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Chapter 11: Confidence Intervals – Large Samples
Note:
When computing the sample size to make an accurate estimate for the
population proportion
, if
̂
is unknown, use a value of 0.5 in the formula
for
̂
. By using
̂
= 0.5, the maximum sample size will be computed.
Example 11-5:
A statistician wishes to estimate, with 95% confidence, the
proportion of adult U.S. citizens who approve of harvesting embryonic stem
cells, assuming no prior study. The statistician wishes to be accurate to within
2.5% of the true proportion. What is the maximum sple size necessary for
the statistician to carry out the analysis?
Solution:
We are given that
= 0.05,
⁄
= 1.95996 and
= 2.5% =
0.025. Since we cannot assume any prior study, we will have to let the
estimate for
be
̂
= 0.50 and in this case the maximum sample size will be
computed from the formula. Substituting into the formula, we get
̂ ̂ (
⁄
)
= (0.50)(1 – 0.5)(1.95996/0.025)
2
= 1536.57728
1537
That is, in order for the statistician to be 95% confident that the estimate is
within 2.5% of the true proportion of people who approve of harvesting
embryonic stem cells, a sample of
at most
1537 people is needed.
We can also use the
Large Sample Confidence Interval for a Single
Population Proportion
workbook to compute the sample size. The output is
shown in
Figure 11- 8
. Observe that the computed sample size from the
workbook is 1536.6 which rounds up to 1537, the same as when the formula
is used.