Stratified random sampling involves partitioning the population into strata that are internally homogeneous on some relevant characteristic, such as gender or region, and then drawing random samples from each stratum. This ensures that each subgroup is adequately represented in the overall sample. It can improve precision of estimates, especially when there are substantial differences between strata. Therefore, the method described in the stem is accurately called stratified random sampling.
Option A:
Cluster sampling selects intact groups or clusters, such as schools or villages, and then includes all or many members of selected clusters. It does not require that clusters be homogeneous internally on a characteristic used for stratification, so it differs from the technique in the stem.
Option B:
Systematic sampling chooses every kth element from an ordered list after a random start and does not involve dividing the population into homogeneous subgroups first. Thus, systematic sampling is not the correct completion.
Option C:
Convenience sampling selects cases that are easiest to access without randomisation or prior formation of strata, typically producing a non-probability sample. It does not guarantee representation of all subgroups, so convenience sampling is not suitable here.
Option D:
Stratified random sampling can use proportional or disproportionate allocation depending on research needs, but in all cases it explicitly draws random samples within each stratum. This defining feature corresponds perfectly to the description in the question.
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