Comparing sample proportion to population proportion

I have a data set consisting of a number of different hospitals. I am trying to compare the proportion for hospital X to the overall proportion in the data set (which includes hospital X).

Should I not use a two sample proportion test for this? I am worried because the overall proportion contains the observations for hospital X, violating the assumption of independence. Please let me know what approach I should use. Also, if there are going to be sample size issues (i.g. a really large hospital would have a greater impact on the overall proportion, is this more of a problem compared to smaller hospitals?)