Question

1. in a city, a list was obtained from each of the 5 neighborhoods in town, and five people were randomly chosen from each neighborhood to be interviewed by the city mayor.

cluster random sample ✓✗

Explanation:

To determine the correct sampling method, we analyze the two main types of cluster and stratified sampling (and also consider simple random or systematic, but here it's about cluster vs others):

Step 1: Recall Cluster vs Stratified Sampling

• Cluster Sampling: Entire clusters (groups) are randomly selected, and all members of the chosen clusters are included.
• Stratified Sampling: The population is divided into strata (groups with similar characteristics), and a random sample is taken from each stratum.

Step 2: Analyze the Problem

The city has 5 neighborhoods (strata/clusters). The method here is: take a list from each neighborhood (stratum) and randomly choose 5 people from each.

• If it were cluster sampling, we would randomly select a few neighborhoods (clusters) and interview all people in those neighborhoods. But here, we sample from every neighborhood (stratum), not just a few clusters.
• This matches Stratified Random Sampling: The population (city) is divided into strata (neighborhoods), and a random sample (5 people) is taken from each stratum.

Answer:

The correct sampling method is Stratified Random Sample (because the population is divided into strata (neighborhoods), and a random sample is drawn from each stratum, unlike cluster sampling where entire clusters are selected and all members are sampled).