To determine the mean number of children per household in a community, Tabitha surveyed 20 families at a playground. For the 20 families surveyed, the mean number of children per household was 2.4. Which of the following statements must be true?

Options

A. The mean number of children per household in the community is 2.4.
B. A determination about the mean number of children per household in the community should not be made because the sample size is too small
C. The sampling method is flawed and may produce a biased estimate of the mean number of children per household in the community.
D. The sampling method is not flawed and is likely to produce an unbiased estimate of the mean number of children per household in the community.

Explanation

To solve the problem, we need to analyze the information given and evaluate the statements based on the survey conducted by Tabitha.

### Step-by-Step Solution:

1. **Understanding the Survey**:
- Tabitha surveyed 20 families at a playground.
- The mean number of children per household for these families is 2.4.

2. **Evaluating the Sampling Method**:
- The families surveyed were specifically chosen from a playground, which may not represent the entire community.
- Families at a playground may have different characteristics compared to families in other areas of the community (e.g., they might have more children because they are at a playground).

3. **Assessing the Statements**:
- **Statement 1**: "The mean number of children per household in the community is 2.4."
- This statement cannot be assumed to be true because the sample may not represent the entire community.

- **Statement 2**: "A determination about the mean number of children per household in the community should not be made because the sample size is too small."
- While the sample size of 20 families is relatively small, the main issue is the biased sampling method rather than the size itself. Therefore, this statement is also not necessarily true.

- **Statement 3**: "The sampling method is flawed and may produce a biased estimate of the number of children per household in the community."
- This statement is true. The method of surveying families at a playground is likely to produce a biased estimate because it does not represent the entire community.

- **Statement 4**: "The sampling method is unbiased and likely to produce an unbiased estimate."
- This statement is false. As discussed, the sampling method is biased due to the location of the survey.

4. **Conclusion**:
- The only statement that must be true based on the information provided is Statement 3: "The sampling method is flawed and may produce a biased estimate of the number of children per household in the community."

### Final Answer:
The correct statement that must be true is: **The sampling method is flawed and may produce a biased estimate of the number of children per household in the community.**

---