I got my iPhone battery replaced but maybe not.

Is it a scam? I took my phone into Best Buy, authorized agent to replace apple battery. They did a diagnostic through apple (he showed me) - it's just a way for big brother to check up on you. Anyway, when I got the phone back it had roughly the same charge as when I left it. It didn't occur to me until later, why would a "new battery" be at 40%? (you would think it would either be uncharged or fully charged). Anyway, the phone is no better at holding a charge and the percentage jumps down in a very erratic way, like one minute it's a 27%, then it suddenly drops to 1%. Anyone else have this problem?