I live in Georgia. My new outlet is in a plastic box and runs from a plastic junction box. The receptacle tester reads open ground even though I attached the copper ground wire to the ground screw. How do I find the ground problem with this outlet?
It reads open because it IS open!
A typical outlet tester, or as Harper calls it, Magic 8-ball, shows Open Ground if it can complete a circuit (i.e., current flows) between Hot & Neutral but can't complete a circuit between Hot & Ground. Since (provided things aren't messed up really bad) this indicates Hot & Neutral are both connected, the logical assumption is "Open Ground".
However, this is not a guarantee. There could be other wacky combinations of broken conductors, reversed conductors, messed up connections, etc. that could show the same light pattern. But assuming for the moment that Open Ground is correct, which is very likely the case, there are a few possibilities:
First of all, plastic has little or nothing to do with this. In fact, if you had a metal box and metal conduit then you would likely have a good ground connection even if the ground wire wasn't connected. That is because metal boxes + metal conduit can form a legitimate grounding path without any wires involved. So plastic doesn't hurt anything here, but they don't help solve the problem either.
Receptacle - Unlikely, but easy to test. Disconnect power and use a multitester to check for continuity between the ground screw and the ground hole on the receptacle. If it is good then you know the problem is not the receptacle. If it is bad, replace it.
Cable - Unlikely, but if there has been any damage to the cable then it is possible the ground wire is broken. I would (carefully) strip a little more of the outer part of the cable off to make sure the ground wire isn't pinched and barely holding on (e.g., if it got nicked when stripping the cable originally).
The other end of the cable - This is the most likely source of the problem. This could be another receptacle or could be all the way back to the panel. If it is another receptacle, see if that receptacle tests correctly. At each location, all grounds should be connected together. At the main panel, grounds & neutral are connected together.
At each location, you should have very low (or 0) voltage & very low (or 0) resistance between the ground wire and neutral wire. Similarly, you should have ~ 120V between hot & ground (same as between hot & neutral) - which is essentially what the outlet tester is testing.
There is one more interesting twist here, which might legitimately cause an "Open Ground": GFCI without ground. Because GFCI takes care of many of the same safety issues that a ground wire helps solve, it is legal in some situations to retrofit GFCI on an ungrounded circuit without running a ground wire. In those situations, any downstream receptacles are supposed to be labelled that they do not have ground. But if they weren't labelled then they would test as "Open Ground" but still be protected from ground faults.