"I am hungry."
Translation:저는 배가 고픕니다.
Yes. 배 means 'belly' or 'stomach', and 고프다 means 'to be hungry' or 'empty'. 배고파 can be used on its own where 나는 is assumed and omitted. It is informal and oftenly heard. In fact I don't believe the formal speech '저는 배가 고픕니다' is used that often at all (my Korean husband has told me he has never used this sentence and can't envisage he will ever use it... because saying 'I'm hungry' in a formal situation itself is awkward and may be considered rude, don't you agree?)
I believe the takeaway message is, use 배고파 with friends, try not to use the formal speech in any situation.