A researcher surveyed a random sample of students from a large university about how often they see movies. Using the sample data, the researcher estimated that 23% of the students in the population saw a movie at least once per month. The margin of error for this estimation is 4%. Which of the following is the most appropriate conclusion about all students at the university, based on the given estimate and margin of error?
Correct answer: D. It is plausible that the percentage of students who see a movie at least once per month is between 19% and 27%.
- A. It is unlikely that less than 23% of the students see a movie at least once per month.
- B. At least 23%, but no more than 25%, of the students see a movie at least once per month.
- C. The researcher is between 19% and 27% sure that most students see a movie at least once per month.
- D. It is plausible that the percentage of students who see a movie at least once per month is between 19% and 27%.
Explanation
Choice D is correct. The margin of error is used to calculate a confidence interval around the sample statistic, in this case, 23%. With a margin of error of 4%, the interval is 23% ± 4%, or from 19% to 27%. This means it is reasonable, based on the sample, to conclude that the true percentage of students who see a movie at least once per month is likely in this range.Choice A incorrectly suggests that the percentage cannot be below 23%, ignoring the margin of error which explicitly allows for that possibility. Choice B miscalculates the upper bound of the interval, not applying the margin of error correctly. Choice C confuses the percentage estimate with the researcher's level of confidence, which are separate concepts.
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