Question #e03f3477 - SAT Suite Question Bank

Modded SAT Question Bank by Abdullah Mallik

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

More than $35.41 percent sign$ of all adults who own televisions use their televisions to watch nature shows.
Between $28.59 percent sign$ and $35.41 percent sign$ of all adults who own televisions use their televisions to watch nature shows.
Since the sample included adults who own televisions and not just those who use their televisions to watch nature shows, no conclusion can be made.
Since the sample did not include all the people who watch nature shows, no conclusion can be made.

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Correct Answer: B

Rationale

Choice B is correct. It's given that based on a sample selected at random, it's estimated that $32 percent sign$ of all adults who own televisions use their televisions to watch nature shows, with an associated margin of error of $3.41 percent sign$ . 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 $32 percent sign minus 3.41 percent sign$ , or $28.59 percent sign$ , and $32 percent sign plus 3.41 percent sign$ , or $35.41 percent sign$ , 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 $28.59 percent sign$ and $35.41 percent sign$ 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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