Alternator Light Goes on and Off

My alternator light sometimes comes on for an hour and later it goes off for a few seconds. I checked the charge with a tester and it indicated that the battery was good as well as the alternator. Then I checked it again when the alternator light turned on and it indicated that the alternatoor was bad. I just put in a new battery and my next step is a new alternator.

Can anyone tell me if they have had this problem?

ps. My speedometer has stopped working as well and my abs light came on, does one have to do with the other?

Thanks.