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 atleast 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 applied to the sample statistic to create an interval in which the population statistic most likely falls. An estimate of 23% with a margin of error of 4% creates an interval of 23% ± 4%, or between 19% and 27%. Thus, it's plausible that the percentage of students in the population who see a movie at least once a month is between 19% and 27%.
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