The mean number of children per household in the community is .
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.
Explanation
Correct answer: C.
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 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.
Why the other choices are wrong
Choice A
Choice A is incorrect because it incorrectly assumes the sampling method is unbiased.
Choice B
Choice B is incorrect because a sample of size could be large enough to make an estimate if the sample had been representative of all the families in the community.
Choice D
Choice D is incorrect because it incorrectly assumes the sampling method is unbiased.