From www.yourdictionary.com

"Usage Note: Infer is sometimes confused with imply, but the distinction is a useful one. When we say that a speaker or sentence implies something, we mean that it is conveyed or suggested without being stated outright: When the mayor said that she would not rule out a business tax increase, she implied (not inferred) that some taxes might be raised. Inference, on the other hand, is the activity performed by a reader or interpreter in drawing conclusions that are not explicit in what is said: When the mayor said that she would not rule out a tax increase, we inferred that she had been consulting with some new financial advisers, since her old advisers were in favor of tax reductions. "

This distinction is also specifically stated on page 49 of Strunk and White - who state that they are "NOT interchangeable".

You could argue with me, or with McG of H, but nobody, and I mean nobody, can argue with Strunk and White.