CAPT RPTR TURNED WRONG WAY WHEN RECEIVING ATC HDG CHANGE. LACK OF CREW COORD IN FOLLOWING CLRNC. FLC ATC REVIEW.

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WHILE CRUISING AT FL390 FROM SDF TO BIL; ZMP GAVE US A 15 DEG HDG CHANGE FOR TFC SEPARATION. THINKING I HEARD 'R;' I TURNED THE HEADING SELECTOR 15 DEGS R OF OUR CURRENT HDG. I HAD TAKEN MY HEADSET OFF EARLIER TO DON THE OXYGEN MASK SO THE FO COULD GO TO THE JOHN. I WAS LISTENING TO ATC WITH THE COCKPIT SPEAKER. THE FO ACKNOWLEDGED THE HDG CHANGE; BUT BECAUSE I DID NOT HAVE MY HEADSET ON; I COULD NOT HEAR HIS READBACK TO ATC. IN APPROX 45 SECONDS; ATC CAME BACK WITH 'CALL SIGN; DID YOU TURN R?' WITHOUT HESITATING; THE FO RESPONDED; 'AFFIRMATIVE.' ATC THEN DIRECTED; 'WELL TURN BACK TO THE L; QUICKLY!' UNTIL I SEE THE ATC TAPE TRANSCRIPT; I WILL NOT KNOW WHAT WAS SAID. THE FO DID NOT CORRECT ME WHEN I TURNED R; BUT HE MAY HAVE BEEN DISTRACTED BY AN FMC MESSAGE. HE WAS CHANGING SPDS ON THE CRUISE PAGE OF THE FMC BECAUSE WE WERE HIGHER THAN OUR OPTIMUM ALT. BEFORE CTR HANDED US OFF; HE GAVE US A NUMBER TO CALL AT ZMP QUALITY ASSURANCE. AFTER LNDG; WE CALLED THE NUMBER; AND WERE TOLD WE WERE GIVEN A L TURN; ACKNOWLEDGED A L TURN; AND TURNED R; MISSING THE OTHER ACFT BY APPROX 3 MI. THE FO MAY HAVE BEEN LAX ON CHKING ME BECAUSE; IN HIS WORDS; 'YOU'RE MORE CAREFUL THAN MOST OTHER PLTS.' I WILL START WEARING MY HEADSET; EVEN WHILE WEARING THE OXYGEN MASK. THE SOUND QUALITY FROM THE COCKPIT SPEAKERS IS NOT VERY GOOD. IF THE CTLR SAID 'L;' I TOOK IT TO MEAN 'R.' PERHAPS I'M PREDISPOSED TO TURN R. ALSO; I MAY NOT HAVE READ BACK THE CLRNC 'CROSS-COCKPIT;' SO THE FO COULD CHK MY UNDERSTANDING.