We can only believe what you have told us, which is that the sink is not vented.
I would not believe Terry's simple test of running some water into the lavatory because of the potentially low flow of the sink's faucet. You would need to drain a full sink or dump a bucket of water into it, and then check to see if the the trap has siphoned.
If there is not a vent, it might be one of those times that an AAV will have to make do.
Thanks I will try this test. Do I basically open the trap and see if its not full of water after draining the full sink?