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CEE 3040
Fall 2008
CEE 304

Section #8 Example Problems Partial solutions
1.
Confidence Intervals for Small Samples:
Environmental Engineering Problem Statement:
An environmental engineer is studying the concentration of organics in a groundwater
source for a rural water supply. Twelve samples yielded a sample mean and sample
standard deviation of 152.3
μ
g/l and 4.8
μ
g/l, respectively.
or
Structural Engineering Problem Statement:
The sample average ultimate tensile strength for a sample of 12 highstrength magnetic
alloy steel rings used in turbine generators was 152.3 ksi, while the sample standard
deviation was 4.8 ksi.
a.) Construct a 99% confidence interval for the true mean concentration of organics in
this source of water assuming individual observations have a normal distribution.
or
Construct a 99% confidence interval for the true mean tensile strength of such rings
assuming individual observations have a normal distribution.
Answer:
n = 12,
x
=152.3,
4.8
x
s
=
,
α
= 1%
σ
is unknown, n is small, so use tdistribution
2,
1
2,
1
,
n
n
s
s
CI
x
t
x
t
n
n
α


=

+
2,
1
0.005,11
3.106
n
t
t

=
=
4.8
4.8
152.3 3.106
,152.3 3.106
12
12
CI
=

+
(
29
148.0,156.6
CI
=
b.) Construct a 90% confidence interval for the true mean concentration of organics in
this source of water assuming individual observations have a normal distribution
or
Construct a 90% confidence interval for the true mean tensile strength of such rings
assuming individual observations have a normal distribution.
Answer:
n = 12,
x
=152.3,
4.8
x
s
=
,
α
= 1%
σ
is unknown, n is small, so use tdistribution
2,
1
2,
1
,
n
n
s
s
CI
x
t
x
t
n
n


=

+
2,
1
0.05,11
1.796
n
t
t

=
=
4.8
4.8
152.3 1.796
,152.3 1.796
35
35
CI
=

+
(
29
150.1,154.5
CI
=
1
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This note was uploaded on 12/01/2010 for the course CEE 3040 at Cornell University (Engineering School).
 '08
 Stedinger

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