Final answer:
The test most likely administered by the psychologist is the Minnesota Multiphasic Personality Inventory (MMPI), a self-report inventory designed to establish a clinical profile through true/false questions.
Step-by-step explanation:
If a psychologist at a community college administered an empirically derived personality test to diagnose an emotionally troubled student, the test most likely administered would be the Minnesota Multiphasic Personality Inventory (MMPI). The MMPI is a self-report inventory composed of a series of true/false questions aimed at establishing a clinical profile of an individual. This is in contrast to projective tests like the Rorschach Inkblot Test or the Thematic Apperception Test (TAT), which rely on ambiguous stimuli to assess unconscious processes, and are often less subject to intentional distortion compared to self-report inventories.