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CEE 3770  Summer 2009
Homework 3 (due on 06/18)
1. An apparel and shoe trade association has 8,900 member ﬁrms. As a part of a study of
the impact of new minimumwage legislation on association members, a random sample of
400 member ﬁrms was selected to estimate
μ
, the mean number of hourlypaid employees
in member ﬁrms. A computer analysis of the sample results showed:
X
= 8
.
31, where
X
denotes the number of hourly paid employees in a ﬁrm. Suppose that you know that
X
is
normal distributed with known variance
σ
2
= 4
.
16
2
.
(a) Construct 94% conﬁdence interval for
μ
.
Solution:
94%
CI
=
X
±
z
α/
2
r
σ
2
n
= 8
.
31
±
z
0
.
03
r
4
.
16
2
400
= 8
.
31
±
1
.
88
·
4
.
16
20
= 8
.
31
±
0
.
39104
(b) If you had constructed a 99% conﬁdence interval, would it have been wider or narrower
than one in (a)?
Solution:
Wider.
2. The EPA standard on the amount of suspended solids discharged into rivers and streams is a
maximum of 60 milligrams per liter daily, with a maximum monthly average of 30 milligrams
per liter. Suppose you want to test a randomly selected sample of
n
water specimens and
estimate the mean daily rate of pollution produced by the mining operation. If you want 95%
conﬁdence interval estimate of width 2 milligrams, how many specimens you need to sample?
Assume prior knowledge indicates that pollution readings in water samples taken during a
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 Spring '08
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