Question
The government of a large city needs to determine whether the city's residents will support the repair of several roads. The government decides to conduct a survey of a sample of the city's residents. Which one of the following procedures would be the most appropriate for obtaining a sample of the city's residents?
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Part 1
Survey a random sample of the residents who use public transportation.
Survey every fifth person to enter the local church on Sunday.
Survey the last 100 residents listed in the telephone directory.
Survey a random sample of persons within each geographical region of the city.
Question content area bottom
Part 1
Survey a random sample of the residents who use public transportation.
Survey every fifth person to enter the local church on Sunday.
Survey the last 100 residents listed in the telephone directory.
Survey a random sample of persons within each geographical region of the city.
Answers
GPT-4o mini
The most appropriate procedure for obtaining a sample of the city's residents among the options provided is:
**Survey a random sample of persons within each geographical region of the city.**
This method is likely to yield a more representative sample of the entire city, as it ensures that various geographic areas, which may have differing perspectives and needs regarding road repairs, are included. By stratifying the sample based on geographic regions, the survey can better reflect the diversity of the city's population. Random sampling within these regions helps to reduce selection bias.
In contrast, the other options have limitations:
- **Surveying a random sample of residents who use public transportation** may exclude those who do not use public transportation, leading to an unrepresentative sample.
- **Surveying every fifth person to enter a local church** may also introduce bias by only capturing the opinions of those who attend that particular church, which may not be representative of the overall city's demographics.
- **Surveying the last 100 residents listed in the telephone directory** may miss many residents not listed in the directory or those who do not have a landline, leading to a biased sample.
Thus, the stratified random sample is the best choice for a representative survey of the city's residents.
**Survey a random sample of persons within each geographical region of the city.**
This method is likely to yield a more representative sample of the entire city, as it ensures that various geographic areas, which may have differing perspectives and needs regarding road repairs, are included. By stratifying the sample based on geographic regions, the survey can better reflect the diversity of the city's population. Random sampling within these regions helps to reduce selection bias.
In contrast, the other options have limitations:
- **Surveying a random sample of residents who use public transportation** may exclude those who do not use public transportation, leading to an unrepresentative sample.
- **Surveying every fifth person to enter a local church** may also introduce bias by only capturing the opinions of those who attend that particular church, which may not be representative of the overall city's demographics.
- **Surveying the last 100 residents listed in the telephone directory** may miss many residents not listed in the directory or those who do not have a landline, leading to a biased sample.
Thus, the stratified random sample is the best choice for a representative survey of the city's residents.