Final answer:
In attributes sampling, the population size has little to no effect on the sample size once the population exceeds approximately 5,000. This is because a sufficiently large sample will capture the population's characteristics due to the law of large numbers.
Step-by-step explanation:
In attributes sampling, the sample size is not significantly affected by the population size once the population exceeds a certain number. The correct answer to the student's question is '5,000'. This threshold is informed by statistical theory suggesting that when populations are large enough, additional size contributes little to the sampling error. Random samples are designed to represent the population as a whole, reflecting a suitable level of accuracy and reliability.
The rationale behind the lack of impact from larger populations is that beyond a certain point, the law of large numbers ensures that the sample is sufficiently representative of the entire population. As the population grows, the proportional impact of each individual observation decreases. Therefore, the sample size needed to approximate the population with a certain level of confidence becomes stable. This stability occurs regardless of whether the population is slightly larger than 5,000 or much larger, as each additional individual's impact becomes negligible.