Also, if you don't want to spend money on a 'test' package, you could just ask your landlord how packages are handled. I'm guessing it's going to be different depending on the setup of the apartments (ie, is there an office, a mail room, does your door open to a hallway or to the outside).
The last apartments I lived in opened to the outside, so it was easy for the UPS person to find my door. You either had to be present to get the package, or put a sign on the door saying it was OK for them to leave the package at the door (therefore relieving them of any liability if the package was stolen). I never had any problems.
The apartments I live in now open to a hallway, and the UPS/FedEx person doesn't bother going upstairs with the packages. He just leaves them inside the small entryway to the apartment building, by the mailboxes. If the package is too large to put in the entryway, he puts a note on the door saying to pick up the package in the store that the apartments are located above. So yeah, all the neighbors tend to see what I'm getting, but *shrug* I don't think they care too much and a lot of diaper sellers (esp. XP Medical) offer discreet shipping anyways.
Anyways, just goes to show that the method for handling packages is gonna differ depending on how the apartments are set up. Just ask the landlord; how packages are handled was was definitely my first question @ both places, and it's probably a pretty common question as well.