I would guess it's not correct. An air gap prevents the inside of your dishwasher from becomming contaminated with backflow from the drain. It is code in most locals to install one so check with your local inspectors to be sure. In the few area's that it's not required the drain hose must be attached up high to the bottom of the countertop. Here's a link that'll show you how they are connected and why.
http://www.home-inspect.com/news/itips_4-03.html