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?
A) It shows that the majority of city residents are in
favor of the dog park.
B) The survey sample should have included more
residents who are dog owners.
C) The survey sample should have consisted
entirely of residents who do not own dogs.
D) The survey sample is biased because it is not
representative of all city residents.

A sample is an outcome of a random experiment. When we sample a random variable, we obtain one specific value out of the set of its possible values. That particular value is called a sample.

So, from the given information:

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.

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 size would not correct the sampling bias. Choice C is incorrect because a survey sample of non–dog owners would likely have a biased opinion, just as a sample of dog owners would likely have a biased opinion.

So, The correct statement is The survey sample is biased because it is not representative of all city residents.Thus, correct option is D.

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