STAT
3504 A5 Questions Solution
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1. A researcher studied
the effects of 3 experimental diets
with varying fat contents on the total lipid
(fat) content
in plasma. Total lipid level is a widely used predictor of coronary heart
disease. 15 male subjects who were within 20% of their ideal
body weight were put into 5 groups of 3 according to age. Within each age group the 3 experimental diets were randomly
assigned to the 3 subjects. The reductions in lipid level
after the subjects were on the diet for a fixed period of time were recorded as follows.
|
Fat Content of Diet
|
15-24
|
25-34
|
Age
35-44
|
45-54
|
55-64
|
|
1 Extremely Low
|
0.73
|
0.86
|
0.94
|
1.40
|
1.62
|
|
2 Fairly Low
|
0.67
|
0.75
|
0.81
|
1.32
|
1.41
|
|
3 Moderately Low
|
0.15
|
0.21
|
0.26
|
0.75
|
0.78
|
a)
What was the blocking variable? Why do you
think this blocking variable was used?
b)
Give the model for the experiment. What is the additional major
assumption that is needed here? How could you do a very rough check of whether
it was violated?
c)
Given that SSTO = 2.75856 set up the ANOVA table and test whether the mean
reduction in lipid level differs for the 3 diets. Use a = .01.
reduction in lipid level differs for the 3 diets. Use a = .01.
d)
If appropriate, carry out all pairwise comparisons between the 3
diet means. Use a = .01. Summarize your results
in words and in a graphical
line summary.
e)
What is the relative efficiency of the RBD in
this case? Would you recommend using the same blocks in a future
experiment? Explain.
Verify your
results using SAS. The data is on my web page under ch2lpr07.dat
col 1 has the response col 2 has
"time elapsed since graduation" col
3 has training method
2. -An experiment was conducted to evaluate the
effect of timing of nitrogen application to the soil
(early, optimum, late)
and 2 different levels of nitrogen fertilizer (1 , 2). 3 fields were each
divided
into 6 plots and the
treatments were randomly assigned to the 6 plots within each field. The data
are amount of nitrogen
absorbed by sweet corn plants grown on the plots.
Use the SAS output given below to help you draw the
appropriate conclusions about the
effects of timing and nitrogen level. Use a = 0.01
Carry out a hypothesis
test to determine whether the blocking was effective. Use a = 0.01
Use the Kimball
inequality to put an upper bound on the overall significance level for all the
tests from (a) and (b).
3. - A software
design company has produced 2 voice recognition packages. The language being
tested is Canadian English. It is desired to
test any differences in recognition accuracy between the 2
packages. It is also desired to test whether
it makes a difference if the packages are in a "trained" or
"untrained" state. A trained state
results from the speaker testing the package having spent time
teaching the software to recognize their
voice patterns by reading words prompted by the software
and repeated as requested by the software.
Each speaker is to record the same reading of 150 words
which will then be fed through both types of
software in both the trained and untrained states. It is
thought that gender and maternal language
(French or English), that is accented or unaccented
English might possibly affect the
recognition accuracy. The speakers available are native English
speakers and bilingual speakers whose first
language is French.
How would you design the experiment? To help
consider the following questions.
a)
What are the factors of interest? What are
their levels?
b)
Would blocking be useful here? If so what
might you choose as blocks?
c)
How many speakers would you need to read the
150 word script? Would you use both native
english and bilingual speakers and how would
you use them?
a)
In actual fact, it turned out that there
were 3 native english males, 3 bilingual (accented)
english male, and 3 native english female
speakers available. How would you set up the
experiment
now?
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