Question the-me
The members of a city council wanted to assess the opinions of all city residents about converting an open field into a dog park. The council surveyed a sample of 500 city residents who own dogs. The survey showed that the majority of those sampled were in favor of the dog park. Which of the following is true about the city council’s survey?
It shows that the majority of city residents are in favor of the dog park.
The survey sample should have included more residents who are dog owners.
The survey sample should have consisted entirely of residents who do not own dogs.
The survey sample is biased because it is not representative of all city residents.
The members of a city council wanted to assess the opinions of all city residents about
Easy-difficulty · SAT Math · Evaluating Statistical Claims — Recognizing bias. Read the question above, select your answer, and check the full explanation below to understand exactly why the correct choice works.
Answer explanation
Choice D is correct. The members of the city council wanted to assess opinions of all city residents. To gather an unbiased sample, the council should have used a random sampling design to select subjects from all city residents. The given survey introduced a sampling bias because the 500 city residents surveyed were all dog owners. This sample is not representative of all city residents because not all city residents are dog owners.
Choice A is incorrect because when the sampling method isn’t random, there is no guarantee that the survey results will be reliable; hence, they cannot be generalized to the entire population. Choice B is incorrect because a larger sample of residents who are dog owners would not correct the sampling bias. Choice C is incorrect because a survey sample of entirely non–dog owners would likely have a biased opinion, just as a sample of dog owners would likely have a biased opinion.
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