A sample consisting of 720 adults who own televisions was selected at random for a study. Based on the sample,

Question

A sample consisting of 720 adults who own televisions was selected at random for a study. Based on the sample, it is estimated that 32 % of all adults who own televisions use their televisions to watch nature shows, with an associated margin of error of 3.41 % . Which of the following is the most plausible conclusion about all adults who own televisions?

Accepted Answer

Choice B is correct. It's given that based on a sample selected at random, it's estimated that 32 % of all adults who own televisions use their televisions to watch nature shows, with an associated margin of error of 3.41 % . Subtracting the margin of error from the estimate and adding the margin of error to the estimate gives an interval of plausible values for the true percentage of adults who own televisions who use their televisions to watch nature shows. This means it's plausible that between 32 % - 3.41 % , or 28.59 % , and 32 % + 3.41 % , or 35.41 % , of all adults who own televisions use their televisions to watch nature shows. Therefore, of the given choices, the most plausible conclusion is that between 28.59 % and 35.41 % of all adults who own televisions use their televisions to watch nature shows. Choice A is incorrect and may result from conceptual errors. Choice C is incorrect. To make a plausible conclusion about all adults who own televisions, the sample must be selected at random from all adults who own televisions, not just those who use their televisions to watch nature shows. Choice D is incorrect. Since the sample was selected at random from all adults who own televisions, a plausible conclusion can be made about all adults who own televisions.

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