Question 41

C) A researcher wants to collect data on a sample of 200 homes in a county. The researcher obtains a sample of 20 homes from each of the 10 townships in the county.

This scenario exemplifies stratified sampling as the researcher divides the population into distinct subgroups, or strata, based on geographical location (the townships), and then selects a proportionate sample from each stratum.

A) A researcher separates the area of a forest into 1,000 small regions. The researcher collects data on all of the trees in each of a sample of 20 small regions.

This option does not demonstrate stratified sampling because the researcher is focusing on specific regions without ensuring that each stratum is represented proportionally. Instead, it resembles cluster sampling where entire clusters are sampled.

B) A researcher samples the population of registered voters in a city by selecting every 100th person on the list of registered voters.

This approach is an example of systematic sampling, rather than stratified sampling. It does not involve dividing the population into strata and sampling from those groups; instead, it simply selects individuals based on a fixed interval.

C) A researcher wants to collect data on a sample of 200 homes in a county. The researcher obtains a sample of 20 homes from each of the 10 townships in the county.

This scenario accurately represents stratified sampling because the researcher systematically selects a specific number of homes from each township, ensuring that all parts of the county are represented in the sample. This method allows for more accurate and generalizable results across the entire population.

D) A researcher uses a computer to obtain a sample of city residents so each resident has an equal chance of being selected.

While this method ensures that every resident has an equal chance of being selected, it does not involve dividing the population into strata. Instead, it reflects simple random sampling, which does not guarantee representation from subgroups within the population.

Conclusion

The correct answer, C, is the only option that accurately illustrates stratified sampling by deliberately dividing the population into strata (townships) and sampling from each one. The other options either reflect different sampling methods or fail to represent the population proportionately, making them unsuitable as examples of stratified sampling.