INTRODUCTION TO ECONOMETRICS II ECO 306 NOUN 24
( ̅)
…[1.09]
V (̅)
.
/
…[1.10]
The term .
/ in the above expression is known as the
finite population correction factor.
For the sample variance , it can be shown that
(
) .
/
…[1.11]
When using
as an estimate of
,
we must adjust with / (
)
…[1.12] Consequently, an unbiased estimator of the variance of the sample mean is given by
̂( ̅)
.
/
…[1.13]
As
a rule of thumb, the correction factor .
/ can be ignored if it is greater than
0.9, or if the sample is less than 10% of the population.
Example 2; Consider the finite population with
N = 4 elements +.
For this population = 3 and
= 5. Simple random samples without replacement of size
n =
2 are selected from the population. All possible samples along with their summary statistics are listed in table 1.1.1.
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