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Chapter 13: Confidence Intervals – Small Samples
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The margin of error is given by
Example 13-3:
A random sample of 16 assistant professors on a particular
campus was surveyed. Their mean salary was $44,000 with a standard
deviation of $1,000. Construct a 99% confidence interval estimate for the
true mean salary for all assistant professors on that particular campus.
Solution:
Given
= 0.01,
/2 = 0.005,
= 16,
= 16-1 = 15,
= 2.9467,
̅
= 44,000,
= 1,000, and
̅
√
= 250.
Thus the 99% confidence interval estimate for the mean salary, using the
formula, is 44,000
2.9467
250 = 44,000
736.675.
Thus, we are 99% confident that the average salary for the assistant
professors at that particular campus will be between $43,263.325 and
$44,736.675.
We can also use the
Small Sample Confidence Interval for a Single
Population Mean
workbook to solve the problem. The appropriate output is
shown in
Figure 13-6
.