The statement being evaluated is whether carefully choosing a sample of 500 people can lead to a good estimate of the average height of Americans. Let's break this down:

• Option A: This is incorrect. While 500 people could be a reasonable sample size for estimating something about a population as large as the American population, carefully choosing the sample will not necessarily eliminate bias. Instead, random sampling is more effective for eliminating bias.

• Option B: This is incorrect. Carefully choosing the sample may actually introduce bias rather than help. A sample that "closely resembles the population" is more likely to be achieved through random selection rather than careful selection, which can introduce subjectivity.

• Option C: This is correct. For the sample to resemble the population, it must be chosen randomly, not carefully. Random sampling reduces bias and increases the likelihood that the sample represents the population.

• Option D: This is incorrect because 500 people, depending on how they are selected, can be a sufficient sample size for making a good estimate, even for a large population. The key issue is not the sample size alone, but also how the sample is chosen.

Thus, C is the correct answer.

Would you like more details or have any questions about this? Here are 5 related questions for further exploration:

1. Why is random sampling typically preferred over selective sampling for estimating population parameters?
2. How does increasing the sample size affect the accuracy of population estimates?
3. What is the role of bias in statistical sampling, and how can it be minimized?
4. How can a researcher determine an appropriate sample size for a given population?
5. What are some common methods for ensuring randomness in selecting a sample?

Tip: A common misconception in statistics is that increasing the sample size alone guarantees an unbiased estimate. It's equally important that the sample is randomly chosen to avoid biases.