Stat 402 B – Exam 2 Take-home Problems
Due at the beginning of the exam on Friday, April 12, 2013
1. [26 pts] The take-home problem for Exam 1 this semester discussed an experiment
that looked at the effects of different dosages of a blood thinner on the International
Normalized Ration (INR), a measure of how fast blood clots, using a completely
randomized design. This problem looks at some additional things that can be done to
expand on the experiment for Exam 1. Instead of controlling for blood type or
randomizing over blood type, researchers decided to use blood type as a second factor
of interest with four levels (O, A, B and AB). In order to have a manageable
experiment the researchers decided to investigate only three dosage levels (0 mg, 5
mg and 10 mg).
a) [2] Is dosage an experimental or observational factor? Explain briefly within the
context of the problem.
b) [2] Is blood type an experimental or observational factor? Explain briefly within
the context of the problem.
c) [1] Factorial crossing of dosage and blood type will be used to form treatments.
How many treatments will there be?
d) [2] Nine people from each blood type (a total of 36 people) are recruited for the
experiment. If the experiment is run as a completely randomized design;
 What size difference in blood type means can be detected with Alpha = 0.05
and Beta = 0.10?
 What size difference in dosage means can be detected with Alpha = 0.10 and
Beta = 0.05?
e) [3] Give a partial analysis of variance table for a completely randomized design
with 9 people for each blood group. Include all the sources of variation and
associated degrees of freedom.
f) [2] If the interaction between dosage and blood type is statistically significant
what would this indicate about the effect of dosage on INR? Explain briefly.
g) [3] In the completely randomized design, what contributes to the sum of squares
error? Be specific and be sure to explain within the context of the problem.
As an alternative to a completely randomized design, a randomized complete block
design is proposed.
h) [2] Why would it be difficult to reuse people in a randomized complete block
design with treatments made by factorial crossing of blood type and dosage?
i) [3] People can be sorted according to their INR before starting the experiment.
Explain how to sort the 36 people recruited for the experiment into blocks
according to initial INR.
j) [3] Give a partial analysis of variance table for your randomized complete block
design using the 36 people recruited. Include all the sources of variation and
associated degrees of freedom.
k) [3] In the analysis of the randomized complete block design, what contributes to
the sum of squares error? Be specific and be sure to explain within the context of
the problem.
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2. [9 pts] A new type of fish food has become available for salmon raised on fish farms.
Your task is to design an experiment to compare the weight gain of salmon raised
over a six-month period on the new and old types of food. Eighty salmon that are
similar in size and weight are available for the experiment. All salmon should be
used in the experiment. There are eight large tanks in a room that has a considerable
temperature gradient. Specifically, tanks on the north side of the room tend to be
much colder than those on the south side. Additionally, because the doors are opened
frequently, more cold air can enters the room by the doors than by the windows. The
arrangement of tanks is shown on the diagram below. The same amount of food will
be given to each tank each day.
The room and the tanks are available to do one feeding experiment.
a) [3] What are the response, conditions and experimental units?
b) [4] Describe a design for this experiment that accounts for the differences in
temperature in different parts of the room. Be specific. Be sure to describe how
you will use randomization in your experiment. From your description someone
else should be able to conduct the experiment.
c) [2] Give a partial analysis of variance table indicating all sources of variability
and degrees of freedom associated with each source.
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