Question
The Hamden board of education wants to know how the community feels about building a new media center for the middle school. They called every tenth person on the registration list of 7,300 voters until they had called a total of 40 voters. Which of the following are true of the sample of 40 voters? Check all that apply.
The sample is not randomly chosen.
The sample should be larger to give more reliable information.
The sample size is too large to make inferences.
The sample size is too small to represent the population.
The sample size is too small and will show larger variation.
The sample is invalid because it randomly chooses voters.
The sample size is too small and can lead to false inferences.
The sample is not randomly chosen.
The sample should be larger to give more reliable information.
The sample size is too large to make inferences.
The sample size is too small to represent the population.
The sample size is too small and will show larger variation.
The sample is invalid because it randomly chooses voters.
The sample size is too small and can lead to false inferences.
Answers
GPT-4o mini
Let's analyze the statements regarding the sample of 40 voters:
1. **The sample is not randomly chosen.**
- **True:** The method of selecting every tenth person from a registration list is systematic sampling, which is a type of non-random sampling.
2. **The sample should be larger to give more reliable information.**
- **True:** Generally, a larger sample size can lead to more reliable information and better representation of the population.
3. **The sample size is too large to make inferences.**
- **False:** A sample size of 40 is typically considered small, not large.
4. **The sample size is too small to represent the population.**
- **True:** While 40 voters can provide some insights, it may not be representative enough of the entire population of 7,300 voters.
5. **The sample size is too small and will show larger variation.**
- **True:** Smaller samples tend to show greater variability and less stability in their estimates.
6. **The sample is invalid because it randomly chooses voters.**
- **False:** The sample is not randomly chosen; it utilizes a systematic approach, as described.
7. **The sample size is too small and can lead to false inferences.**
- **True:** A smaller sample size can indeed lead to drawing incorrect conclusions about the larger population.
### Summary:
- The true statements are:
- "The sample is not randomly chosen."
- "The sample should be larger to give more reliable information."
- "The sample size is too small to represent the population."
- "The sample size is too small and will show larger variation."
- "The sample size is too small and can lead to false inferences."
1. **The sample is not randomly chosen.**
- **True:** The method of selecting every tenth person from a registration list is systematic sampling, which is a type of non-random sampling.
2. **The sample should be larger to give more reliable information.**
- **True:** Generally, a larger sample size can lead to more reliable information and better representation of the population.
3. **The sample size is too large to make inferences.**
- **False:** A sample size of 40 is typically considered small, not large.
4. **The sample size is too small to represent the population.**
- **True:** While 40 voters can provide some insights, it may not be representative enough of the entire population of 7,300 voters.
5. **The sample size is too small and will show larger variation.**
- **True:** Smaller samples tend to show greater variability and less stability in their estimates.
6. **The sample is invalid because it randomly chooses voters.**
- **False:** The sample is not randomly chosen; it utilizes a systematic approach, as described.
7. **The sample size is too small and can lead to false inferences.**
- **True:** A smaller sample size can indeed lead to drawing incorrect conclusions about the larger population.
### Summary:
- The true statements are:
- "The sample is not randomly chosen."
- "The sample should be larger to give more reliable information."
- "The sample size is too small to represent the population."
- "The sample size is too small and will show larger variation."
- "The sample size is too small and can lead to false inferences."