A.P. Statistics: Experimental Design
Name ____________________________________
Answer each of the following questions using complete sentences.
1.) 1999 AP Statistics Free Response
The dentists in a dental clinic would like to determine if there is a difference between the number of new cavities in
people who eat an apple a day and in people who eat less than one apple per week. They conducted a study of 50 people
in each group.
Fifty clinic patients who report that they routinely eat an apple a day and 50 clinic patients who report they eat less
than one apple a week will be identified. The dentists will examine the patients and their records to determine the number
of new cavities the patients have had over the past two years. They will then compare the number of new cavities in the
two groups.
a.) Why is this an observational study and not an experiment?
b.) Explain the concept of confounding in the context of this study. Include an example of a possible
confounding variable.
c.) If the mean number of new cavities for those who ate an apple a day was significantly smaller than the mean
number of new cavities for those who ate less than one apple a week, could one conclude that the lower
number of cavities can be attributed to eating an apple a day?
2.) 2000 AP Statistics Free Response
High cholesterol levels in people can be reduced by exercise or by a drug treatment. A pharmaceutical company has
developed a new cholesterol-reducing drug. Researchers would like to compare its effects to the effects of the
cholesterol-reducing drug that is currently available on the market. Volunteers that have a history of high cholesterol and
who are currently not on medication will be recruited to participate in a study.
a.) Explain how you would carry out a completely randomized experiment for the study.
b.) Describe an experimental design that would improve the design in (a) by incorporating blocking.
c.) Can the experimental design in (b) be carried out in a double blind manner? Explain.
3.) 2001 AP Statistics Free Response
Students are designing an experiment to compare the productivity of two varieties of dwarf fruit trees. The site for
the experiment is a field that is bordered by a densely forested area on the west side. The field has been divided into eight
plots of approximately the same area. The students have decided that the test plots should be blocked. Four trees, each of
two varieties, will be assigned at random to the four plots within each block, with one tree planted in each plot.
The two blocking schemes shown below are under consideration. For each scheme, one block is identified by the
white region and the other block indicated by the grey region in the figures.
a.) Which of the blocking schemes, A or B, is better for this experiment? Explain your answer.
b.) Even though the students have decided to block, they must randomly assign the varieties of the trees to the
plots within each block. What is the purpose of this randomization in the context of the experiment?
A.P. Statistics: Chapter 5 Multiple Choice Review
1.) A certain high school has 2,350 students. The student body officers are interested in creating activities to have the
freshman become more involved. Which is the best method that will give the appropriate representation of the
freshman at that school?
A.) During the lunch hour, ask some freshman their choice of activities.
B.) Take a simple random sample of the entire student body and ask their choice of activities.
C.) Take a simple random sample of the freshman class only and ask their choice of activities.
D.) Take a simple random sample of nonfreshman and ask which activities they would have liked when they
were freshman.
E.) The student body officers should make the decision based on their experiences as freshman.
2.) What is the purpose of stratification in sampling?
A.) To reduce variability in response.
B.) To increase the sample size.
C.) To restrict which members of the population can be sampled.
D.) To reduce response bias.
E.) To ensure an equal probability of a particular being sampled.
3.) A machine stamps out metal pieces. An inspector checks every 20th piece for defects and size. This is an example of
A.) Random Sampling
B.) Systematic Sampling
C.) Stratified Sampling
D.) Cluster Sampling
E.) Quota Sampling
4.) The state board of education wishes to study the attitudes of parents whose children are taking an experimental
curriculum. The state consists of urban, suburban, and rural communities of different cultural backgrounds. Which
sampling method is likely to yield the most reliable measure of parent’s attitudes?
A.) Simple random sample
B.) Stratified random sample
C.) Cluster sample
D.) Voluntary response sample
E.) Convenience sample
5.) Which of the following is NOT a result of a study’s design process?
A.) Undercoverage
B.) Voluntary response bias
C.) Response bias
D.) Sampling error
E.) Nonresponse bias
6.) When performing an experiment using an experimental group and a control group, which of the following is
important?
A.) The control group and the experimental group are similar.
B.) The control group and the experimental group have different backgrounds.
C.) The experimental group is more interested in the research than the control group.
D.) The control group’s interest in the experiment is maintained.
E.) The experimental group and the control group should communicate with each other as much as possible.
7.) The placebo effect refers to changes in subjects cause by
A.) The administration of an active ingredient.
B.) Separation from real-life conditions.
C.) Evaluating the response variable.
D.) The attention of the experiment itself.
E.) Lack of randomization of treatments.
8.) What is the purpose of blocking in the design of an experiment?
A.) To reduce variability within treatment groups.
B.) To reduce variability between treatment groups.
C.) To make randomization of treatments more efficient.
D.) To blind subjects as to which treatment group they are in.
E.) To decrease the chance of the placebo effect.
9.) To study a cause-effect relationship between variables, which of the following types of studies should be employed?
A.) Simple Random Sample
B.) Stratified Random Sample
C.) Observational Study
D.) Comparative Experiment
E.) Census
10.) To ensure that the results of an experiment can be generalized from a sample to a population, a researcher should
A.) use blocking
B.) use a control group
C.) conduct it on a random sample of the population
D.) repeat the study several times
E.) use blinding