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# 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 . Which of the following is the most appropriate conclusion about all students at the university, based on the given estimate and margin of error?

- It is unlikely that less than of the students see a movie at least once per month.
- At least , but no more than , of the students see a movie at least once per month.
At least , but no more than 25%, of the students see a movie at least once per month.
- The researcher is between 19% and 27% sure that most students see a movie at least once per month
- It is plausible that the percentage of students who see a movie at least once per month is between 19% and 27% .

Hint:

- We will first find maximum and minimum percent of the students in the population saw a movie at least once per month using the error margin, and then get the answer.

## The correct answer is: It is plausible that the percentage of students who see a movie at least once per month is between 19% and 27% .

### Explanation:

- We have given 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%.
- We have to find which of the option is the most appropriate conclusion about all students at the university.
- Step 1 of 1:

There was a 4% error estimation error. But it didn’t specify whether it was caused by over estimation or under estimation.

So, the researcher is between (23 - 24) % and (23+24)%

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

- Hence, Option D is correct.

There was a 4% error estimation error. But it didn’t specify whether it was caused by over estimation or under estimation.

So, the researcher is between (23 - 24) % and (23+24)%

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