), we need to minimize
.
24
n
A
+
.
24
n
B
.
This is 0.163 for choice (1) and 0.107 for
choice (2). Choice (2) has smaller width.
(b) By looking at the expression above, the
CI width is minimized when
1
n
A
+
1
n
B
is
as small as possible with
n
A
+
n
B
= 100.
Based on part(a), the width is smaller for
the values of
n
A
and
n
B
that are closer
together.
Thus the ’natural’ conjecture
is that the CI width can be minimized if
n
A
=
n
B
= 50. This is the correct answer.
It is primarily for this reason that most
scientific studies comparing 2 (or more)
groups have equal sample sizes.
Grade Distribution
9099:22
8089:41
7079:26
median =
79
6069:17
5059:13
below: 8
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 Fall '08
 Staff
 Normal Distribution, Standard Deviation, Null hypothesis, Trigraph, binomial formula results

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