Residents of a town were surveyed to determine whether they are satisfied with the concession stand at the local park.

Question

Residents of a town were surveyed to determine whether they are satisfied with the concession stand at the local park. A random sample of 200 residents was selected. All 200 responded, and 87% said they are satisfied. Based on this information, which of the following statements must be true?

I. Of all the town residents, 87% would say they are satisfied with the concession stand at the local park.
II. If another random sample of 200 residents were surveyed, 87% would say they are satisfied.

Accepted Answer

Choice A is correct. The purpose of surveying a random sample of residents is to approximate the percent of the town residents that are satisfied with the concession stand. The sample doesn&rsquo;t necessarily get the same result as surveying every resident of the town, nor would another sample necessarily have identical results. Therefore, although it&rsquo;s possible that either statement we or statement Iwe could prove true by surveying every resident of the town, these statements cannot be proven true solely based on the results of the sample. Choice B is incorrect because surveying a sample of the town residents may not have the same result as surveying all the town residents. Choices C and D are incorrect because surveying a different sample of residents could yield different results.

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