Research Methodology - Dr. Krishan K. Pandey

Sampling Fundamentals 165
(ii) Standard error of proportion of successes
bp ⋅ qg
n
(iii) Standard error of the difference between proportions of two samples:
F
HG
1 1
σ p p p q
1 − = ⋅ +
2 n n
1 2
where p = best estimate of proportion in the population and is worked out as under:
n p + n p
p =
n + n
1 1 2 2
1 2
q = 1 – p
n 1 = number of events in sample one
n 2 = number of events in sample two
Note: Instead of the above formula, we use the following formula:
p1 q1
p q
− = +
n n
σ p p
1 2
when samples are drawn from two heterogeneous populations where we cannot have the best
estimate of proportion in the universe on the basis of given sample data. Such a situation often arises
in study of association of attributes.
1
2 2
(b) In case of sampling of variables (large samples):
(i) Standard error of mean when population standard deviation is known:
σ p
σ X =
n
where
σ p = standard deviation of population
n = number of items in the sample
Note: This formula is used even when n is 30 or less.
(ii) Standard error of mean when population standard deviation is unknown:
where
σ
X
σ s = standard deviation of the sample and is worked out as under
σ s =
n = number of items in the sample.
=
σ
s
n
ΣdXi− Xi
2
n − 1
2
I
KJ