Question

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

a population of 1,200 and a sample of 600
a population of 1,200 and a sample of 600

a population of 2,000 and a sample of 100
a population of 2,000 and a sample of 100

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
a sample of 40 to represent the number of people on a bus

Answer 1

The 10% condition is a rule of thumb used in statistics that states that when sampling without replacement, the sample size should be no more than 10% of the population size in order for the sampling distribution to be approximately normal.

Let's evaluate the scenarios:

1. **A population of 1,200 and a sample of 600**:
- Sample size (600) is 50% of the population size (1,200).
- **Does not satisfy the 10% condition.**

2. **A population of 2,000 and a sample of 100**:
- Sample size (100) is 5% of the population size (2,000).
- **Satisfies the 10% condition.**

3. **A sample of 10 to represent the number of students in a classroom**:
- Without specific information about the population size, we can't determine the 10% condition.
- **Cannot assess.**

4. **A sample of 40 to represent the number of people on a bus**:
- Similarly, we need the population size to determine if the 10% condition applies.
- **Cannot assess.**

Based on the evaluations, only scenario 2 (the population of 2,000 and a sample of 100) satisfies the 10% condition.