Roadblock State police set up a roadblock to estimate the percentage of cars with up-to-date registration, insurance, and safety inspection stickers. It would be too inconvenient and costly to check every vehicle that passes through a checkpoint, so they decide to stop about
of the vehicles. a) Why would a simple random sample be unreasonable for this situation. b) Identify two possible sampling schemes that could be used. Explain how randomization would be used in each.
The Correct Answer and Explanation is:
Why would a simple random sample be unreasonable for this situation?
A simple random sample would be unreasonable for this situation due to practical limitations. At a roadblock, the police cannot afford to stop every vehicle that passes, nor would it be feasible or efficient to select vehicles randomly from the entire population. Here are some reasons:
- Traffic Flow: In a busy checkpoint, the random sampling process could cause delays, leading to interruptions in the traffic flow. It would be logistically challenging to stop cars at random without causing congestion or creating traffic bottlenecks.
- Ethical and Legal Concerns: Randomly stopping cars without any targeted approach could be seen as arbitrary or discriminatory, leading to issues with public perception and legal challenges regarding fairness.
- Time Constraints: Stopping every vehicle randomly would require a lot of time, and the police may only have limited resources to conduct the survey efficiently. This means they wouldn’t be able to sample a large enough number of vehicles to get a reliable estimate in a short amount of time.
b) Identify two possible sampling schemes that could be used. Explain how randomization would be used in each.
- Systematic Sampling:
In systematic sampling, the police could stop every nth vehicle that passes the checkpoint. For example, they might decide to stop every 5th or 10th car. The starting point could be chosen randomly by selecting a vehicle at random from the first few that pass the checkpoint. This method ensures that the sample is spread out across time without overwhelming the police with too many stops.- Randomization: Randomization is used by selecting the starting vehicle randomly. From that point, every nth car would be stopped. This reduces bias, as the sample isn’t systematically skewed toward certain groups of drivers.
- Stratified Sampling:
If the police suspect that the proportion of cars with up-to-date registration, insurance, and inspection stickers varies by factors such as the type of vehicle (e.g., commercial vs. private) or time of day (e.g., morning vs. evening rush hour), they could divide vehicles into strata based on these factors. They could then sample a specific number of cars from each group. For example, they might stop a certain number of cars in the morning and evening, or a set proportion from each type of vehicle.- Randomization: Within each stratum (e.g., commercial vs. private vehicles), random sampling could be used to select which vehicles to stop. This ensures that each subgroup of vehicles is represented fairly, providing a more accurate estimate of the overall population.
Both methods help in reducing bias and ensuring a more representative sample while considering the constraints of a roadblock situation.
