Which of the following best describes the difference between a stratified sample and a cluster sample?

• A. In a stratified sample, the population is divided into clusters and all clusters are sampled; in a cluster sample, only one stratum is chosen and sampled.
• B. In a stratified sample, the population is divided into subgroups ($\mathrm{strata}$) based on a characteristic, and random samples are taken from each $\mathrm{stratum}$; in a cluster sample, the population is divided into clusters, some clusters are randomly selected, and all members of chosen clusters are included.
• C. Both stratified and cluster samples involve dividing the population into groups and randomly selecting individuals from each group.
• D. A stratified sample involves randomly selecting entire clusters, while a cluster sample involves randomly selecting individuals from each stratum.

Answer: (B)

Verified step by step guidance

1. Understand that both stratified sampling and cluster sampling involve dividing the population into groups, but the way these groups are used differs.
2. In stratified sampling, the population is divided into subgroups called strata based on a specific characteristic (e.g., age, income level). Then, a random sample is taken from each stratum to ensure representation across all subgroups.
3. In cluster sampling, the population is divided into clusters, which are often naturally occurring groups (e.g., schools, neighborhoods). Instead of sampling from every cluster, a random selection of entire clusters is made, and all members within those selected clusters are included in the sample.
4. Recognize that stratified sampling aims to improve precision by ensuring all strata are represented, while cluster sampling is often used for practical convenience and cost reduction by sampling entire groups.
5. Compare the definitions carefully to identify that the correct description is: stratified sampling involves sampling from every stratum, whereas cluster sampling involves selecting some clusters and including all members from those clusters.