Unformatted text preview: the localizer (certain
distance left and right of the runway). When an
airplane deviates from the localizer, it is called
an exceedence.
an
Suppose in a random sample of 250 landings for
a certain airline, 30 exceed the runway. Estimate
the percentage of exceedences with a 95%
confidence interval. With a 99% confidence
interval.
interval.
G. baker, Department of Statistics
G.
University of South Carolina; Slide 15 Effect of Level of Confidence on a
Effect
Confidence Interval
Confidence
For a given sample size, as one increases
the level of confidence, what happens to
the width of the confidence interval?
the
What is the consequence of this change in
interval width?
interval
G. baker, Department of Statistics
G.
University of South Carolina; Slide 16 Effect of Sample Size on a
Effect
Confidence Interval
Confidence
At a given level of confidence, as one
increases the sample size what happens to
the width of the confidence interval?
the
So choose your sample size before you
estimate a proportion with a confidence
interval
interval
G. baker, Department of Statistics
G.
University of South Carolina; Slide 17 Sample Size
ˆ
ˆ
p (1 − p )
n Maximum Error = e = zα/2 (solving for n)
2 ˆ
ˆ
zα / 2 p (1 − p)
n=
2
e
G. baker, Department of Statistics
G.
University of South Carolina; Slide 18 Sample Size
If you can’t guess a value for
If 2 ˆ
p : 2 zα / 2 (.5)(.5) zα / 2
n=
=2
2
e
4e
What sample size would you recommend
to estimate the proportion of exeedences
with a 95% confidence interval and
maximum error of 2%?
maximum
G. baker, Department of Statistics
G.
University of South Carolina; Slide 19 Research Update!
Recent research shows that we get better
coverage for (1α)100% CI’s on
coverage
phat if we alter the CI formula.
95%CI:
95%CI: where
where ˆ
p ± zα / 2 x+2
ˆ
p=
n+4 ˆ
ˆ
p (1 − p )
n+4
(Agresti/Coull)
G. baker, Department of Statistics
G.
University of South Carolina; Slide 20 Statistical Hypothesis
A statistical hypothesis iis an assertion or
s
statistical
conjecture concerning one or more
population parameters.
population
Exa...
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 Fall '13
 Wang
 Statistics

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