Question

For which of the following scenarios does the 10% condition apply?(1 point)
Responses

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 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 40 to represent the number of people on a bus

Answer 1

The 10% condition is a guideline used in statistics to ensure that the sample size is small relative to the population, which helps to ensure that the sample can be treated as representative of the population without introducing bias due to sampling.

The 10% condition states that your sample size (n) should be less than or equal to 10% of the population size (N) for the sampling method to be valid.

Let's evaluate each scenario:

1. **A population of 2,000 and a sample of 100**:
Sample size (100) is 5% of the population (2,000), which is less than 10%.
**Condition met.**

2. **A population of 1,200 and a sample of 600**:
Sample size (600) is 50% of the population (1,200), which is greater than 10%.
**Condition not met.**

3. **A sample of 40 to represent the number of people on a bus**:
This scenario doesn't provide a population size to evaluate against. Without the population size, we can't apply the 10% condition.
**Condition can't be determined.**

4. **A sample of 10 to represent the number of students in a classroom**:
Similar to the sample of 40, we don't have information on the population size, so we can't determine the condition.
**Condition can't be determined.**

Based on this evaluation, the only scenario where the 10% condition clearly applies is:

- **A population of 2,000 and a sample of 100.**