After replacing my starter, I had noticed the vacuum ball hanging and a hose disconnected after pulling out the wheel well guard. I’m not sure if I I broke the hose or even where it connects. Any suggestions on how to fix this problem would be much appreciated.

 

Should be 2 hoses on the vacuum ball(vacuum reservoir)

One hose goes to the firewall very left on passenger side between fender and heater fan box, there will be a grey vacuum line with it(grey one goes to heater hose bypass valve)
Your Vent direction(defrost, panel, floor), won't work if this hose is disconnected

The other hose runs to engine's vacuum manifold, has several vacuum hoses connected at that spot, vents also won't work if this hose is disconnected

You can repair these hard plastic vacuum lines with correct size rubber hose, just slide the tight fitting rubber hose over both ends of the broken hard line, a splice
or
Replace the whole line with rubber vacuum hose
No clamps are needed with vacuum hoses as they PULL TOGETHER and do not try to push apart like say a heater hose does, that needs a clamp

 

I think that hose goes to the FPD fuel pusle dampener and then from that vantage point travels to the front manifold vaccuum on the side of the throttle body, next to the bypass idle valve. At the throttle body it makes a connection with another red wire and makes it's way to the Evap emissions canister control (sometimes near the battery cables).

If it's the line I'm thinking of, it is important and you have to connect it.