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Week 9 Practice Problems
These problems all use the
t
distribution for tests of significance in Gaussian response
models.
1.
A measurement system is tested by repeatedly measuring a known standard with
certified known value 1.000 cm. The data are
1.03, 1.04, 1.02, 0.99, 1.02, 1.00
Consider the model
,
~
(0, ),
1,.
..,6 independent
ii
i
YR
R
G
i
μ
σ
=+
=
a)
What would it mean about the measurement system if
1
>
?
b)
Is there any evidence that
differs from 1? [Your answer should show all
5 steps of a test of significance]
c)
Find a 95% confidence interval for
. Is
0
=
in the confidence interval?
2.
Suppose we have data
1
,...,
n
y
y
and the model xx
,
~
(0, ),
1,.
..,
independent
i
R
G
in
=
with
ˆˆ
10.7,
1.77
==
. We are interested in assessing if there is any evidence
that
differs from 10.
a)
Calculate the pvalue for testing the hypothesis
10
=
if
and
30.
10,20
n
=
b)
What happens to the strength of evidence against the hypothesis as
n
increases?
3.
Suppose we have the following data on a response and explanatory variates
x
y
x
y
2.95
4.51
2.24
4.24
1.44
3.56
5.28
3.66
2.08
4.76
0.54
4.52
1.92
3.11
4.33
4.15
1.15
3.28
0.47
4.29
4.28
5.47
0.53
3.33
1.31
4.22
1.88
3.30
4.86
4.28
1.72
3.43
6.43
5.06
0.22
2.93
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This note was uploaded on 03/20/2011 for the course STATISTICS 231 taught by Professor Mckay during the Spring '10 term at Waterloo.
 Spring '10
 McKay

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