Midterm
1. Consider the following Completely Randomized Design in which percentage yield of a
product is studied as the percent of one of its constituents is changed. Use
α
=
.
01
for all tests.
(a) Test whether the linear model is better than the intercept model, and whether the
linear model is as good as the quadratic model (the quadratic model is equivalent
to the cell means model in a 3level design).
(b) Construct separate power curves for each of the above hypotheses, using a reason
able estimate of
σ
2
in your power analysis, and assuming the researcher wanted
to be able to detect a linear contrast of 1 and a quadratic contrast of 2. What
conclusions can you reach about the sample sizes needed to detect effects for the
two hypothees? Do the sample sizes seem unreasonable in comparison to the size
of the pilot experiment?
15
20
25
23.72
31.48
33.44
24.83
33.12
35.22
21.96
30.96
34.23
24.54
29.98
32.97
23.69
31.99
35.20
2. Consider the following SAS output from analysis of a BIBD.
(a) If the grand mean is 17.36, compute ˆ
τ
1
, . . . ,
ˆ
τ
a
.
(b) Compute estimates of
V
(ˆ
τ
),
V
(˜
τ
), and an appropriate estimate of
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 Spring '08
 JohnM.Grego
 Statistics, Trt Block Trt

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