling
C) multistage sampling
D) convenience sampling
8. A study of the effects of running on personality involved 231 male runners who each ran
about 20 miles a week. A news report (New York Times, Feb. 15, 1988) stated, “The
researchers found statistically significant personality differences between the runners and
the 30-year-oldmale population as a whole.” A headline on the article said, “Research has
shown that running can alter one’s moods.” Which of the following statements about the
study is true?
A) It was not a designed experiment
B) It was an experiment, but not a double-blind experiment
C) It was a double-blind experiment, but not a randomized
D) It was a randomized, double-blind experiment
One hundred volunteers who suffer from severe depression are available for a study.
Fifty are selected at random and are given a new drug that is thought to be particularly
effective in treating severe depression. The other 50 are given an existing drug for
treating severe depression. A psychiatrist evaluates the symptoms of all volunteers after
four weeks in order to determine if there has been substantial improvement in the
severity of the depression.
9.
The study described above would be double-blind if
A) neither drug had any identifying marks on it
B) the volunteers were not allowed to interact during the four weeks
C) neither the volunteers nor the psychiatrist knew which treatment any person had
received
D) all of the above
Chapter 5 Review 10.
Referring to the study described above, suppose volunteers were first divided into men
and women, and then half of the men were randomly assigned to the new drug and half
of the women were assigned to the new drug. The remaining volunteers received the
other drug. This would be an example of
A) Replication
B) confounding. The effects of gender will be mixed up with the effects of the drugs
C) a block design
D) a matched-pairs design
11. Will a fluoride mouthwash used after brushing reduce cavities? Twenty sets of twins
were used to investigate this question. One member of each set of twins used the
mouthwash after each brushing; the other did not. After six months, the difference in the
number of cavities of those using the mouthwash was compared with the number of
cavities of those who did not use the mouthwash. This experiment uses
A) random placebos
B) double-blinding
C) double replication
D) a matched-pairs design
12. A stratified random sample is similar to which of the following experimental designs?
A) a block design
B) a double-blind experiment
C) an experiment with a placebo
D) a confounded, nonrandomized study
Choose a simple random sample of size three from the following employees of a small
company.
1. Bechhofer 2. Brown 3. Ito 4. Kesten 5.Kiefer 6. Spitzer 7. Taylor 8.Wald 9. Weiss
Use the numerical labels attached to the names above and the list of random digits
below. Read the list of random digits from left to right, starting at the beginning of the list.
11793 20495 05907 11384 44982 20751 27498 12009 45287 71753 98236 66419
84533
Chapter 5 Review 13.)Referring to the information above, the simple random sample is
A) 117
B) Bechhofer, then Bechhofer again, then Taylor
C) Bechhofer, Taylor, Weiss
D) Kesten, Kiefer, Taylor
14.)
Referring to the information above, which of the following statements is true?
A) If we used another list of random digits to select the sample, we would get the same
result that we obtained with the list used here.
B) If we used another list of random digits to select the sample, we would get a
completely different sample than that obtained with the list used here.
C) If we used another list of random digits to select the sample, we would get at most
one name in common with the sample obtained here.
D) If we used another list of random digits to select the sample, it would be just as likely
that the sample that we obtained here would be selected as any other set of three
names.
15.) A simple random sample of 1200 adult Americans is selected, and each person is
asked the following question: In light of the huge national deficit, should the
government at this time spend additional money to establish a national system of
health insurance? Only 39% of those responding answered yes. This survey
A) is reasonably accurate since it used a large, simple random sample
B) probably overstates the percentage of people that favor a system of national health
insurance
C) probably understates the percentage of people that favor a system of national health
insurance
D) is very inaccurate, but neither understates nor overstates the percentage of people
that favor a system of national health insurance. Since simple random sampling was
used, it is unbiased
Chapter 5 Review 16.) A news release for a diet products company reports: “There’s good news for the 65
million Americans currently on a diet.” Its study showed that people who lose weight
could keep it off. The sample was 20 graduates of the company’s program who
endorse it in commercials. The results of the sample are probably
A) biased, overstating the effectiveness of the diet
B) biased, understating the effectiveness of the diet
C) unbiased since these are nationally recognized individuals
D) unbiased, but they could be more accurate. A larger sample size should be used
17.) A public opinion poll in Ohio wants to determine whether registered voters in the state
approve of a measure to ban smoking in all public areas. They select a simple
random sample of 50 registered voters from each county in the state and ask
whether they approve or disapprove of the measure. This is an example of a
A)
systematic sample
B) stratified sample C) multistage sample D) simple random sample
18.) A marketing research firm wishes to determine if the adult men in Laramie, Wyoming,
would be interested in a new upscale men’s clothing store. From a list of all residential
addresses in Laramie, the firm selects a simple random sample of 100 and mails a brief
questionnaire to each. The chance that all 100 homes in a particular neighborhood in
Laramie end up being the sample of residential addresses selected is
A) the same as for any other set of 100 residential addresses
B) exactly 0. Simple random samples will spread out the addresses selected
C) reasonably large due to the “cluster” effect
D) 100 divided by the size of the population of Laramie
19.) You are testing a new medication for relief of depression. You are going to give the
new medication to subjects suffering from depression and see if their symptoms
have lessened after a month. You have eight subjects available. Half of the subjects
are to be given the new medication and the other half a placebo. The names of the
eight subjects are given below.
1. Blumenthal 2. Costello 3. Duvall 4. Fan 5. House 6. Long 7. Pavlicova 8. Tang
Using the list of random digits 81507 27102 56027 55892 33063 41842 81868
71035 09001 43367 49497 starting at the beginning of this list and using single-digit
labels, you assign the first four subjects selected to receive the new medication,
while the remainder receive the placebo. The subjects assigned to the placebo are
A) Blumenthal, Costello, Duvall, and Fan
Chapter 5 Review B) Blumenthal, House, Pavlicova, and Tang
C) House, Long, Pavlicova, and Tang
D) Costello, Duvall, Fan, and Long
A television station is interested in predicting whether voters in its viewing area are in
favor of federal funding for abortions. It asks its viewers to phone in and indicate whether
they support/are in favor of or are opposed to this. Of the 2241 viewers who phoned in,
1574 (70.24%) were opposed to federal funding for abortions.
20. Referring to the information above, the viewers who phoned in are A) a voluntary
response sample B) a convenience sample C) a probability sample D) a population
21. Referring to the information above, the sample obtained is A) a simple random
sample B) a single-stage sample C) a census D) probably biased
22. In order to assess the opinion of students at the University of Minnesota on campus
snow removal, a reporter for the student newspaper interviews the first 12 students he
meets who are willing to express their opinion. The method of sampling used is
A) simple random sampling B) convenience sampling C) voluntary response D) a census
23.)In order to take a sample of 90 members of a local gym, I first divide the members
into men and women, and then take a simple random sample of 45 men and a
separate simple random sample of 45 women. This is an example of
A) a block design
B) a stratified random sample
C) a double-blind simple random sample
D) a randomized comparative experiment.
24. A1992 Roperpoll found that 22% of Americans say that the Holocaust may not have
happened.The actual question asked in the poll was: Does it seem possible or
impossible to you that the Nazi extermination of the Jews never happened? Twentytwo percent responded “possible.” The results of this poll cannot be trusted because
A) undercoverage is present. Obviously those people who did not survive the Holocaust
could not be in the poll
B) the question is worded in a confusing manner
C) we do not know who conducted the poll or who paid for the results
D) nonresponse is present. Many people will refuse to participate and those that do will
be biased in their opinions
Chapter 5 Review 25. A researcher is interested in the cholesterol levels of adults in the city in which she
lives. A free cholesterol screening program is set up in the downtown area during the
lunch hour. Individuals can walk in and have their cholesterol levels determined for
free. One hundred and seventy three people use the service, and their average
cholesterol is 217.8. The sample obtained is an example of
A) a SRS, since the experimenter did not know beforehand which individuals would
come to the screening
B) a stratified sample of high and low cholesterol individuals
C) a sample probably containing bias and undercoverage
D) a multistage sample of varying cholesterol levels
26.
In order to determine if smoking causes cancer, researchers surveyed a large sample
of adults. For each adult they recorded whether the person had smoked regularly at
any period in his or her life and whether the person had cancer. They then compared
the proportion of cancer cases in those who had smoked regularly at some time with
the proportion of cases in those who had never smoked regularly at any point. The
researchers found there was a higher proportion of cancer cases among those who
had smoked regularly than among those who had never smoked regularly. This is
A) an observational study
B) an experiment, but not a double-blind experiment
C) a double-blind experiment
D) a block design
27.)In order to investigate whether women are more likely than men to prefer Democratic
candidates, a political scientist selects a large sample of registered voters, both men
and women. She asks every voter whether they voted for the Republican or the
Democratic candidate in the last election. This is
A) an observational study
B) a multistage sample
C) A double-blind experiment
D) a block design
Chapter 5 Review 28. A market research company wishes to find out whether the population of students at a
university prefers brand A or brand B of instant coffee. A random sample of students is
selected, and each student is asked first to try brand A and then to try brand B, or vice
versa (with the order determined at random). They then indicate which brand they
prefer. This is an example of A) an experiment B) an observational study, not an
experiment C) stratified sampling design D) block design
29.
Sickle-cell disease is a painful disorder of the red blood cells that affects mostly blacks
in the United States. To investigate whether the drug hydroxyurea can reduce the
pain associated with sickle-cell disease, a study by the National Institute of Health
gave the drug to 150 sickle-cell sufferers and a placebo to another 150. The
researchers then counted the number of episodes of pain reported by each subject.
The response is A) the drug hydroxyurea B) the number of episodes of pain C) the
presence of sickle-cell disease D) the number of red blood cells
A group of college students believes that herbal tea has remarkable restorative powers.
To test their theory they make weekly visits to a local nursing home, visiting with
residents, talking with them, and serving them herbal tea. After several months, many of
the residents are more cheerful and healthy.
30. The explanatory variable in this experiment is the
A) emotional state of the residents
B) herbal tea
C) fact that this is a local nursing home
D) college students
31. The confounding variable in this experiment is the
A) emotional state of the residents
B) herbal tea
C) fact that this is a local nursing home
D) visits of college students
Chapter 5 Review 32.
A study to determine whether or not a football filled with helium traveled farther when
kicked than one filled with air found that, while the football filled with helium went, on
average, farther than the one filled with air, the difference was not statistically
significant. The response
A) is the gas, air or helium, with which the football is filled
B) does not exist without statistical significance
C) is the number of kickers
D) is the distance the football traveled
New varieties of corn with altered amino acid patterns may have higher nutritive value
than standard corn, which is low in the amino acid lysine. An experiment compares two
new varieties, called opaque-2 and floury-2, with normal corn. Corn- soybean meal diets
using each type of corn: are prepared at three different protein levels, 12%, 16%, and
20%, giving nine diets in all. Researchers assign 10 one-day-old male chicks to each
diet and record their weight gains after 21 days. The weight gain of the chicks is a
measure of the nutritive value of their diet.
33. Referring to the information above, the experimental units in this experiment are
A) variety and protein level
B) the weight gains
C) the 90 one-day-old male chicks
D) opaque-2 and floury-2
34.
Referring to the information above, the treatments are
A) 9 different combinations of variety and protein level
B) the three levels of protein
C) the 90 one-day-old male chicks
D) opaque-2 andfloury-2 varieties of corn
35.
Which of the following is not a major principle of experimental design?
A) control B) replication C) randomization D) segmenation
Chapter 5 Review 36. Two variables in a study are said to be confounded if
A) one cannot separate their effects on a response variable
B) they are highly correlated
C) they do not have a normal distribution
D) one of them is a placebo
Researchers wish to determine if a new experimental medication will reduce the
symptoms of allergy sufferers without the side effect of drowsiness. To investigate this
question, the researchers give the new medication to 50 adult volunteers who suffer
from allergies. 44 of these volunteers report a significant reduction in their allergy
symptoms without any drowsiness.
37. Referring to the information above, this study could be improved by
A) including people who do not suffer from allergies in the study in order to represent a
more diverse population
B) repeating the study with only the 44 volunteers who reported a significant reduction
in their allergy symptoms without any drowsiness, and giving them a higher dosage this
time
C) using a control group
D) all of the above
38.
Referring to the information above, the experimental units are
A) the researchers
B) the 50 adult volunteers
C) the 44 volunteers who reported a significant reduction in their allergy symptoms
without any drowsiness.
D) the six volunteers who did not report a significant reduction in their allergy symptoms
without any drowsiness.
SOLUTIONS: 1.) C 7.) C 2.) A 8.) A 3.) A 9.) C 4.) D 10.) C 5.) D 11.) D 6.) A 12.) A 13.) C 14.) D 15.) C 16.) A 17.) B 18.) A 19.) D 20.) A 21.) D 22.) B 23.) B 24.) B 25.) C 26.) A 27.) A 28.) A 29.) B 30.) B 31.)D 32.)D 33.)C 34.)A 35.)D 36.)A 37.) C 38.) B