The 10% condition is a guideline used in statistical sampling to ensure that sampling without replacement does not significantly affect the probabilities in a sample. It states that if the sample size is less than 10% of the population size, the sample can be considered to be independent, and the results can be regarded as representative of the population.
Let's evaluate each scenario based on the 10% condition:
A. A sample of 40 to represent the number of people on a bus.
- This scenario does not provide the population size (the number of people on the bus), so we cannot determine if the sample is less than 10% of the population. Therefore, we cannot apply the 10% condition here.
B. A population of 1,200 and a sample of 600.
- Here, the sample size (600) is 50% of the population (1,200). This exceeds the 10% threshold; thus, the 10% condition does not apply.
C. A sample of 10 to represent the number of students in a classroom.
- Again, the population size (the total number of students in the classroom) is not given, so we cannot judge whether the sample is less than 10% of the population. The 10% condition cannot be applied here.
D. A population of 2,000 and a sample of 100.
- Here, the sample size (100) is 5% of the population (2,000), which is less than 10%. Therefore, the 10% condition applies in this scenario.
In summary, the scenario that qualifies under the 10% condition is D.