A B737-500 ON APPROACH TO AMA GOT A GPWS TERRAIN WARNING WHEN THEY DESCENDED BELOW THEIR CLEARED ALTITUDE.

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WHILE BEING VECTORED FOR AMA 22 LDA WE WERE CLRED TO 6000 FT THEN TURNED TO A 030 DEG HDG FOR A R DOWNWIND AND A DSCNT TO 5000 FT. WHILE BEING GIVEN A TURN TO BASE; WE BELIEVED WE GOT A CLRNC TO 4000 FT. LOOKING BACK ON THIS NOW; IT MAKES NO SENSE TO BE CLRED TO 4000 FT. WHILE IN THE TURN TO BASE AND A VERY SLOW DSCNT TO 4000 FT WE BROKE OUT OF THE CLOUDS AT APPROX 4400 FT. MY FO SAID HE FELT LOW AT THE SAME TIME I STARTED A CLB FOLLOWED BY A GPWS OBSTACLE WARNING. I CONTINUED THE CLB USING THE FOM TERRAIN AVOIDANCE MANEUVER DURING WHICH WE RECEIVED AN ATC RADIO CALL OF LOW ALT WARNING CLB TO 5000 FT. BY THAT TIME WE WERE LEVELING AT 5000 FT. THE APCH WAS CONTINUED UNEVENTFULLY. WE WERE CONVINCED AT LEAST DURING THE EVENT THAT WE WERE CLRED TO 4000 FT. WE WERE IN POOR WX CONDITIONS THAT WERE DETERIORATING AND IN A HIGH LEVEL OF TASK SATURATION IN THE COCKPIT. THANKFULLY WE FOLLOWED PROCS AND CORRECTED THE SITUATION. THIS APPEARS TO BE OUR MISTAKE. WE STARTED DOWN TO 4000 FT NO MATTER IF WE HEARD IT WRONG OR SET IT WRONG IN THE MCP. A FASTER REACTION TO OUR ERROR; HOWEVER WE GOT THERE; WOULD HAVE PREVENTED THE DEV AND FOLLOWING WARNINGS. THANKFULLY; ALL THE SAFETY NETS WERE WORKING AND THE MISTAKE WAS CORRECTED IN AN EXPEDITIOUS AND SAFE MANNER. WE DO BELIEVE WE HEARD AND ACKNOWLEDGED 4000 FT. AFTER TALKING TO THE AMA SUPVR; THIS APPEARS TO NOT BE THE CASE AND IN RETROSPECT; IT MAKES NO SENSE THAT WE WOULD HAVE BEEN.