Inferring wire gauge from cable size
I don't think you can safely infer it, but what I would recommend is to find an area in your house that has some cable with slack and the wires exposed - maybe the breaker panel.  Take note of the diameter and overall appearance of the cable, and then check the wires themselves.  As @lqarry said, you can use wire strippers to see what gauge the wire fits.  Now compare that to the cable in question.