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into two subpopulations 1 and 2, such that a proportion p of the full population is in1 Let fi X…

 into two subpopulations 1 and 2, such that a proportion p of the full population is in1 Let fi X denote the conditional population distribution of X on i  into two subpopulations 1 and 2, such that a proportion p of the full population is in1 Let fi X...

Suppose that it makes sense to assume i.i.d. sampling whenever we take a sample from either the full population or either of the subpopulations, i.e., whenever the sample sizes we are considering are small relative to the sizes of these populations. We implement stratified sampling by taking a simple random sample of size ni from sub into two subpopulations 1 and 2, such that a proportion p of the full population is in1 Let fi X...

into two subpopulations 1 and 2, such that a proportion p of the full population is in1 Let fi X...

when X is based on a simple random sample of size n from the full population and into two subpopulations 1 and 2, such that a proportion p of the full population is in1 Let fi X... s is called proportional stratified sampling. (f) Under what conditions is there no benefit to proportional stratified sampling? What do you conclude about situations in which stratified sampling will be most beneficial?