A community organization wishes to know the proportion of subjects who feel financially comfortable in a certain town.
Based on last year’s census, $64\%$ of the town residents felt financially comfortable. In this year’s survey, $56$ out of $115$ randomly chosen subjects expressed feeling financially comfortable. The organization wishes to determine if the residents’ opinion of financial comfort has changed from last year.
If the town has a population of $n = 500$, why would it be incorrect to use a normal probability calculation on proportions?