iPhone 4 will not default to WiFi connection

I recently switched carriers and got a new iPhone 4. Having had the phone for a week, I checked my data usage. It showed that I had used over 500mb of cellular data, despite the fact that I am almost constantly connected to wifi. To figure out what the problem was, I double checked to make sure I was actually connected to the wifi network and then reset my stats so I could monitor my usage today. With cellular data turned on and being connected to wifi, I have accessed safari and opened a few applications. At first I thought my usage may be normal (at around 14kb), but it continues to go up and after about 10 minutes Im up to 15kb sent and 36kb received. If I turn off cellular data the wifi connection is working and I am able to use the phone as normal, without incurring additional cellular data. Why would this be happening? I had been using an iPhone 4 with my previous carrier and never had this problem. Is my phone defective or am I missing something?
Black MacBook