When I failed the smog test the computer gave a P1443 code which on every Ranger site I checked indicated an EVAP Control System Purge Solenoid or Purge Control Valve problem. It also showed the following values for HC and CO readings:

HC in ppm MAX GP MEAS RESULTS
15 mph 55 281 114 GROSS POLLUTER
25 mph 39 231 33 PASS

CO in % MAX GP MEAS
15 mph 0.70 2.00 4.16 GROSS POLLUTER
25 mph 0.84 2.14 0.70 PASS

I put in a new purge valve solenoid but the CEL (check engine light) stayed on after having driven it for perhaps 20 miles. I disconnected the battery, cleared the code, and have now driven it for close to 100 miles (city streets and freeway) and the light HAS NOT come back on. Have I solved my problem? Mechanic in the neighborhood said it might need a week or two to reset and come back on and doesn't think the high scores shown above (GP - gross polluter) have anything to do with the purge valve. If I knew that much about auto engines I might have been a mechanic instead of a retired teacher. We're talking about a '96 Ranger 2.3 L with about 120,000 miles.
Appreciate any advice you can lend.

 

Yes, it can take awhile for that code to reset, EVAP is one of the only systems that runs even when engine/key is off.
General rule when resetting an EVAP code is to keep fuel level in tank above 1/4 and no higher than 3/4, if you have no code coming back after a week then you should be fine.

But this code is not the reason for the high HC and CO readings.
EVAP prevents gas fumes in the fuel tank from escaping into the air.

The HC and CO is coming out the exhaust system.
Best thing would be regular tune up items.
On fuel injection that means:
New air filter
Clean the MAF sensor, look here: Ford Ranger Mass Air Flow Cleaning, Removal and Installation
MAF sensor tells computer how much fuel to add.

Replace spark plugs, if engine has random misfires each misfire dumps Oxygen in the exhaust pipe because it wasn't burned up.
O2 sensor only "sees" oxygen, not fuel, so when it "sees" too much oxygen computer "sees" that as Lean exhaust, so adds more fuel, so more HC.
Check the tips of the spark plugs as they are removed, blackish residue means a rich condition, Google: spark plug tip images
Picture is worth a thousand words

Spark plug wires usually last thru 2 or 3 sets of spark plugs.

O2 sensors are rated for 100k miles, so yours are due for a change, there are two of these on a '95 and up 4 cylinder engine.
Upstream O2 is the one closest to the engine, computer uses this one to adjust air/fuel mix in real time.
Downstream O2 is on the exhaust after the Cat Converter, this one is used to see if Cat Converter is cleaning up the exhaust, computer compares Upstream reading and Downstream reading, if exhaust emissions are not far enough apart Computer will set a code and turn on CEL.
BUT(big but) this is assuming BOTH O2 sensors are in good operating condition.

Put a can of SeaFoam in the fuel tank, this can clean up injectors, I do this once a year on all my fuel injected vehicles, seems to eliminate most of the random misfires that develop over that year.
Tips of fuel injectors get dirty and at lower flow(idle and near idle RPMs) they drip instead of spray, since fuel is not fully mixed with air it will make a Lean exhaust so computer richens the mix at lower RPMs, Seafoam cleans the tips.

The Cat converter may be failing, but it for sure will fail early if the HC isn't lowered
I would change the O2 sensors first then drive truck for at least 50 miles, the new O2 sensors will tell you if there is a problem with Cat.

You already know to unhook the battery to reset computer after changing any parts or even spark plugs, to rest computer, so do that.