STAT 3504
Assignment 4
DUE:
Monday March 22
1.
In a study of length of hospital stay (in number of days) of persons in
4
income groups, the
parameters are as follows:
μ
1
= 5.1,
2
= 7.9,
3
= 7.9,
4
= 9.5,
σ
= 2.8
Assume single fixed factor levels ANOVA model I is appropriate.
What are the values of the
τ
i
if
the ANOVA model is expressed in the
factor effects
formulation with
r
=
i
r
1
=
i
.
∑
?
2.
A study was carried out to compare
3
different display panels for use by air traffic controllers.
Each
display was tested in a simulated emergency condition.
12
highly trained air traffic controllers took
part in the study.
4
controllers were randomly assigned to each display panel.
The time (in seconds)
to stabilize the emergency condition was recorded. The results are given below.
Display Panel
A
21
27
24
26
B
24
21
18
19
C
40
36
35
32
a)
Use PROC ANOVA in SAS to find the ANOVA table and the fitted means for each display
panel (remember the MEANS statement).
State the null and alternative hypotheses for
testing whether the true mean stabilization times differ for the
3
display panels.
b)
Define indicator (dummy) variables for a regression approach to the analysis of variance in
such a way that the regression coefficients of these variables are the factor level effects
τ
i
.
Give the regression model.
c)
Set up the
Y
,
X
, and
β
matrices.
d)
Use SAS to obtain the fitted regression equation (and Anova table).
e)
Express
Y
,
Y
,
Y
3.
2.
1.
(obtained in part (a)) in terms of the
β
ˆ
's
of the regression equation.
f)
Set up the null and alternative hypotheses for testing for inequality of the true mean
stabilization times.
g)
Why is the hypothesis test in part (f) equivalent to the hypothesis test of part (a)?
3.
The Marketing Department of a large supermarket chain is interested in whether the number of
packages of disposable razors sold in a week differs for
4
different price levels.
5
stores are
randomly assigned to each of the
4
price levels (79, 99, 119, & 139 cents).
The number of packages
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 Spring '10
 Ann
 Statistics, Normal Distribution, Regression Analysis, pairwise comparisons, factor effects

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