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Chapter 11: Confidence Intervals – Large Samples
sampling distribution for
̂
is approximately normally distributed, and so
from the
Empirical Rule
, approximately 95% of the observed
̂
values will
lie within 2 standard deviations of the mean,
̂
. This situation can be
described by
Figure 11-2
.
Figure 11-2:
Display of two standard deviations from the mean of
̂
Thus, the approximate 95 percent confidence interval estimate the true
proportion of female high school seniors who plan to attend college after
graduation is 0.85
2
0.0357 = 0.85
0.0714. That is, we are
(approximately) 95% confident that the true proportion of female high school
seniors who plan to attend college after graduation will lie between 0.7786
and 0.9214, or between 77.86% and 92.14%.
Note:
We say the margin of error is
0.0714 or
7.14%.