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

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Statistics

In stratified sampling, there are two methods of sample sizeallocation to the strata: optimal allocation andproportional-to-size allocation. Suppose interest lies inestimating the mean of the population using Å­strat(y). Let Voptshow the variance of Å­strat(y) under optional allocation and Vpropshow the variance of Å­strat(y) under proportional-to-sizeallocation.

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

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

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