In the process of getting the upper radiator hose out of the way to gain access to the starter, I notice a thin black hose near the bottom of the engine bay that is detached at one end. It's maybe ~8-10mm diameter & a foot long, I'd guess. I didn't see anything leaking out from the hose, although the car has not been driven in awhile. Where should this be attached? I'm new to DIY car repair, so pardon my ignorance.

The arrow points to the general location it extends from. I draped it over the radiator to get a better look. Edit: radiator hose, that is.

 

Transmission breather/vent tube. See image.

 

Well, that's a relief. Thank you kindly!