Standard Sampling Methods and Analyses - Introduction to Ecological Sampling - page 21

K

∑

µ= NN /

ii

µ , (2.22)

i = 1

and the corresponding sample estimate is

K

∑

y yN = / , (2.23)

s i i

i 1

=

with estimated variance

K

∑

·· .

Var( y NyN )

2

Var( /

2

= (2.24)

s i i

i = 1

· , the square root of the estimated
variance, and an approximate 100(1 − α)% confidence interval for the popu-
lation mean is given by

The estimated standard error of y s is SE() y

/2 ·

yz y ± SE() , (2.25)

s s

α

where z α/2 is the value exceeded with probability α/2 for the standard nor-
mal distribution.
It sometimes happens that the population being dealt with is effectively
infinite. For example, if samples are taken at point locations in a field, then the
number of possible points can be regarded as infinite. In that case, Equations
(2.22) to (2.24) can be modified by replacing N i / N by the proportion of the
population in stratum i . Hence, for sampling points in a field, this would be
the proportion of the area in the whole field that is in stratum i . Also, in this
situation the finite population corrections would not be needed because n i / N i
would be zero for all strata.
If the population total is of interest, then this can be estimated by

· TNy

s

(2.26)

s

with estimated standard error

···

SE() SE( s . TN y (2.27)

Again, an approximate 100(1 − α)% confidence interval takes the form

· · ·

Tz T ± SE() . (2.28)

s

α /2