STATISTICAL INFERENCE
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Statistical Inference uses sample
data and statistical procedures to:
Estimate population parameters; or
Test whether or not a population
parameter is likely to satisfy some
specified value.
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STATISTICAL INFERENCE
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Estimation of population parameters
 The
process of using a statistic to infer about
the value of an unknown parameter with a
specified level of certainty
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Test whether a population parameter is likely
to satisfy some specified value
 The
use of sample data to accept or to reject a
statement about a parameter value or about a
population distribution
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Properties of Point Estimators
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Bias describes the location of an estimator;
Efficiency is a measure of the amount of variation in
the sampling distributions for alternative estimators
of a parameter;
Consistency describes how the sampling distribution
of an estimator concentrates around the parameter
values as the sample size increases; and
Sufficiency is a measure of the use of information.
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ESTIMATION
The process of using a statistic to infer about the
value of an unknown parameter with a specified
level of certainty:
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Large Sample 100(1 - )% Confidence Interval
for ;
Small Sample 100(1 - )% Confidence Interval
for ; and
Confidence Limit for 
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Interval Estimation
Procedure
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Want to use X to estimate X.
How reliable is a point estimate?
Develop a measure of reliability by
finding an interval of numbers
within which we expect the true
value of the population mean to be
contained.
Have X, but do not know X.
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Interval Estimation
Procedure
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Large-Sample 100( 1 -  )%
Confidence Interval for X is X +
Z/2  X.
The interval X + 1.96 X is called
a Large-Sample 95% Confidence
Interval for the population mean.
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