Yes, a hospital is a SSTB. Below is a short definition of an SSTB from IRS.GOV. 

An SSTB is a trade or business involving the performance of services in the fields of health, law, accounting, actuarial science, performing arts, consulting, athletics, financial services, investing and investment management, trading, dealing in certain assets or any trade or business where the principal asset is the reputation or skill of one or more of its employees or owners.