Which example best illustrates a study that qualifies as research with human subjects according to federal regulations?

The example given showcases research involving human subjects as defined by federal regulations because it directly engages individuals (students) and examines their performance in relation to identifying traits (gender-related stereotypes) and understanding how these stereotypes affect outcomes (math test performance). This interaction with human participants and the collection of data specifically concerning their behaviors and experiences are integral to the definition of research involving human subjects.

This example fits well under the regulations as it could have implications on educational outcomes, gender equality in education, and psychological effects based on societal stereotypes. The direct involvement of human participants denotes that ethical considerations for their treatment and rights are paramount.

The other options do not meet the criteria for research with human subjects. For instance, the survey on college students focuses on collected data without direct intervention or deeper engagement with the participants. Furthermore, studies that solely analyze public records or statistical models based on historical data do not involve any direct interaction with living individuals, which is a key component in classifying research as involving human subjects according to federal guidelines.