311 - AIR system not working - Single, Right or Rear HO2S - Air Injection
314 - AIR inoperative, Left or Front HO2S - Air Injection
First, those codes are for the SMOG / AIR system, not the EGR, which is OK, since the hoses you replaced under the CAI are SMOG related (I think you replaced the lines to the AIRB and AIRD valves).
When you did the KOER test, the computer made the car run rich on purpose, then operated the two valves, and then looked at the O2 sensors. With the valves open, the computer expected the car to move towards a lean condition. These codes indicate that did not happen.
The check engine light will not come on because of these codes.
I wouldn't worry about it if you don't have any other symptoms. The change in vacuum hose is not the cause of the codes. You could have one of the valves sticking or something. The pump could be shot. It is hard to sya for sure, as there is no way to test any of the components individually.
I would yank the crap out, personally. It isn't working anyhow and won't affect driveability
2006 GT - Vortech polished w/ intercooler, Eibach suspension, Hurst short-throw, some other goodies - tuned by Paul's High Performance. It moves...
and it collects dust admirably while parked for repairs in the garage...
SOLD - 1995 Black Mustang GT, AODE. Loved it, but I had to let it go...