Question

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?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 1

D) It is plausible that the percentage of students who see a movie at least once per month is between 19% and 27%.

Explanation:

We are told that the researcher estimated that 23% of the students in the population saw a movie at least once per month.

Thus it is the sample statistic.

We are also told that margin of error for this estimation is 4%.

If we apply this margin of error to the sample statistic, we will get an interval range for the population statistic.

Thus, the interval will be;

23% ± 4%,

This gives us an interval of between 19% and 27%.

Therefore, we can conclude that it is probable/plausible that the percentage of students in the population who see a movie at least once a month is between 19% and 27%

So option D is correct