Among the 1,147 owner complaints naming this part, car battery is named in 68% of them, more than any other part.
Other parts named in the same complaints. Car battery: 68%; Starter motor: 14%.
Owners name the car battery most often in the same complaint, which is not proof that one caused the other. Ask the shop whether it checked the car battery too, so you are not quoted twice for one visit.
Data and chart by CalcScrape: Alternator Replacement Cost Calculator