Am I responsible to replace an item that was lost because I shipped it to the wrong address?

I take it that you did not insure the package. Have you contacted the post office and asked them to contact the people at the address you did send it to. Did you ship it within the same state? In the end you have a legal concept named called a bailee and bailor relationship. You temporarily have possession of someone else's property. Even though this was not a commercial transaction you had possession and should have exercised reasonable care. Ethically, even though you had good intentions, you messed up. You are the cause of the loss. Without knowing all the facts, it would appear that you are legally responsible for the loss.