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  1. Which of the following is NOT a characteristic of stratified random sampling?

(A) Random sampling is part of the sampling procedure.

(B) The population is divided into groups of units that are similar on some characteristic.

(C) The strata are based on facts known before the sample is selected.

(D) Each individual unit in the population belongs to one and only one of the strata.

(E) Every possible subset of the population, of the desired sample size, has an equal chance of being selected.

The correct answer is (e), but why (e)? isn't every subset of the population has an equal chance of being selected. the idea of stratified sampling?

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Stratified sampling allocates a part of the sample to each stratum. So, for example, subsets where you allocate the whole sample to one stratum has probability zero of being selected. – Stefan Hansen Oct 21 '12 at 14:56

The correct answer is $E$.

For stratified random sampling, we get to choose the sample size for each stratum. By picking larger/smaller numbers for one group, we're changing their probability of being selected without changing anyone else's. That means that (unless by coincidence) the chance of different samples being selected is not the same.

It seems like you're thinking of 'simple random sampling'. That has the property of independence, which means that every possible subset of the sample size has the same chance of occurring. While simple random sampling is used in stratified random sampling, the extra leeway in picking the sample sizes for each strata changes the independence property, and means choice $E$ is not true.

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