a ___is a detailed study of the life and activities of a group of people in which researchers may live with that group over a period of years

Ethnography

Explanation:

The objective of ethnogrsphy is to study the daily life and activities of a group of people

Researchers can be found living with the group they are studying over a period of years, this mostly happens when they focus on the study of foreign cultures. Researchers can also not necessarily travel far and wide to do this study but also with their own environment, it can be used for organizations communities, sects or cults.

The answer is: an ethnography.

Explanation:

Ethnography is a research method that consists of the study of the everyday life of a group of people. When social researchers first began using this method, it was common for them to live with the group they were studying over a period of years, since they focused on the study of foreign cultures. However, although ehnography still implies the submersion of the researcher into the community or culture he is studying, it doesn't necessarily have to be a foreign non occidental culture.

Within this method, researchers can use several research techniques to gather data, participant and non participant observation, interviews, etc.