Final answer:
Cluster sampling involves dividing the population into clusters and randomly selecting some to make up the sample. To sample 36 ETS exam scorers, divide them into clusters, randomly select enough clusters to reach the desired sample size, and select individuals within those clusters if necessary.
Step-by-step explanation:
To select a cluster sample of 36 people hired by ETS to score the Statistics Exams, one must understand that cluster sampling involves dividing the population into clusters and then randomly selecting some of these clusters to be included in the sample. In this case, the clusters might be based on characteristics such as location, recruitment period, or scoring department. Here's how to select the cluster sample:
- Divide all people hired to score exams into clusters. For example, if they are hired from different sessions or locations, each session or location can be seen as a distinct cluster.
- Number each cluster accordingly.
- Use a random number generator to select cluster numbers. For instance, if there are nine clusters, use the random number generator to select four clusters out of the nine.
- If the size of the selected clusters is larger than the desired sample size, consider selecting individuals randomly within the clusters until the sample size of 36 is reached.
This approach ensures that the sample is representative of the population since each cluster is likely to contain a diverse representation of participants, and each member of the population has an equal chance of being included in the sample, within the confines of the selected clusters. The choice of clusters over other sampling methods may be justified by factors such as logistical convenience, cost-effectiveness, or the structure of the population being studied.