1
Ch 8 NotesAGB
3/15/2010
Chapter 8
–
Statistical Inference: Confidence Intervals
First, reviewing what we have learned:
Statistics is a way of dealing with the uncertainty of how our world
works
Decision making with imperfect data
Based on our perceptions which have been influenced by
prior learning, both formal (schooling) and informal (our own
experimentations)
Statistics works with theoretical models
We form a hypothesis and then we test it to determine if
our model is right
We test the underlying conditions and assumptions about
the model first to make sure we can use it.
Ex. Binomial has only two outcomes, etc.
Sampling error cannot be eliminated if we are working with samples.
We look for patterns in data when attempting to develop the theoretical model
Descriptive statistics:
organization, summarization and display of data in
order to make sense of it
Inferential statistics:
sample used to draw conclusions about a population;
uses probability to help determine likelihood of something happening
Used to clarify or prove a current hypothesis
Confidence Intervals
We construct a interval around a point estimate with some confidence that
the interval contains the population parameter.
Population parameters are unknown while sampling parameters are known.
We are trying to use the “known” to estimate what the unknown is.
We can‛t
be sure we are right but we can have a certain confidence
about it.
The larger the better is the rule of thumb for samples when using them to
estimate the population proportion.
Assumptions about the population are based on randomized
experiments or a random sample.
We use the CLT which says that the sampling distribution of a
statistic is usually a normal distribution.
Sample size depends on the level of accuracy needed
not
the size of
the population.
Needed level of accuracy based on:
o
Safety issues
–
will someone be hurt if you are wrong?
o
Cost issues
–
what will it cost you or your company if
you are wrong?
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2
Ch 8 NotesAGB
3/15/2010
Point and Interval Estimates of Population Parameters
Point Estimate and Interval Estimate
#
A
point estimate
is a
single number
that is our “best guess” for the parameter
#
An
interval estimate
is an
interval of numbers
within which the parameter value is
believed to fall.
#
A
point estimate
doesn‛t tell us how close the estimate is likely to be to the
parameter
#
An
interval estimate
is more useful
o
It incorporates a margin of error which helps us to gauge the accuracy of
the point estimate
Properties of Point Estimators
#
Property 1:
A good estimator has a sampling distribution that is centered at the
parameter
o
An estimator with this property is
unbiased
The sample mean is an unbiased estimator of the population mean
The sample proportion is an unbiased estimator of the population
proportion
#
Property 2:
A good estimator has a
small standard error
compared to other
estimators
o
This means it tends to fall closer than other estimates to the parameter
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 Winter '10
 C.Eckerle
 Math, Statistics, Normal Distribution, Levin

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