Stat 402 B – Exam 1 Take-home Problems
Due at the beginning of the exam on Friday, February 19, 2010
1. [25 pts] A U.S. drug company is developing a new compound for lowering serum cholesterol
and wishes to conduct an experiment to determine the new compound’s effectiveness.
Elevated serum cholesterol levels are associated with higher incidence of heart attacks and
strokes. Lowering serum cholesterol is important to the health of many individuals. Dosage
is an important consideration and so the drug company wishes to test its new compound at
different dosage levels (10 mg, 20 mg and 40 mg). Total cholesterol can be determined by a
simple blood test. Because the drug is expected to change the cholesterol, change in
cholesterol from beginning to end of the experiment is important. The drug company will use
48 people between the ages of 50 and 64 in the experiment.
a) [3] What are the response, conditions and experimental material for the experiment?
b) [4] According to the U.S. Census there were approximately 43 million people in the U.S.
between the ages of 50 and 64 with the following breakdown.
Age
%
50 to 54
44%
55 to 59
31%
60 to 64
25%
i. Describe the make up of a sample of 48 that is representative of the U.S. with respect
to age.
ii. Describe the make up of a sample of 48 that is more uniform with respect to age.
c) [1] If the 48 people are split evenly among the treatment groups, give a combination of
Alpha, Beta, and
Δ
σ
that correspond to this allocation of people to groups.
d) [2] Explain what a control group would be for this experiment.
e) [3] What is the advantage of having a control group for this experiment?
f) [1] If a control group is included in the experiment and the 48 people are split evenly
among a control group and the three treatment groups, give a combination of Alpha,
Beta, and
Δ
σ
that correspond to this allocation of people to groups.
g) [7] For the representative sample of 48 you described in b),
i. Explain how to use JMP to randomly assign individuals to a control group and three
treatment groups so that each control/treatment group has the same number of people.
ii. Turn in your JMP data table that shows the random assignment. The JMP table must
clearly show the assignment of individuals to control/treatment groups and what age
group each individual is in must be evident.
iii. Comment on how representative each treatment group is in terms of age.
h) [4] Suppose at the end of the experiment there are statistically significant differences
among sample mean changes in cholesterol for the different dosages and that the optimal
dosage is determined to be 20 mg. What generalization can you make if the experiment:
i. Used the representative sample you describe in b)?
ii. Used the more uniform sample you describe in b)?