In SRSWOR of size n from a population with N units if p is the proportion of sampled units having a given attribute, then unbiased estimate of V(p) is

Question

Question

This question was previously asked in

SSC CGL Tier-II ( JSO ) 2016 Official Paper ( Held On : 2 Dec 2016 )

Answer 1

Explanation

Suppose that a simple random sample of size n is selected and n₁ unit in this sample belong to the class C.

Lert p = n₁/n be the sample proportion of units in the class C.

⇒ y̅ = n₁/n = p

⇒ S²_y = npq/(n – 1)

We have two cases

(i)- SRSWOR

When p is an unbiased estimator of P

⇒ Var(p) = [(N – n)/(N – 1)] × PQ/n

⇒ Est. Var(p) = [(N – n)/N] × pq/(n – 1)

⇒ rse(p) = √Var(p)/P

⇒ √[(N – n)/(N – 1)] × √)Q/Pn

∴ Var(p) = [(N – n)/(N – 1)] × PQ/n

Important Points

For SRSWR

p is an unbiased estimator of P

(ii) - Var (p) = PQ/n

Est Var(p) = PQ/(n - 1)

rse(p) = √Var(p)/P = √Q/Pn