my 05 neon would not start so I got new battery ,but I'm not sure if my alternator is working
I did start the car and disconnect the battery and car shut it self off is this the sign
of bad alternator?

 

Generally. It is also a not so safe way of testing for it too.

 

The best way to test to see if your alternator is charging is to find a friend with a multimeter. Have him to place the leads on the battery terminals while the car is in both a running state and not.
Charging well the alternator should be putting out close to maybe slightly over 14 volts
If it's barely over 12 volts take the alternator off and have it tested further at a local parts store.

 

I vote test the alternator itself with the multimeter and save yourself the trouble of removing it.