The problem I have is as follows. I have enrolment data describing the number of male and female preferences for two broad fields of education: i) Information Technology and ii) Engineering. The data reflects "first preferences", that is, the number of people who wrote down on paper that their most preferred degree was either one in the field of Information Technology or the field of Engineering. The data does not reflect actual enrolments. The numbers are as follows:
Female: 266 (~13%)
Male: 1783 (~87%)
Female: 684 (~12.5%)
Male: 4773 (~87.5%)
The question I am trying to answer is: is there a statistically significant difference between the gender ratios of Engineering versus Information Technology, and at what level of significance?
I apologize if this is a noob question. I only have relatively basic background knowledge in statistics and tests of significance and this problem didn't seem to fit any of the methods I am familiar with. I'm hoping someone might be able to point me in the right direction as to which statistical test(s) would be appropriate given the dataset and any caveats I should be aware of.