Download ̂ X̄ n z X̄ ̂ X̄ n t X̄

Logic for estimation of population parameters from sampling
By Nasser Abbasi
Nov 10, 2007
Math 502 CSUF
Which population
parameter to
estimate?
population mean
Population Variance
Population propertion

p
(Next page)
Population Median
Let
n  sample size
X̄  sample mean
Let C. I. be confidence level (95% etc..)
Let
is population standard
No
deviation
 known?
Regardless of
sampling
method?
Type of Sampling?
Sampling
Without
replacement
n
s2 
1
n−1
 X̄ 
Yes
∑x i − x̄  2
(uses finite population
correction term)
Sampling
With
replacement
i1
s
n
1−
n
N
Let N = population size
 X̄ 

n
1−
n−1
N−1

n
 X̄ 
Since sample std is used
instead of population std,
then use the Student tdistribution with degree of
freedom = n-1
For given C.I., Look up t 
2
from Student t distribution table
̂  X̄ n  t 2  X̄
For given C.I., Look up z
from Z distribution table

2
̂  X̄ n  z 2  X̄