I just purchased a 3 inch diameter mechanical test plug (expansion plug) in order to "permanently" seal a toilet drain in my basement. The true diameter of the drain pipe seems to be 3 and 1/8 inches however and so I can't seem to hand tighten the wingnut sufficiently to seal it off tightly; it lifts right out. What am I doing wrong? Should I use a wrench to tighten it?

You don't have the power in your bare hand to tighten the plug to make a positive seal. Place the plug inside the toilet pipe, tighten by hand as much as you can - than take pliers and keep turning the wing nut until it is tightly against the wall of the pipe.

Hope that explains

Milo