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Chapter 11: Confidence Intervals – Large Samples
we can solve for the sample size
to get
Note:
This formula will yield the minimum sample size that is required.
Example 11-4:
A confidence interval for a population proportion is to be
constructed and must be accurate to within 0.01 (1%) unit of the true
proportion. What is the minimum sample size
needed to provide the
desired accuracy with 99 percent confidence if it is known from previous
studies that a good estimate for the proportion is 0.8?
Solution:
We are given that
= 1% = 0.01,
⁄
= 2.5758 (to four decimal
places),
̂
0.8, and
= 0.01. Substituting into the formula, we get that the
sample size
̂ ̂ (
⁄
)
= (0.80)(1 – 0.8)(2.5758/0.01)
2
= 10615.5930
10,616.
That is, in order to be 99 percent
certain that the estimate is within 1 percent
of the true population proportion, the
minimum sample size
needed is
10,616.