Name:_____________________________
AP Statistics
Experimental and Sampling Design - Major Topic I
The new company Five-Hour Brainergy has decided to statistically prove that their supplement will help
students do better when studying for/taking a big exam. Describe how the company could choose students
from your high school using the following sampling design methods.
a. Convenience sample
b. Simple random sample
c. Cluster random sample
d. Stratified random sample
e. Systematic random sample
f. Voluntary response sample

When do we need to choose a block design over a completely randomized?

When do we need to choose a matched pair design over a completely randomized?
Design a completely randomized experiment to determine the effectiveness on the supplement on tests.
Design an experiment that incorporates blocking.
Design a matched pair design.
“ Blocking is used to control the factors you can see; Randomization helps balance the ones you cannot
see.”
Richard L. Scheaffer, Chief Faculty Consultant,1997-1999
MODIFIED 2004
Researchers who are studying a new type of contact lens. Twelve volunteers are available to participate
in this study. Information on these volunteers (number 1 through 12) is shown in the table below.
Participant Gender Age Eye Color
1
Male
21
blue
2
Female 20
green
3
Male
47
brown
4
Female 60
blue
5
6
Female
Male
62
61
blue
green
Participant Gender Age Eye Color
7
Male
58
brown
8
Female 44
brown
9
Male
44
brown
10
Female 24
green
11
12
Male
Female
23
46
blue
green
(a) These researchers want to conduct an experiment involving two type of contact lenses (new and
current). They believe that the effectiveness of the lens changes with age but not gender. Because
researchers want the size of the blocks in an experiment to be equal to the number of treatments,
they will use blocks of size 2 in their experiment. Identify the volunteers (by number) that would be
included in each of the six blocks and give the criteria you used to form the blocks.
(b) Other researchers believe that the effectiveness of the lens differs with both age and gender. These
researchers will also use blocks of size 2 in their experiment. Identify the volunteers (by number)
that would be included in each of the six blocks and give the criteria you used to form the blocks.
(c) Other researches believe that the effectiveness of the lens differs with eye color and age. These
researchers will also use blocks of size 2 in their experiment. Identify the volunteers (by number)
that would be included in each of the six blocks and give the criteria you used to form the blocks.
(d) The researchers in part (b) decide to select three of the six blocks to receive the new contact lenses
and to give the other three blocks the current type. Is this an appropriate way to assign treatments?
If so, describe a method for selecting the three blocks to receive the new type. If not, describe an
appropriate method for assigning treatments.
MODIFIED 2003
There have been many studies recently concerning coffee drinking and cholesterol level. While it is known
that several coffee-bean components can elevate blood cholesterol level, it is thought that a new type of
paper coffee filter may reduce the presence of some of these components in coffee.
The effect of the new filter on cholesterol level will be studies over a 10-week period using 300 nonsmokers
who each drink 4 cups of caffeinated coffee per day. Each of these 300 participants will be assigned to one
of two groups: the experimental group, who will only drink coffee that has been made with the new filter,
or the control group, who will only drink coffee that has been made with the standard filter. Each
participant’s cholesterol level will be measured at the beginning and at the end of the study.
(a) Describe an appropriate method for assigning the subjects to the two groups so that each group will
have an equal number of subjects.
(b) Describe an appropriate method for assigning the subject to the two groups so that each group may have
a different number of subjects.
(c) Suppose a difference research team decided to allow the participants to choose which filter to use. How
might that self-selection process jeopardize a statistically valid comparison of the two treatments?
Provide a specific example.
(d) In this study, the researchers chose to include a group who only drank coffee that was made with the
standard filter. Why is it important to include a control group in this study even though cholesterol
levels will be measured at the beginning and at the end of the study?
(e) Could the experiment be run double-blind? Explain.
(f) Why would the researchers choose to use only nonsmokers in the study?
(g) What statistical disadvantage would occur because the researchers only used nonsmoker in this study?
(h) Turns out that some of the 300 participants take cholesterol reduction medication and some of the 300
participants follow a special diet to reduce cholesterol. Since both conditions will affect the cholesterol
level, you decide to block by either medication or by diet. How would you decide which one of these
two variables to use as a blocking variable?
(i) If a research team decides to collect data to answer the question of the effects of the new filter on
cholesterol reduction as an observational study, explain how
Vocabulary:
Block
Placebo
Completely Randomized Design
Random Assignment
Confounding
Randomized Block Design
Control Group
Replication
Double Blind
Observational Study
Experiment
Matched Pairs
Experimental Unit/Subject
Response Variable
Explanatory Variable
Treatment
Homogenous
Response Variable
Population
Sample
Census
Bias
Voluntary Response
Convenience Sample
Simple Random Sample
Non-response
Stratified Random Sample
Undercoverage
Multistage Random Sample
Response Bias
Systematic Random Sample
Single Blind
Cluster Random Sample
Three Principles of Experimental Design