FLC OF A DC9-50 CLBED IN RESPONSE TO A TCASII RA DURING CRUISE ONLY TO FIND OUT FROM ATC THAT THE TARGET WAS LEVEL AT A HIGHER ALT. THEIR CLB WAS STOPPED SHORTLY DUE TO THE TCASII RA STOPPED AND ATC ADVISING THAT THE ONLY TFC NEARBY WAS CONFIRMED LEVEL AT A HIGHER ALT.

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WE WERE OPERATING A FLT FROM MEM TO SAT. APPROX 20 MI S OF EMG AT FL310 WE RECEIVED A TCASII TA. OUR DISPLAY INDICATED THE INTRUDER WAS 12:30 - 1 O'CLOCK POS AND 6 MI 500 FT BELOW OUR ALT. WE CONTACTED ATC TO VERIFY AND THEN RECEIVED AN RA TO 'CLB; CLB.' WE IMMEDIATELY COMPLIED WITH THE TCASII RA SINCE WE WERE IMC AND DID NOT HAVE THE ACFT IN SIGHT. ATC SAID THAT HE DID HAVE AN ACFT IN THAT RELATIVE POS BUT HIS ALT WAS FL330. ATC ASKED THE OTHER ACFT TO VERIFY HIS ALT WAS FL330; WHICH IT WAS. THE RA CEASED AND WE STOPPED OUR CLB AT FL314. WE ARE REQUIRED TO COMPLY WITH ALL RA'S UNLESS WE CAN CONFIRM THAT IT IS UNSAFE TO DO SO; WHICH WE COULDN'T DO SINCE WE WERE IMC. EARLIER RPTS FROM OTHER ACFT WERE OF SEVERE TURB WITH 1 ACFT RPTING AN ALT EXCURSION OF 1000 FT. WITH THIS IN MIND; WE HAD EVERY REASON TO BELIEVE OUR TCASII. IT IS NOW OBVIOUS THAT OUR TCASII MISREAD THE OTHER ACFT'S ALT AND ISSUED A FALSE AND DANGEROUS RA. ATC SAID THAT THE OTHER ACFT'S MODE C INDICATED FL330 THE ENTIRE TIME.