B767. N90 APCH CTLR CLRED THE ACFT TO 3000 FT; WHEN HE INTENDED TO CLR THE ACFT TO 4000 FT.

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ON DSCNT TO JFK AT 8000 FT; NEW YORK APCH GAVE US A CLRNC TO 3000 FT WHICH THE CAPT READ BACK AND THEN FOLLOWED ACR PROC BY SETTING 3000 FT IN THE ALT WINDOW AND HE THEN POINTED TO IT. I (FO) ACKNOWLEDGED HEARING THE ATC CTLR'S INSTRUCTION BY ALSO POINTING TO 3000 FT AND SAYING ALOUD '3000 FT' AT WHICH TIME I CONTINUED THE DSCNT TO 3000 FT. AT APPROX 3100 FT AND I BELIEVE AFTER A FREQ CHANGE WHERE THE ALT LEAVING AND CLRED TO WAS READ BACK; THE ACT CTLR TOLD US WE WERE ONLY CLRED TO 4000 FT TO WHICH WE REPLIED THAT WE HAD BEEN CLRED TO 3000 FT. WE WERE THEN TOLD TO SLOW TO 190 KTS AND GIVEN RWY 22R FOR LNDG; BUT NO VECTOR WAS GIVEN UNTIL LATER FOR THE APCH. NO FURTHER DISCUSSION WAS MADE BTWN THE CTLR AND OUR ACFT REGARDING THE DISAGREEMENT ON THE ALT; AND WE MADE A NORMAL UNEVENTFUL APCH AND LNDG. THE CTLR WAS EXTREMELY BUSY; AND I BELIEVE THAT HE INADVERTENTLY GAVE US AN ALT THAT HE DID NOT MEAN TO. WE COMPLIED WITH ALL OF THE CTLR'S INSTRUCTIONS. THE CAPT AND I FOLLOWED COMPANY ACR PROCS AND PRACTICES TO THE LETTER AND I FEEL THIS WAS AN ATC RATHER THAN A PLT ERROR. SUPPLEMENTAL INFO FROM ACN 582822: NOTE: CTLRS WERE EXTREMELY BUSY AND I BELIEVE THAT FIRST CTLR CLRED US TO 3000 FT INSTEAD OF 4000 FT BY MISTAKE. PRECEDING ACR Y FLT WAS AT 4000 FT AND SLIGHTLY L OF OUR FLT PATH DURING PHASE IN QUESTION AND IT IS PROBABLE THAT FIRST CTLR ISSUED ERRONEOUS CLRNC OR WRONGLY ADVISED NEXT CTLR OF OUR CLRED ALT. ACR SOP FOLLOWED THROUGHOUT ENTIRE APCH.