Is Fed-Ex responsible for giving away my package to someone else?

I had an iPhone that was coming in couple days ago and I saw the delivery confirmation. To my surprise, it said it was delivered and signed by someone else. I called Fed-ex and they refuse to take responsibility because they said someone was at the house and they signed it. (No one was at home at the time) They showed the signature, but no one that is living in the house is named "Sarah." There wasn't even a last name! What do I do?!

File a claim with fedex

Unless the recipients signature was required, Fed Ex did their job.

Sue fedex. The delivery driver probably signed it and just left it on your door step or front porch. They could have delivered it to a next door neighbor

Yes, they are. They either delivered to the wrong address or the delivery person stole it (it has happed before.)

If the package was never delivered to your address then the delivery was not completed.

Start by contacting the credit card company to revert the charges (remember that you are not responsible for items that never reached your address.)

Inform the seller that the delivery company failed to deliver the purchased item as promised, and let the seller deal with Fed-Ex.