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Hourly rate negotiation tips for paid internship
They likely have an intern (job title) pay-scale that maxes out somewhere below $30/hr in order to meet the FLSA (that exempt vs non-exempt stuff you were seeing). As a PhD student, you could probably negotiate up into the ~$25/hr range, but from a benefits standpoint, they might not be able to pay you $35/hr without making you an exempt, full-time employee.