Why if the AC thermostat is set at 76 and it shows a current temp of 72 is it still running?

First use a trusted thermometer to determine what the actual temperature is at the thermostat. If the air temperature is below 76* then check these things.Make sure there are no direct or indirect sources of heat, i.e., sunshine, ect.(1)The thermostat is out of calibration. If the thermostat IS NOT DIGITAL, then the first check is to see if it is level. You must remember that when you stand by a thermostat for a period of time, it is also sensing your body heat. After making sure it is level and secure, step away for a while so it can adjust to the surrounding air. If it is level and there are no holes behind the thermostat that would allow air from inside the wall to affect its reading, if yours is a Mercury bulb or bi-metal stat, see if the room indicator dial is accurate. That is a simple fix to adjust, it is usually an Allen key, but allot of times you can gently turn it by hand. Then if it is not reading correctly, find the manuals online so you will understand how it functions. (2) If your thermostat is not accurate, it takes a very thin thermostat wrench to calibrate it. I would suggest looking at the thermostats manufacture�s website and download the installation manual. If it is a standard thermostat, they are relatively inexpensive and you might want to cut the wasted time and replace it. If it is digital, then I would highly recommend reading the manual on your particular model. Some thermostats have what is called "intelligent recovery". That means if you set a programmable thermostat for settings that do not make sense, it will do what is most economical. I doubt that is what is happening here, but the more you read about what you actually have, I am confident you will figure out what exactly it is doing or not doing. IceMan