Which research method involves the researcher participating in the lives of those being studied?

The correct choice is ethnography because this research method is characterized by the researcher immersing themselves in the daily lives of the subjects they are studying. Ethnographers often engage in prolonged observation and participation in the community or group they are investigating, which allows them to gain an insider perspective on the social practices, beliefs, and interactions of that group. This immersive approach helps to produce rich, qualitative data that can reveal complex social dynamics and cultural context.

In contrast, experimentation focuses on testing hypotheses under controlled conditions, typically without the researcher being involved in the subjects' daily lives. Case studies provide detailed analyses of a particular individual, group, or situation, but they do not necessarily require the researcher’s active participation in the lives of the subjects. Surveys involve collecting data from a sample of subjects through questionnaires or interviews, again without the need for the researcher to be involved in the participants' daily activities. Thus, ethnography stands out as the method that centers on deep participation and observation, allowing for a comprehensive understanding of the subjects’ experiences.