A survey was conducted on a random sample of students at a college campus to study student opinions on the new honors program. Out of the students surveyed, 78% rated the new honors program as "very rigorous" with a margin of error of 3% and a confidence interval of 90%.

Question

What does the margin of error imply?

Answer 1

The margin of error (MOE) of 3% in this survey implies that the true proportion of all students who would rate the new honors program as "very rigorous" is likely to be within 3 percentage points above or below the reported percentage of 78%.

In practical terms, this means that if the survey were repeated multiple times, we would expect that in 90% of those instances, the true percentage of all students rating the program as "very rigorous" would fall between 75% (78% - 3%) and 81% (78% + 3%).

This MOE reflects the uncertainty inherent in sampling and indicates the range of values within which the true opinion of the entire student population can be reasonably expected to lie, given the confidence level of 90%.