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ST 310 Midterm Exam
October 14, 2008
1. Consider the following population of four units:
ID
1
234
y
25
03
66
0
.
(a) Enumerate (list) all possible samples of size 2, and demonstrate that
¯
y
is unbiased for
μ
.
(b) In the classical model
y
1
,...,y
n
∼
i.i.d.
N
(
μ, σ
)
,
¯
y
is also unbiased for
μ
. Yet in the finitepopulation model of part (a), the variance of
¯
y
is half
of the variance of
¯
y
in the classical model. Why?
1
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View Full Document 2. Briefly comment on the advisability of using a normalapproximation (nom
inal) 95% confidence interval (
¯
y
±
1
.
96
×
SE) in each of the following sce
narios:
(a) Highly skewed data,
n
=10
,
N
=20
.
(b) Symmetric data, no outliers,
n
= 900
,
N
= 1000
.
(c) Symmetric data, no outliers,
n
= 100
,
N
,
000
.
(d) Highly skewed data,
n
= 1000
,
N
= 100
,
000
.
2
3. Your client states “I know that the statistical procedures you use are unbiased,
and I understand that the math guarantees that. However, I cannot believe that
the estimate you’re giving me is correct, even taking standard error into ac
count.” Give the client two purely statistical and two nonstatistical scenarios
that could account for the apparently anomalous result.
3
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View Full Document 4. A stratified sample of the net worth (assets  liabilities) of 40 banks near fail
ure, and 40 financially sound banks, yields the following data, in $B(near fail
ure = stratum 1; financially sound = stratum 2):
¯
y
1
=0
.
63
,
SD
1
.
22
,
¯
y
2
=
1
.
07
,
SD
2
.
34
. There are 200 banks near failure, and 1000 financially
sound banks, in the population.
(a) Calculate the standard error of the stratified estimator
¯
y
ST
in this case.
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This note was uploaded on 01/28/2012 for the course STATISTICS 3010 taught by Professor Ooz during the Spring '11 term at Cornell University (Engineering School).
 Spring '11
 Ooz

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