Looks like it is in addition to any air that comes in from where the Big Mouth enters since it comes in from the bottom.
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This is not correct. It adds a second air inlet to the box and does not replace the stock inlet that the Velossa Big Mouth uses. This ST200 airbox is basically a plastic version of Mountune's airbox (metal).
Now as to where exactly that hose "should" go, that's up for debate.
Mountune's recommendation was to route the hose to rest just behind the fog light. Unfortunately there's no active airflow in that area. I believe I read a user that tested it a while back and found that it had no effect on airflow at idle, but at speed it helped a tiny bit.
I'm personally considering doing something similar to what Sekred did and connect the hose to an opening made in the fog light housing. It's the same idea as Mountune's original location, just with the added benefit of being hooked up to a velocity stack installed next to the fog light. This is documented at
http://www.fiestastforum.com/forum/threads/399-Sektune-Cold-Air-Intake.
Ford appears to use an entirely different approach. They've routed the hose to rest somewhere towards the lower middle of the car, behind either the radiator or the intercooler. Evidence of this can be seen in this picture provided by an ST200 owner that gave us the only view I've seen thus far of where that hose is located on a stock ST200.