In simple random sampling, it is also true that each member of the population is equally likely to be selected, the chance for each member being equal to the sample size divided by the population size. Show that this fact is also true for stratified random sampling with proportional allocation.

The statement given in the question is "In simple random sampling, it is also true that each member of the population is equally likely to be selected, the chance for each member being equal to the sample size divided by the population size."

We have to show that this fact is also true for stratified random sampling with proportional allocation.

From the concept of stratified sampling, we know that In stratified sampling, the population is divided into strata or subpopulations, and then samples are taken from each stratum.

We also know that each stratum's members should ideally be homogeneous in terms of the attribute under examination.

The strata are frequently sampled in proportion to their size in stratified sampling, which is known as proportionate allocation.

The approach below shows how to build stratified (random) sampling with proportional allocation step by step.

Proportional Allocation using Stratified Random Sampling:

Step 1: Subdivide the population into groups (strata).

Step 2 Take a basic random sample proportional to the size of each stratum, that is, the stratum sample size equals the overall sample size times the stratum size divided by the population size.

Step 3: As a sample, use all of the members from Step 2.