Town Counsel Survey: Choosing a Random Sample of 30 Residents
Town counsel is conducting a survey of the town residents. Which method would be a valid way to choose a random sample of 30 residents?
A) Writing names on papers and drawing 30 randomly.
B) Surveying the first 30 houses on a random street.
C) Seeking 30 volunteers at a town council meeting.
D) Selecting the first 30 residents arriving at a council meeting.
Final answer:
The correct method for choosing a random sample of 30 residents is A) writing names on papers and drawing 30 randomly. This method ensures each resident has an equal chance of being included in the sample, fulfilling the requirement for randomness in sample selection.
Explanation:
The valid way to choose a random sample of 30 residents for a town council survey is by writing names on papers and drawing 30 randomly. This method ensures that each resident has an equal chance of being selected, which is a key principle in obtaining a random sample. Options B, C, and D involve non-random selection methods that could introduce bias and are not truly random because not all residents have an equal chance of being chosen.
Examples of Sampling Methods:
- A systematic sampling method is applied when you select the first house randomly and then every eighth house in the neighborhood, similar to the study in San Jose.
- Convenience sampling is when a woman in the airport only asks certain travelers to evaluate the airport's service.
- Cluster sampling is used when a teacher selects entire rows of students to assess homework completion.
- Random selection is when a researcher uses a computer to generate random numbers, and people corresponding to these numbers are chosen.