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 United States into geographical clusters (e.g., states). Randomly select a few states (e.g., 5 states). Then, sample all individuals within those selected states.
• Stratified Sampling Example:
• Divide the US population into strata based on a characteristic (e.g., age groups: 18 - 25, 26 - 40, 41 - 60, 61+). From each stratum, randomly select a proportionate number of individuals (e.g., if 20% of the population is in 18 - 25 age group, 20% of the sample is taken from this stratum).
• Comparison:
• Similarity: Both involve dividing the population into groups.
• Difference in Groups: In cluster sampling, clusters are heterogeneous (a state has diverse people), while in stratified sampling, strata are homogeneous (an age - group stratum has people of similar age).
• Sampling from Groups: In cluster sampling, whole clusters are sampled; in stratified sampling, samples are taken from each stratum.

Answer:

• Cluster Sampling Example: Divide the US into state - clusters, randomly select some states, and sample all in those states.
• Stratified Sampling Example: Divide the US population into age - based strata, and sample proportionally from each stratum.
• Comparison: Both divide the population. Clusters are heterogeneous (sampled whole), strata are homogeneous (sampled proportionally from each).