Stratified Sampling

Question

A certain population is divided into 5 strata so that N1=2000, N2=2000, N3=1800, N4=1700, N5=2500. Respective Standard Deviations are 1.6, 2.0, 4.4, 4.8 and 6.0 and further expected sampling cost in the first two strata is $4 per interview and in the remaining three is $6 per interview. How should a sample of size 226 be allocated to the five strata if we adopt proportionate sampling design.

Answer 1

Steve

As the sampling is proportionate sample the same proportion within each stata

N1 + N2 + N3 + N4 + N5 = 10000

You sample 226 out of these

So that is a proportion of 226 / 10000.

So in 1st strata, sample (226 / 10000) x 2000 = 45.2

In 2nd strata, sample (226 / 10000) x 2000 = 45.2

3rd strata sample 40.68 (same method)

4th sample 38.42

5th sample 56.5

Obviously the sample numbers have to be integers so round these to nearest integer

45, 45, 41, 38, 57, adding these gives 226.

Mike