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.
