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Unformatted text preview: (2.12) is on the conTable 2.2: Some choices of a and resulting values of 1 −
a
2
5
10 1
.
a2 1 − (1/a2 )
75%
96%
99% servative side; the probability on the lefthand side of (2.12) may be much closer to one than the
righthand side. Often in practice other conﬁdence intervals are used which are based on diﬀerent
assumptions (see Example 3.6.10).
Example 2.9.2 Suppose the fraction p of telephone numbers that are busy in a large city at a
given time is to be estimated by p = X , where n is the number of phone numbers that will be
n
tested and X will be the number of the tested numbers found to be busy. If p is to be estimated to
within 0.1 with 96% conﬁdence, how many telephone numbers should be sampled, based on (2.12)?
Solution: For 96% conﬁdence we take a = 5, so the halfwidth of the conﬁdence interval is
a
2.
√ = √5 , which should be less than or equal to 0.1. This requires n ≥ ( 2.5 )2 = 625.
0.1
2n
n 2.10 The law of total probability, and Bayes formula Events E1 , . . . , Ek are said...
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 Spring '08
 Zahrn
 The Land

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