The households in a town arc to be sampled in order to estim

The households in a town arc to be sampled in order to estimate the average amount of assets per household that are readily convertible into cash. The households are stratified into high-rent and a low-rent stratum. A house in the high-rent stratum is thought to have about nine times as much assets as one in the low-rent stratum. and Sh is expected to be proportional to the square root of the stratum mean. There are 4000 households in the high-rent stratum and 20,000 in the low-rent. How would you distribute a sample of 1000 households between the two strata? If the object is to estimate the difference between assets per household in the two strata. how should the sample be distributed?

Solution

We need to use disproportionate stratified sampling as the mean or the average of the strata is proportional to the square root of stratum mean.

Thus, if lower stratum mean = x,

upper stratum mean = 9x

Taking square roots, the ratio would be 3 : 1

Hence sampling has to be in ratio,3 :1

Hence, 750 from upper mean stratum and 250 from the lower mean stratum

To check the difference between the two groups, we would sample in the equal ratio proportion

Thus, 500 samples from each strata

Hope this helps