AN ACR CAPT MISINTERPRETED THE CTR CTLR'S DISCUSSION OF WHY THE ALT WAS ASSIGNED TO BE A CLRNC TO A SIMILAR SOUNDING; HIGHER ALT. THE CAPT READ BACK THE ALT AND BEGAN THE CLB. THE CTLR INTERVENED JUST AS THE RPTING CAPT RECEIVED A TCASII RA.

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OUR FLT DEPARTED MCI ENRTE TO STL. WE CHKED IN WITH ZKC AND WERE ASSIGNED 15000 FT. WE WERE LATER ASSIGNED FL200. THE FO SET 200 IN THE ALT WINDOW OF THE MODE CTL PANEL (MCP). SINCE I WAS THE PF; I POINTED TO THE ALT DISPLAY AND REPEATED; 'FL200.' I WAS HAND-FLYING THE AIRPLANE UTILIZING THE FLT DIRECTOR. THE FLT DIRECTOR AND I WERE BOTH PREPARED TO LEVEL AT FL200. THE FO WENT OFF THE ATC RADIO TO RELAY OUR TKOF TIME TO THE COMPANY. WHILE HE WAS OFF THE RADIO; THE CTLR TOLD US TO LEVEL OFF AT FL200; UNTIL CLR OF TFC; AT WHICH POINT WE WOULD BE CLRED HIGHER. HOWEVER; I HEARD HIM SAY FL220. I READ BACK THAT WE WOULD CLB AND MAINTAIN FL220; HIGHER CLR OF TFC. NOT HEARING A CORRECTION OR CHALLENGE FROM THE CTLR; I WAS CONFIDENT THAT WE WERE NOW CLRED TO FL220. I SET 220 IN THE ALT WINDOW OF THE MCP. THE LAST ATC INSTRUCTION RECEIVED WAS AROUND 18000 FT. THE FO CAME BACK UP ON THE ATC RADIO. I TOLD HIM THAT WE WERE NOW CLRED TO FL220; AND POINTED TO THE 220 NOW SET IN THE ALT WINDOW ON THE MCP. HE ACKNOWLEDGED THE NEW ALT. HAVING NOT HEARD THE CTLR'S CLRNC OR MY READBACK; HE COULD NOT HAVE CAUGHT THE ERROR. PASSING 21200 FT; WE SIMULTANEOUSLY WERE ASKED BY THE CTLR IF WE WERE LEVELING AT FL200 AND GOT A FLEETING TCASII RA AT 10-11 O'CLOCK. THE RA WAS A SINGLE 'CLB' INSTRUCTION. THE CTLR TOLD US TO LEVEL AT FL230. I INCREASED THE RATE OF CLB AND WE LEVELED AT FL230. AFTER LNDG IN STL; I CALLED ZKC AND TALKED TO THE ARTCC SUPVR. HE WAS VERY COURTEOUS AND TOLD ME THAT THEY WERE IN THE PROCESS OF LISTENING TO THE TAPES. DURING THE CONVERSATION HE TOLD ME THAT THE TAPES HAD BEEN REVIEWED AND THAT THEY WOULD FILE THE EVENT AS A PLTDEV.