Unformatted text preview: area = (.2291)(2) = .4582.
The probability is .4582 that the sample proportion will be
ECO 3411
45
within +/.05 of the actual population proportion. Properties of Point Estimators
• Before using a sample statistic as a point estimator,
statisticians check to see whether the sample statistic has
the following properties associated with good point
estimators.
– Unbiasedness
– Efficiency
– Consistency ECO 3411 46 Properties of Point Estimators
• Unbiasedness
If the expected value of the sample statistic is equal to
the population parameter being estimated, the sample
statistic is said to be an unbiased estimator of the
population parameter. ECO 3411 47 Properties of Point Estimators
• Efficiency
Given the choice of two unbiased estimators of the
same population parameter, we would prefer to use the
point estimator with the smaller standard deviation, since
it tends to provide estimates closer to the population
parameter.
The point estimator with the smaller standard
deviation is said to have greater relative efficiency than the
other. ECO 3411 48 Properties of Point Estimators
• Consistency
A point estimator is consistent if the values of the
point estimator tend to become closer to the population
parameter as the sample size becomes larger. ECO 3411 49 Other Sampling Methods
•
•
•
• Stratified Random Sampling
Cluster Sampling
Systematic Sampling
Convenience Sampling ECO 3411 50 Stratified Random Sampling The population is first divided into groups of
The population is first divided into groups of elements called strata..
elements called strata Each element in the population belongs to one and
Each element in the population belongs to one and only one stratum.
only one stratum. Best results are obtained when the elements within
Best results are obtained when the elements within each stratum are as much alike as possible
each stratum are as much alike as possible (i.e. a homogeneous group).
(i.e. a homogeneous group). ECO 3411 51 Stratified Random Sampling A simple random sample is taken from each stratum.
A simple random sample is taken from...
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 Winter '08
 Staff
 Point Estimators

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