INEN314 Homework #7
(Due 10/31)
1. [6pts]
Sample size allocation. Suppose we are testing the hypotheses
:
0
H
2
1
µ
=
:
1
H
2
1
≠
where
2
1
σ
and
2
2
are known. Resources are limited, and consequently the total sample size
N
n
n
=
+
2
1
.
How should we allocate the
N
observations between the two populations to obtain the most powerful test?
[Hint: The most powerful test is the one that minimizes the denominator of the corresponding test statistic.]
2. [6pts]
The mean content of coffee cans filled on a particular production line are being studied.
The target
mean of contents is 16.0 oz, and from past experience it is known that the population standard deviation of
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 Spring '10
 M
 Statistics, Standard Deviation, mean content, Sample size allocation

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