DURING CHK RIDE BY FAA ACI; THE FO MISUNDERSTOOD CLRNC AND STARTED APCH AND DSCNT BEFORE APCH CTLR ISSUED CLRNC.

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IT WAS AN FAA CHK RIDE WITH FAA EXAMINER ON BOARD DURING THE SIC CHK RIDE PORTION OF FLT CHK. WHILE SIC WAS IN THE PROC TURN; THE FAA EXAMINER PULLED AN ENG TO SIMULATE ENG OUT. WHILE ON THE APCH; I; THE PNF PER THE FAA REQUESTS; ASKED GRIFFIS APCH TO COMMENCE THE APCH AS WE TURNED INBOUND ON THE PROC TURN. DUE TO RADIO COM PROBLEMS; SCRATCHY; BROKEN; POOR RECEPTION; TRAINING DISTRS; HVY WORKLOAD; ETC; WE ALL THOUGHT WE HEARD CLRED FOR THE APCH; NOT ADVISE WHEN READY FOR THE APCH. I THEN RECONFIRMED WE WERE STARTING THE APCH; STARTING OUR DSCNT TO INITIAL APCH ALT. EVIDENTLY ATC NEVER HEARD OUR TRANSMISSIONS. THE SIC LOOKED AT FAA EXAMINER AND CIRCLING 1 MORE TIME TO LOSE MORE ALT. I ADVISED ATC; NEVER HEARD CONFIRMATION; SWITCHED RADIOS; ONLY TO CATCH ATC INSTRUCT US TO TURN L 330 DEG CLB 6000 FT; YOU'RE NOT CLRED FOR APCH. SIC NEVER HEARD INSTRUCTIONS. I TOOK OVER CTL OF ACFT TO COMPLY WITH INSTRUCTIONS IMMEDIATELY. WE CONTINUED AIRWORK FOR 1.5 HRS AFTER WITH NO OTHER EVENTS. FAA LIKED CREW COORD AND MY DECISION TO TAKE ACFT CTLS AND CHANGE RADIOS. ALL THOUGHT CLRED FOR APCH BASED ON POOR RADIO RECEPTION/XMIT.