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a sample distribution with the same mean mu
but whose standard deviation is sigma/rad(n).
No matter what population the random
sample comes from, the shape of the
sampling distribution is Normal as long as
the sample size is large enough. Confidence Intervals for
Proportions 51.9% of all sea fans on the Las Redas Reef
It is probably true that 51.9% of all sea fans
on the Las Redas Reef are infected
We don’t know exactly what proportions of
sea fans on the Reef are infected, but we
know that it’s within the interval 51.9% +/4.9%. That is, between 42.1% and 61.7%. 3 10/30/2011 Technically
◦ We don’t know exactly what proportion of sea fans
on the Reef is infected, but the interval from 42.1%
to 61.7% probably contains the true proportion We
We are 95% confident that between 42.1% and
61.7% of Las Redas sea fans are infected
◦ Now that’s a confidence interval!
◦ The interval calculated and interpreted here is
sometimes called a one-proportion z-interval
onez- Confidence interval:
Confidence interval p-hat +/- 2 SE(p-hat)
The extent of the interval on either side of phat is called the margin of error (ME)
◦ Use the same approach for all other situations
◦ Not just proportions!
◦ General format: Estimate +/- ME
+/- Formally, 95% of samples this size will
produce confidence intervals that capture the
We are 95% confident that the true proportion
lies in our interval
Our uncertainty is about whether the
particular sample we have at hand is one of
the successful ones of one of the 5% that fail
to produce an interval that captures the true
◦ Randomization Condition: Were the data sampled at
random or generated from a properly randomized
◦ 10% Condition: If the sample exceeds 10% of the
population, the probability of a success changes so
much during sampling that Normal model might
not be appropriate The more confident we want to be, the larger the
margin of error will be!
Tension between certainty and precision Sample
Sample Size Ass...
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This document was uploaded on 02/11/2014.
- Spring '14