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Chapter 11: Confidence Intervals – Large Samples
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The general equation used in constructing a (1 -
)
100 percent confidence
interval for the population proportion for large samples is given next.
Note:
The margin of error is given by
Example 11-2
:
In a random sample of 100 adults, 54% of them said that
they go to bed between 10:00 pm and midnight. Determine a 90%
confidence interval estimate for the true proportion of adults who go to bed
between 10:00 pm and midnight.
Solution:
The sample proportion
̂
= 0.54 and the standard deviation for
the sample proportion
̂
=
√ ̂
̂
= 0.0498. (Verify).
Since we need to find the 90% confidence interval estimate,
= 10% = 0.1
and
= 0.1/2 = 0.05. Thus
⁄
= 1.6449. (Refer to
Figure 11-4
).
Thus, the 90% confidence interval estimate for the proportion of adults who
go to bed between 10:00 pm and midnight, using the formula, is 0.54
1.645
0.0498 = 0.54
0.0819. That is, we are 90% confident that the true
proportion of adults who go to bed between 10:00 pm and midnight is
between 0.4581 and 0.6219 or between 45.81% and 62.19%.
We can use the
Large Sample Confidence Interval for a Single Population
Proportion
workbook to help with the computations.
Figure 11- 5
shows a
portion of the output. It shows that the 90% confidence interval the