Notes 12
Recall
:
The sample mean
x
is the best estimate of the population mean
μ
.
This is an example of a
point estimate.
Point Estimate
: a singlevalue
estimate of the population parameter.
Instead of being restricted to a single value for an estimate, a range of values can be used as an
estimate. This is called an
Interval Estimate
.
Interval Estimate
: an interval that is estimated to contain the value of a population parameter.
Example
:
The sample mean height for American men is 69". (Point Estimate)
Instead, we can say that the mean height of American men is between 67.5" and 70.5" (Interval
Estimate).
How do you determine the size of this interval?
How do you determine the upper and lower boundaries for this interval?
These questions are answered using
COglyph1197FIDEglyph1197CE Iglyph1197TERVALS
.
The Idea Behind the Confidence Interval
Recall that 95% of the zscores fall within 2 standard deviations of the mean.
We can rewrite the previous statement as it is equivalent to saying the probability that z lies
between 2 and 2 is approximately equal to .95.
or
P( 2 < z < 2 ) =0.95
Recall this graph and assume we
have a standard normal distribution
with
μ
=0 and σ=1.
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Notes 12
Therefore, our level of confidence is just simply the probability of a population parameter being
contained in a confidence interval for a point estimate of a sample.
Example:
So using the same example from the previous page:
The mean height of American men is between 67.5 and 70.5 inches with a level of confidence of
C =.95
can be read as the following:
Whenever a sample of American men is drawn and a confidence interval is constructed from the
sample data, 95% of the samples (of American men) will yield an interval that actually contains
the mean height of
all
men.
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 Spring '08
 BATEH
 Statistics, Normal Distribution, Standard Deviation, Tampa

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