B737-300 IS CLRED TO CROSS KAYLA AT 15000 FT BUT PF THOUGHT IT WAS 11000 FT. THE WRONG ALT HAD BEEN ENTERED IN THE ALT ALERT. ATC RECLRED THEM TO 13000 FT.

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OUR FLT WAS CRUISING AT FL240 INBOUND TO STL FROM MCI. STL WAS EXPERIENCING BAD WX AND WE WERE BEING VECTORED MANY TIMES; DSNDED AND SLOWED DOWN. THERE WAS A LOT OF RADIO TFC; WITH THE UNUSUAL INCREASE IN WORKLOAD IN THE COCKPIT; AS WELL AS IN ATC. WE NEXT RECEIVED A FINAL VECTOR TO INTERCEPT THE TRAKE 7 STAR WITH A MULTIPLE DSCNT CLRNC TO CROSS AN 11 NM DME FIX (THE SAME SPOT AS THE DEPICTED INTERSECTING KAYLA). THE CLRNC WAS TO DSND TO FL200 WITH A PLT'S DISCRETION TO CROSS 11 DME AT 15000 FT. I WAS THE PF; MY FO WAS WORKING THE RADIOS AND READ BACK THE CLRNC THE WAY HE HEARD IT. UNFORTUNATELY; MY FO SET THE WRONG ALT (20000 FT) IN THE MCP ALT ALERTER; THEN WENT OFF FREQ TO GET THE NEW ATIS. WHEN THE ALERTER SOUNDED I DISCOVERED FL200 SET IN THE ALT WINDOW OF THE ALERTER. I THEN CONFIRMED WITH HIM IF WE HAD 'BEEN CLRED ON DOWN;' AS I THOUGHT WE HAD BEEN; AND HE REPLIED YES. I LOOKED AT THE STAR INTXN ALT AND RESET THE MCP ALT ALERTER TO 11000 FT AND CONTINUED THE DSCNT. AT APPROX 13300 FT THE CTLR ASKED US OUR ALT; WE ANSWERED AND WERE TOLD WHAT HE HAD WANTED WAS 15000 FT. BUT BEFORE WE COULD REPLY OR EVEN CLB BACK TO 15000 FT; THE CTLR TOLD US TO JUST STAY AT 13000 FT. HE THEN SAID IT WAS NO PROB AND TO CALL APCH ON THE NEXT FREQ. THERE WAS NO TFC CLOSE TO US AND THE REST OF THE FLT WAS UNEVENTFUL. TO ME THE PROB WAS CAUSED BY A DEV FROM OUR SOPS AND POOR CREW COM. HAD THE MCP ALT ALERTER BEEN SET PROPERLY THE FIRST TIME OR I CAUGHT THE DEV IN SETTING THE ALERTER; THIS PROB WOULD NOT HAVE AROSE. PROPER PHRASEOLOGY WOULD HAVE HELPED ALSO.