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Unformatted text preview: a constant, even though we don’t
know its value. The variable p is random, and therefore the interval p − a p(1−p)
n ,p +a p(1−p)
n is also random. For example, if a = 5, then, before we start taking the poll, we would have 96%
conﬁdence that p will be in this random interval. This interval is not quite suitable for use as
a conﬁdence interval, because it depends on the unknown parameter p, so we wouldn’t know the
interval. However, p(1 − p) ≤ 0.25 for any p ∈ [0, 1], so if we replace p(1 − p) by 0.25 in deﬁning
the conﬁdence interval, it makes the conﬁdence interval larger, and therefore it can only increase
the probability that the true parameter is in the interval. In summary, we have:
P p∈ a
p − √ ,p + √
2n ≥1− 1
a2 (2.12) The larger the constant a is, the greater the probability that p is in the random interval. Table
2.2 shows some possible choices of a and the associated upper bound in (2.10), which is the level
of conﬁdence associated with the interval. The conﬁdence interval given by...
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This note was uploaded on 02/09/2014 for the course ISYE 2027 taught by Professor Zahrn during the Spring '08 term at Georgia Institute of Technology.
- Spring '08
- The Land