In stratified sampling, there are two methods of sample size allocation to the strata: optimal allocation...

In stratified sampling, there are two methods of sample size allocation to the strata: optimal allocation and proportional-to-size allocation. Suppose interest lies in estimating the mean of the population using ŭstrat(y). Let Vopt show the variance of ŭstrat(y) under optional allocation and Vprop show the variance of ŭstrat(y) under proportional-to-size allocation.

(a) [4 marks] Show, with detailed steps, that Vopt <= Vprop.

(b) [2 marks] under what conditions Vopt = Vprop? provide a proof for your answer.

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orchestra answered 11 months ago

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