The way you absolutely get HOSED (har, har) is if you don't have insurance! Most medical facilities participate in various insurance plans, under which they are limited in how much they can charge. That isn't the case if you're uninsured--you could wind up paying double or triple the insured fee.
The best advice I can give you is that the price is negotiable, but it's much easier to do it IN ADVANCE! You could probably ask a friend with insurance to find out how much he or she would pay for a sleep study, then negotiate for the same fee.
Machines are taking over the world.