(Solved): b) A stratified population has five strata. The stratum size \\( N_{h} \\) and mean and variance \\ ...

b) A stratified population has five strata. The stratum size \\( N_{h} \\) and mean and variance \\( \\bar{y}_{h} \\) and \\( S^{2} h \\) of variables are as followse Calculate the overall population mean and variance \\( \\bar{y} \\) ansd \\( \\mathrm{S}^{2} \\). For stratified SRS of size about 80, determine the appropriate stratum sample sizes under proportional allocation and Nyman's allocation. Workout (for the same total size of sample) the efficiency of SRS mean \\( y \\) as an estimate of \\( \\bar{Y} \\), relative the stratified sample means for the two methods of allocation.