Battery Light is on on 2001 Ford Escape

I just bought this vehicle and the battery light is on. The dealer said they did a diagnostic and it is the alternator. How can I be sure?

Asked by for the 2001 Ford Escape
Take it to almost any chain parts store. Most have a battery /alternator voltage and amp tester and they can ck it for you.
ok..took care of that. Now the coolant light is on but the coolant levels are all full. Now what? Suggestions please!
2 more answers
i dont know.any suggestions
Had the same issue with '01 Escape "Battery Lamp" after diagnose and voltage about 12.6 changed Alternator which requires removal of right drive axle and separating lower control arm. Which after those parts showing wear I did lower ball joints, struts, brakes, sway links, and alternator, only for light to come on! The jokes on me, ITS NOT A BATTERY LAMP , BUT COOLANT RESAVOIR LAMP !!!! add coolant light goes out!