Question

give an example of how you would create a sample from the population of the united states using cluster sampling and stratified sampling. then, compare and contrast these two methods.

Explanation:

Cluster Sampling Example: Divide the US states (geographical clusters). Randomly select a few states (e.g., California, New York, Texas). Then sample all residents within those selected states. This is useful when it's difficult to access the whole population directly.
Stratified Sampling Example: Divide the US population by age groups (strata: 0 - 18, 19 - 30, 31 - 50, 51+). Determine the proportion of each age - group in the population. Then sample from each age - group in those proportions. This ensures representation from each subgroup.
Comparison: In cluster sampling, the clusters are heterogeneous internally but represent the whole population. In stratified sampling, the strata are homogeneous internally (e.g., by age), and sampling is done proportionally from each stratum to ensure all subgroups are represented. Cluster sampling is often more cost - effective for large populations, while stratified sampling provides more precise estimates when the strata are well - defined.

Answer:

Cluster Sampling: Divide US into state clusters, randomly pick some states and sample all residents in them. Stratified Sampling: Divide US population by age groups, sample proportionally from each age group. Comparison: Cluster sampling uses heterogeneous clusters, stratified sampling uses homogeneous strata for more precise representation.