Week 6 Practice Problems
1.
(using the
2
χ
and
t
tables) Find the following
a)
a constant
c
so that
2
30
(
)
0.975
Pc
>=
b)
a constant
c
so that
2
20
(
)
0.975
c)
constants
so that
12
,
cc
2
11
02
()
c
<<=
0
.
9
5
d)
Repeat a) to c) with
2
replaced by student’s
t
.
e)
estimate
2
15
(2
P
>
5
)
f)
estimate
6
(
 2)
Pt
>
2.
In a pilot study to test a complex questionnaire to be used in a large survey, 10
volunteers agreed to be surveyed. A key response variate was a score based on the
answers to 25 different questions. The data are shown below with some
summaries.
average
stdev
score
57.6
58.3
56.4
57.4
56.1
58.3
49.9
55.6
51.8
56.1
55.74
2.78
The researchers decided to model the data using a simple Gaussian response
model
0
,
,...,
~
(0, ) independent
ii
YR
R
R
G
μ
σ
=+
a)
What do the parameters
and
represent?
b)
What are the estimates of
and
?
c)
What are the distributions of the corresponding estimators?
d)
Find a 90% confidence interval for
and
.
e)
Provide an informal and a formal interpretation for the CI for
3.
The form of a 95% CI for
is
ˆˆ
(,)
ab
where
a
and
b
are chosen based on the
confidence level. We can think of
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 Spring '10
 McKay
 Normal Distribution, key response variate, Gaussian response, relative error bounds

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