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I have been charged large amounts of data usage on my Iphone while it was on wifi. Went through several session with AT&T and they had me replace the sim card and when that did not fix the problem, they advised me that the phone itself was bad and needed to be replaced. It is an Iphone 4 that I've had for about 2 years. Does this seem like a likely issue, or is it just AT&T making up excuses for overcharging me?
Being on Wi-Fi does not disable the cellular data.
Even when on Wi-Fi, once the device goes to sleep, the Wi-Fi shuts off to conserve battery.
The only way to stop using data over the cellular network is to turn that feature off via Settings > General > Network > Cellular Data.

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