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STA6126 Chapter 5,Page 1 of 4
Revised on 8/22/2011 11:05 AM
Chapter 5
Statistical Inference
Methods of Statistical Inference:
Point Estimation
Interval Estimation
Significance Tests (Chapter 6)
5.1 Point Estimation
A point estimator of a parameter is the sample statistic that predicts the value of the parameter.
A point estimator of the population mean is the sample mean:
X
ˆ
X
A point estimator of the population variance is the sample variance:
22
XX
ˆ
S
A point estimator of the population proportion is the sample proportion
ˆ
p
Desirable properties of Point Estimators:
Efficiency
Unbiasedness
Normality
The above estimators have the following properties:
1.
They are
efficient
, i.e. one cannot find other estimators that have smaller standard errors
and these estimators are closer to the true parameter values.
2.
They are
unbiased
. In repeated sampling the estimates average out to give the true values
of the parameters. (S is not an unbiased estimator of
but its bias is small and decreases
as the sample size increases.)
3.
The sample mean and the sample proportion have approximate normal distributions (but
not the sample variance).
General formula for a confidence interval
CI = (Estimate
Margin of Error)
ME = Margin of Error = (table value) × (Standard Error of Estimate)
The width of a CI
Increases as the confidence level increases
Decreases as the sample size increases.

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STA6126 Chapter 5,Page 2 of 4
5.2 CI for population proportion
:
Using the general formula we may also write
An approximate confidence interval for
is
p
ME
and
1
p(
p )
ME
z
n
When np ≥ 15 and n(1 – p) ≥ 15
5.3 Confidence interval for the mean

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