Systematic sampling involves arranging the population in some order, choosing a random starting point and then selecting every kth element, where k is the sampling interval determined by the ratio of population size to desired sample size. This method is simpler to implement than simple random sampling while still maintaining an element of randomness. Because the stem explicitly mentions selecting every kth element after a random start, it describes systematic sampling.
Option A:
Cluster sampling focuses on selecting entire groups or clusters, such as schools or classes, often for reasons of cost and convenience. It does not rely on selecting every kth element from a list, so it does not match the feature described in the question.
Option B:
Systematic sampling ensures that the sample is spread relatively evenly across the ordered list, which can be advantageous when the list has no hidden periodicity that coincides with the sampling interval. The process of choosing a random start and then every kth case corresponds exactly to the stemβs description, confirming systematic as the correct answer.
Option C:
Quota sampling is a non-probability method in which the researcher fills pre-specified quotas for particular subgroups, often using convenience within each subgroup. It does not involve selecting elements at a fixed interval from a list and does not rely on random starts. Therefore, quota is not an appropriate answer here.
Option D:
Purposive sampling involves deliberately choosing cases judged to be particularly informative rather than following a fixed interval rule. It is commonly used in qualitative research and does not follow the mechanical pattern described in the stem. Hence, purposive sampling is not correct for this question.
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