Introduction to econometrics II eco 356 faculty of social sciences course guide course Developers: Dr. Adesina-Uthman

Download 1.75 Mb.

View original pdf

Page	17/96
Date	10.11.2023
Size	1.75 Mb.
	#62567

1 ... 13 14 15 16 17 18 19 20 ... 96

Introduction to Econometrics ECO 356 Course Guide and Course Material

( ) ./ …[1.11]
Table 1.1.1
…[1.14] Could also be obtained from table 1.1.1 1.1.3.5 Estimation of Population Mean

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.
Table 1.1.1 Simple Random Sampling

Samples

Probability

mean

Variance
(0,2)
1 2
(0,4)
2 8
(0,6)
3 18
(2,4)

3 2

INTRODUCTION TO ECONOMETRICS II

ECO 306

NOUN
25
(2,6)
4 8
(4,6)
5 2 We see in this example that V (
̅)
/
/
/ Similarly,
(
) .
/

…[1.14]
Could also be obtained from table 1.1.1
1.1.3.5 Estimation of Population Mean
If we are interested in estimating a population mean from a simple random sample, we have
̂
̅
∑

Download 1.75 Mb.

Share with your friends:

1 ... 13 14 15 16 17 18 19 20 ... 96