[all of the above, plus] the usual scheme is that a Level III writes and approves the testing procedures, and Level II's perform those tests i.a.w. those procedures. L/II can work w/o supervision*, and can be the 'final signature' on a test report. L/I's have to work under direct supervision by a L/II or L/III, and have to have their reports countersigned by a L/II or L/III.
L/III is required to perform random audits of the L/II's and L/I's performing testing, to ensure that they are working within the boundaries of the approved procedure.