I built an 8ft x 6ft shop in my bedroom and can run my x2 mill with stock gear drive and my roommates can't hear a thing so I have some success in the area even if blind luck and overbuilding . I'd suggest googling for sound isolation boxes for more info and pictures (if you can avoid getting lost for hours, I can't).
There are 2 things that need to be controlled, vibration and airborne sound waves. Isolate the compressor from the floor of the box with some sort of resiliant material. Make the inside of the box big enough so that there was good airflow around the compressor.
Either line the inside of the box with sound isolating insulation (rockwool) and/or have an inner and outer wall for dead air. Using denser thicker material such as sheetrock, mdf or homosote for the walls will absorb more sound waves than light thin stuff. If using an inner wall try to isolate it as much as possible from the outer wall e.g. staggered studs, box in a box or resiliant fasteners. If doubling up on wall material using resiliant glue like Green Glue would help.
Make sure to seal gaps with caulk and use something like weatherstripping around the access door.
Next we have to deal with the pesky ventilation problem. For that I'd suggest muffler boxes (inlet and outlet)with baffles or corners lined with insulation. Every time sound waves have to change direction there's a drop in noise level so the more changes the better. Put a fan(s) inside the main box at the inlet and/or outlet for air circulation around the compressor. Wire up the fan as is most convenient for you.
Some of this stuff might be overkill but I bet you could build a box 2x2x1.5 fairly cheap, that's just about dead silent with the compressor running, assuming your measurements included room for insulation/airgap and airflow.
As this is my first technical post I'd appreciate questions, constructive criticism and clever snide remarks 

