How do I make a smoke alarm stop chirping?

The smoke alarm was chirping last night (low battery), so I took it out and then today I put a new battery in it and tested it. According to the test, the battery is installed correctly - yet the smoke alarm is still giving the low battery chirps! The new battery I put in it was fresh out of an unopened, recently bought package of batteries. It is an older smoke detector that's hard-wired, but relies on the battery in order to work, just like the battery-operated ones do.