Lecture 8 Part II.pdf


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Be Careful!
The following statement is NOT true for
interpreting a confidence interval:

Answer
If we want 95% confidence, then Z=1.96.
Confidence z


95%
1.96



The probability that µ lies between
143.22 and 162.78 is .95.

µY is in Y ± Zσ Y

Once you have inserted your sample
results into the confidence interval
formula, the word PROBABILITY can
no longer be used to describe the
resulting confidence interval.
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Exercise (4)

µY
µY
µY
µY

where σ Y = σ Y / n

is in 28.834 ± 1.96σ Y

where σ Y = 7.095 / 92 = .7397

is in 28.834 ± 1.96(.7397)
is in 28.834 ± 1.450
is between 27.384 and 30.284
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Answer

•  National Association of Colleges and Employers
•  Sample of n=92 Sociology BAs, graduating 2000-01
•  Variable: starting salary (Y) in thousands

We are 95% sure that the interval $27.384K and
$30.284K contains the average salary in the population
of new soc BAs, 2000-01

–  Cases: 38.0, 28.0, 28.0, 24.6, …
•  Find and interpret the 95% confidence interval.

Just an average.
Doesn t mean 95% of individual salaries are in the
interval.

Y = 28.834

σ Y = 7.095
38

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