C172 PLTS HAVE FUEL STARVATION AND LAND ON INTERSTATE HWY.

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I BELIEVE THE FAILURE WAS DUE TO FUEL EXHAUSTION. MR X HAD AGREED TO HELP ME WITH INST TRAINING. HE IS A HIGHLY RESPECTED EXAMINER IN THE AREA. I HAD CHKED THE FUEL LEVEL AND FOUND THE TANKS FULL DURING THE PREFLT. I ALSO USED MY INDEX FINGER AND FELT FUEL AT THE POINT OF JUST BELOW MY SECOND KNUCKLE. IT WAS GETTING DARK AT THAT TIME. I INFORMED MR X PRIOR TO DEP THAT THIS WAS AN UNFAMILIAR ACFT TO ME. HE CALLED GND FOR AN IFR RELEASE TO ZZZ1 FROM ZZZ. HE COPIED AND REPEATED THE CLRNC. WE TAXIED TO THE RUNUP AREA. ALL WAS NORMAL AND DEPARTED. THE TACHOMETER TO ZZZ1 WAS 1.7 HRS. WE TOOK A BREAK SO MR X COULD BRIEF ME. HE ASKED ME TO CHK FUEL AFTER THE GND TRAINING. I INFORMED MR X WE HAD JUST BELOW 1/2 TANK PER SIDE. HE THOUGHT OUT LOUD FOR A MOMENT WITH TIME AND FUEL CONSUMPTION FIGURES AND STATED WE HAD ENOUGH FUEL. I DIDN'T DISPUTE THIS WHEN IT SEEMED ODD TO USE MORE THAN 1/2 TANK PER SIDE TO GET TO ZZZ1. WE DEPARTED IFR TO ZZZ. DURING VECTORING FOR THE ILS FOR RWY 28R AT ZZZ; THE ENG SPUTTERED. MR X TOOK THE CTLS. HE SET MIXTURE RICH AND APPLIED CARB HEAT. IT SPUTTERED A WHILE LONGER WHILE HE SLID THE MIXTURE CTL BACK AND FORTH. THE ENG REGAINED PWR AND THE PROB WAS EXCUSED AS POSSIBLE CARB ICING; AS WE JUST DSNDED THROUGH A LAYER OF CLOUDS. AT THIS POINT; WE WERE ALREADY ESTABLISHED ON THE LOC AND WERE INTERCEPTING THE GS. A FEW MINS HAD PASSED WITH NO FURTHER OCCURRENCE OF TROUBLE. TRACON INFORMED US TO CLOSE THE FLT PLAN AFTER LNDG DUE TO THE TWR WAS NOT OPEN. THIS WAS AT APPROX XD30. MR X STILL HAD THE CTLS AND THE ENG SPUTTERED BRIEFLY AND QUIT COMPLETELY. MR X IMMEDIATELY DECLARED AN EMER. WE INFORMED TRACON WE COULD NOT MAKE THE RWY; INFORMED THEM THE INTERSTATE WAS OUR CHOICE IF IT WERE CLR AND LOST CONTACT. MR X MADE THE CHOICE AND PUT THE ACFT DOWN ON THE INTERSTATE; S OF ZZZ. WE EXITED THE ACFT SAFELY AND BEGAN WARNING APCHING TFC. IN RETROSPECT; I SHOULD HAVE DISPUTED THE FUEL LEVEL IN ZZZ1. I COULD HAVE SUGGESTED AN ALTERNATE BECAUSE I WAS CONSTANTLY GAZING AT THE DIMINISHING LEVELS ON THE GAUGES. DURING THE FIRST SPUTTER; WE COULD HAVE MADE ZZZ2 ARPT. BUT ALL THE WHILE; I FELT MY JUDGEMENT WAS IRRELEVANT TO HIS LEVEL OF SKILL. I SHOULD AND WILL NOW ALWAYS TRUST WHAT I FEEL AND QUESTION WHAT DOES NOT MAKE SENSE TO ME. TOTAL TACHOMETER TIME WAS 3.6 HRS. I AM NOT IFR RATED YET. THIS WAS AN INSTRUCTIONAL FLT FOR ME.