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Problem-Solving and Data Analysis / Evaluating statistical claims: Observational studies and experiments Difficulty: Hard

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?

The mean number of children per household in the community is 2.4.

A determination about the mean number of children per household in the community should not be made because the sample size is too small.

The sampling method is flawed and may produce a biased estimate of the mean number of children per household in the community.

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.

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Explanation

Choice C is correct. In order to use a sample mean to estimate the mean for a population, the sample must be representative of the population (for example, a simple random sample). In this case, Tabitha surveyed 20 families in a playground. Families in the playground are more likely to have children than other households in the community. Therefore, the sample isn’t representative of the population. Hence, the sampling method is flawed and may produce a biased estimate.

Choices A and D are incorrect because they incorrectly assume the sampling method is unbiased. Choice B is incorrect because a sample of size 20 could be large enough to make an estimate if the sample had been representative of all the families in the community.