A cluster sample involves dividing the population into separate groups, or clusters, and then selecting entire clusters randomly as the sample. Each cluster should ideally be representative of the diversity within the overall population.
Let's analyze the answer choices based on this concept:
- Option A: [tex]$1370,1371,1504,1630,1472,6410,9052,8134$[/tex]
- These addresses span across multiple clusters rather than from a single cluster.
- Option B: [tex]$1471,1623,1374,9064,1474,7292,1503,1509$[/tex]
- Similar to Option A, these addresses are from different clusters.
- Option C: [tex]$6417,1477,1628,7296,9063,8133,1374,1509$[/tex]
- These addresses are also from various clusters.
- Option D: [tex]$7281,7284,7285,7288,7289,7292,7293,7296$[/tex]
- These addresses are all within a specific cluster from the section of the grid with numbers starting with 72xx. This matches the criteria for a cluster sample as they are all within a contiguous block and thus represent a single subset of the population.
Given that a cluster sample should include homes from the same cluster, the correct answer is:
D. [tex]$7281,7284,7285,7288,7289,7292,7293,7296$[/tex]
