To determine the mean number of children per household in a community, Tabitha surveyed 20 families at a playground. For...

1. TRANSLATE the problem setup

• Given information:
  • Tabitha wants to find the mean number of children per household in a community
  • She surveyed 20 families at a playground
  • The sample mean was 2.4 children per household
• The question asks what statement must be true about this situation

2. INFER the key statistical issue

• The critical question isn't about the sample size (20 families) or the calculated mean (2.4)
• The real issue is: Where did Tabitha collect her sample?
• Families at a playground are not representative of all households in a community

3. INFER why the sampling location creates bias

• Think about who you'd find at a playground:
  • Families with children are much more likely to be there
  • Households without children (young couples, empty nesters, single adults) are systematically excluded
• This creates sampling bias - certain groups are over/under-represented

4. INFER the impact on results

• Since families with children are overrepresented, the sample mean of 2.4 likely overestimates the true community mean
• You cannot reliably generalize from this biased sample to the entire community

5. Evaluate the answer choices

• Choice A: Wrong - biased sample can't estimate population parameter
• Choice B: Wrong - sample size isn't the main problem
• Choice C: Correct - sampling method is flawed and creates bias
• Choice D: Wrong - the method is definitely flawed

Answer: C

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak INFER reasoning about sampling bias: Students focus on the numbers (sample size 20, mean 2.4) rather than critically evaluating the sampling method. They don't recognize that surveying at a playground systematically excludes households without children.

This leads them to select Choice A (The mean number of children per household in the community is 2.4) because they assume the sample mean equals the population mean.

Second Most Common Error:

Misunderstanding statistical validity: Students recognize something might be wrong but focus on sample size rather than sampling bias. They think "20 families seems small" without considering the more fundamental issue of representativeness.

This may lead them to select Choice B (determination should not be made because sample size is too small).

The Bottom Line:

This problem tests whether students understand that where you sample is just as important as how many you sample. A large sample from a biased location is still biased, while a smaller representative sample can be more reliable.