Stratified random sampling involves dividing the population into relatively homogeneous strata based on characteristics such as gender, region or discipline and then drawing random samples from each stratum. This ensures that important subgroups are adequately represented in the final sample. It can increase the precision of estimates, especially when subgroup differences are substantial. Because the stem mentions dividing the population into homogeneous subgroups and sampling from each, it describes stratified random sampling.
Option A:
Stratified random sampling uses random selection within each stratum, preserving probabilistic principles while controlling subgroup representation. This approach leads to a sample that mirrors the composition of the population with respect to chosen stratification variables. These features align exactly with the process outlined in the stem, making stratified random the correct answer.
Option B:
Simple random sampling selects units from the population without any prior subdivision, giving each element an equal chance of being chosen, but it does not guarantee representation of specific subgroups. Since the question specifies dividing the population into subgroups first, simple random is not the best match.
Option C:
Systematic sampling selects every kth element from an ordered list after a random start, without necessarily dividing the population into strata. Although it is a probability method, it does not follow the subgroup-based approach described in the stem. Therefore, systematic is not appropriate here.
Option D:
Cluster sampling divides the population into clusters, often based on natural groupings such as schools or villages, and then selects some clusters, usually sampling all or many elements within chosen clusters. Clusters are not necessarily homogeneous, and the method focuses on groups rather than ensuring representation from all subgroups. Thus, cluster sampling does not fit the description given.
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