Final answer:
Clustered random sampling is effective for studying large populations dispersed over a wide area by randomly selecting groups, or clusters, for sampling rather than individuals, making it cost-effective and simplifying data collection.
Step-by-step explanation:
The primary rationales for employing a clustered random sampling design are twofold. First, it is cost-effective and efficient, especially when dealing with a large population dispersed over a wide area. Second, it simplifies the process by selecting groups (clusters) rather than individuals, which can be less time-consuming and easier to manage. In a clustered random sampling design, the population is divided into clusters based on certain characteristics, and then entire clusters are randomly selected to participate in the survey or study. One should aim for the chosen clusters to be as representative as possible of the entire population to ensure accurate inferences about the population parameters.
For example, in an educational study, if a researcher wants to understand the average reading skill level of middle school students in a large school district, rather than testing every student, they might randomly select a few schools (clusters) and test all students within those selected schools.