We present the results of a research whose purpose was to find out what a sample of experts (statisticians and statistics university professors) and university students understood exactly by confidence intervals. To this end, a questionnaire was answered by 41 experts and 297 students. The results show that both, students and professors, possess misconceptions regarding confidence intervals. The conception that these intervals contain sample means or single values of the population instead of possible parameter values, and the interpretation of significance levels as a measure of certainty, without any frequency referent, were found to be the most generalized misconceptions.