A B737-500 CAPT DID NOT CATCH HIS FO'S PROGRAMMING MISTAKE; CAUSING THEM TO UNDERSHOOT THEIR CRUISE ALT.

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FO SET UP FMC AT THE GATE. I VERIFIED THE RTE AND PERFORMANCE DATA. NOTED THE CRUISE ALT HE HAD SET AND CHKED THAT THE PRESSURIZATION SYS WAS SET FOR THE SAME ALT. I DID NOT XCHK THE CRUISE ALT WITH THE PDC; AS IS MY USUAL PRACTICE. I BELIEVE THAT I HAD RELAXED MY VIGILANCE A BIT BECAUSE THE FO (WHOM I WAS FLYING WITH FOR THE VERY FIRST TIME AND FIRST LEG) FLEW THE SAME ACFT I HAD FLOWN IN THE MIL AND WE KNEW SOME OF THE SAME PEOPLE. AT ANY RATE; HE HAD SET EVERYTHING UP FOR FL310; WHILE THE PAPERWORK INDICATED FL350. THIS WAS OVERSIGHT #1. DURING OUR CLBOUT; ZNY CLRED US TO FL350; WHICH I SET IN THE ALT WINDOW. HOWEVER; THE AUTOPLT LEVELED US OFF AT FL310. I'M NOT CERTAIN HOW LONG WE WERE AT FL310 WHEN THE CTLR ASKED US TO VERIFY OUR ALT. AT THIS POINT I NOTED THE ALT WINDOW SET FOR FL350 BUT WE WERE LEVEL AT FL310. I RESPONDED TO THE CTLR; 'WE'RE AT FL310; BUT YOU WANTED US AT FL350; RIGHT?' HE RESPONDED; 'AFFIRMATIVE;' AND I INITIATED A CLB TO FL350; REPROGRAMMING THE FMC. I CHKED THE PAPERWORK AT THIS POINT AND NOTED EVERYTHING CONSISTENT WITH FL350. I'M STILL NOT SURE WHY THE FO SET UP EVERYTHING FOR FL310. CONTRIBUTING FACTORS MAY BE LOWER ALERTNESS DUE TO XA00 WAKE-UP AFTER 4 HRS SLEEP FOR AN XC45 SHOW TIME AND 2 HR DRIVE TO ARPT. ALSO; AS PREVIOUSLY STATED; I HAD LOWERED MY GUARD SLIGHTLY DUE TO THE FO'S BACKGND. AND THIRDLY; WE WERE PROBABLY TALKING DURING THE CLB ABOUT THE MIL; FAMILY; ETC. DOING THE 'GETTING TO KNOW YOU' ROUTINE. AS A RESULT; I DID NOT CATCH THE COMPUTER STOPPING THE CLB PREMATURELY UNTIL THE ATC QUERY.