The actual temperature of the background radiation is also predicted. I can't remember exact values from the lectures, but I remember them being correct to within a degree or two (in kelvins).
Also, as was noted, the background radiation was not known about before the big bang theory. In fact, the
lack of any known background radiation was used to discredit the theory if I remember correctly. I seem to remember it first being discovered in the late 60's (but I may be wrong about the date) by astronomers using a radio telescope. They discovered an annoying staticy hiss that they couldn't remove. They thought it was pigeon crap on the dish they were using, but that wasn't it. They found it in every direction they pointed the dish. Lo and behold, there was the background radiation
Added in edit: Ooops, I meant to make that a general reply rather than a reply to you specifically Paul.
This message has been edited by happy_atheist, 11-30-2004 08:06 PM