The primary method archaeologists use to study history is
(2) examining artifacts of a specific people
Explanation:
The primary method archaeologists use to study history is based around the artifacts that the set of people have left behind as they are evidences that are less to be tinkered with and usually found for civilizations long gone with no written records.
Often, it is only archaeology that an determine the life and times of people of the ancient times and it is even valuable for modern period because it often unearths things that were not recorded but are to be true.