Question
For which of the following scenarios does the 10% condition apply?(1 point)
Responses
a population of 2,000 and a sample of 100
a population of 2,000 and a sample of 100
a population of 1,200 and a sample of 600
a population of 1,200 and a sample of 600
a sample of 10 to represent the number of students in a classroom
a sample of 10 to represent the number of students in a classroom
a sample of 40 to represent the number of people on a bus
Responses
a population of 2,000 and a sample of 100
a population of 2,000 and a sample of 100
a population of 1,200 and a sample of 600
a population of 1,200 and a sample of 600
a sample of 10 to represent the number of students in a classroom
a sample of 10 to represent the number of students in a classroom
a sample of 40 to represent the number of people on a bus
Answers
GPT-4o mini
The 10% condition states that the sample size should be less than 10% of the population size to ensure independence in sampling (i.e., the samples are not overly dependent on one another).
Let's evaluate each scenario:
1. **A population of 2,000 and a sample of 100**:
- Sample size = 100
- 10% of the population = 200
- Since 100 is less than 200, this scenario meets the 10% condition.
2. **A population of 1,200 and a sample of 600**:
- Sample size = 600
- 10% of the population = 120
- Since 600 is greater than 120, this scenario does not meet the 10% condition.
3. **A sample of 10 to represent the number of students in a classroom**:
- In this case, we need to know the total number of students in the classroom. Assuming typical classroom sizes, a sample of 10 is unlikely to be more than 10% of a reasonable classroom population, but without a specific population size, we cannot conclude its adequacy.
4. **A sample of 40 to represent the number of people on a bus**:
- Similarly, this scenario requires knowing the population size (i.e., how many people fit on a bus). For most buses, capacity is usually much higher than 40, thus assuming it is more than 400, we can infer that this situation possibly does meet the condition.
**Conclusion**: The first scenario (population of 2,000 and a sample of 100) is the clear scenario that fulfills the 10% condition. The other scenarios lack sufficient context or do not meet the criteria.
Let's evaluate each scenario:
1. **A population of 2,000 and a sample of 100**:
- Sample size = 100
- 10% of the population = 200
- Since 100 is less than 200, this scenario meets the 10% condition.
2. **A population of 1,200 and a sample of 600**:
- Sample size = 600
- 10% of the population = 120
- Since 600 is greater than 120, this scenario does not meet the 10% condition.
3. **A sample of 10 to represent the number of students in a classroom**:
- In this case, we need to know the total number of students in the classroom. Assuming typical classroom sizes, a sample of 10 is unlikely to be more than 10% of a reasonable classroom population, but without a specific population size, we cannot conclude its adequacy.
4. **A sample of 40 to represent the number of people on a bus**:
- Similarly, this scenario requires knowing the population size (i.e., how many people fit on a bus). For most buses, capacity is usually much higher than 40, thus assuming it is more than 400, we can infer that this situation possibly does meet the condition.
**Conclusion**: The first scenario (population of 2,000 and a sample of 100) is the clear scenario that fulfills the 10% condition. The other scenarios lack sufficient context or do not meet the criteria.