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?

Options

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%.

Answer

D

Explanation

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%.
Choice A is incorrect and may result from interpreting the estimate of 23% as the minimum number of students in the population who see a movie at least once per month. Choice B is incorrect and may result from interpreting the estimate of 23% as the minimum number of students in the population who see a movie at least once per month and adding half of the margin of error to conclude that it isn’t possible that more than 25% of students in the population see a movie at least once per month. Choice C is incorrect and may result from interpreting the sample statistic as the researcher’s level of confidence in the survey results and applying the margin of error to the level of confidence.