Transcript Statistical Inference - Lyle School of Engineering

EMIS 7370/5370 STAT 5340
NTU MA-520-N
Probability and Statistics for Scientists and Engineers
Statistical Inference
Estimation and Tests of Hypotheses
UPDATED 10/17/03
Dr. Jerrell T. Stracener,
SAE Fellow
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Statistical Inference
• Statistical Inference is the process of arriving at
conclusions or decisions concerning the parameters
of populations on the basis of information contained
in samples.
• The theory of statistical inference may be defined
to be those methods by which one makes inferences
or generalizations about a population from a sample.
• Statistical inference may be divided into two major
areas: estimation and tests of hypotheses. We shall
treat these two areas separately
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Statistical Inference
To distinguish clearly between the two areas,
consider the following examples.
1) A candidate for public office may wish to estimate
the true proportion of voters favoring him by
obtaining the opinions from a random sample of
100 eligible voters. The fraction of voters in the
sample favoring the candidate could be used as
an estimate of the true proportion of the
population of voters. A knowledge of the
sampling distribution of a proportion enables one
to establish the degree of accuracy of our
estimate. This problem falls in the area of
estimation.
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Statistical Inference
2) Now consider the case in which a trucking
company is interested in finding out whether
brand A tires last longer than brand B tires. They
might hypothesize that brand A is better than
brand B and, after proper testing, accept or reject
this hypotheses. In this example we do not
attempt to estimate a parameter, but instead we
try to arrive at a correct decision about a prestated hypotheses. Once again we are dependent
on sampling theory to provide us with some
measure of accuracy for our decision.
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