Question

when a random sample of first - year college students is surveyed, 38% of these students say they are undecided about what major to pursue in college. the survey is reported to have a 2.8% margin of error at a 95% level of confidence. based on this information, which one of the following interpretations is most accurate?
for this result to be valid, at least 2.8% of the population must have been included in the sample.
95% of the students in the sample gave survey results that are within 2.8% of the true population percentage.
there is a 2.8% chance that the sample percentage was computed incorrectly.
the population percentage is guaranteed to be exactly 2.8% higher than the sample percentage.
the population percentage is very likely to be within 2.8% of the sample percentage.

Explanation:

The margin of error at a certain confidence - level (in this case 95%) gives a range within which the true population parameter is likely to lie. A 2.8% margin of error at 95% confidence means that we are 95% confident that the true population percentage is within 2.8% of the sample percentage. It does not mean a specific percentage of the population must be in the sample, nor does it mean that a certain percentage of sample results are within the margin of error, or that there is a chance of incorrect computation in the way described, or that the population percentage is a fixed amount higher than the sample percentage.

Answer:

The population percentage is very likely to be within 2.8% of the sample percentage.