ESTIMATION OF THE MEAN
INTRO :: ESTIMATION
Definition
The assignment of plausible value(s) to a
population parameter based on a value of
a sample statistic is called estimation.
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INTRO :: ESTIMATION
The sample statistic used to estimate a
population parameter is called estimator.
Examples …
sample mean estimator population mean
…
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INTRO :: ESTIMATION
The estimation procedure involves …
1.
2.
3.
4.
Select a sample.
Collect the required information from the
members of the sample.
Calculate the value of the sample statistic.
Assign plausible value(s) to the
corresponding population parameter.
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POINT ESTIMATES &
INTERVAL ESTIMATES


A Point Estimate
An Interval Estimate
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A Point Estimate
Definition
The value of a sample statistic that is used
to estimate a population parameter is
called a point estimate.
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INTERVAL ESTIMATES

Usually, whenever we use point estimation,
we calculate the margin of error associated with
that point estimation.
Point Estimate w/out M.E. not very useful!!!!
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Interval Estimates
Definition
In interval estimation, an interval is
constructed around the point estimate,
and it is stated that this interval is likely to
contain the corresponding population
parameter. Gives a range of plausible
values for the parameter of interest.
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Interval estimation.
x  
$1130
x  $1370
$1610
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Interval Estimates


Definition
Each interval is constructed with regard to a given
confidence level and is called a confidence
interval. The confidence level associated with a
confidence interval states how much confidence we
have that this interval contains the true population
parameter. The confidence level is denoted by
(1 – α)100%.
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INTERVAL ESTIMATION OF A
POPULATION MEAN:
Confidence Interval for μ w/ Large Sample
The (1 – α)100% confidence interval for μ is
The value of z used here is read from the
standard normal distribution table for the given
confidence level.
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Finding z for a 95% confidence level.
Total shaded area
is .9500 or 95%
μ
-1.96
0
x
1.96
z
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