Yes, it is possible to have a 1965 Cessna 150F. True, the F model is considered a 1966 for parts purposes, however the FAA recognizes and records the date of the A/W certification. A check with the FAA Civil Aircraft Registry reveals that N1114T (the referenced aircraft in the Barnstormers ad) is serial number 15061846 and that this airframe received it?s A/W Certificate on 8/20/65.
I discovered this anomaly when my 150F was newly purchased. Interior parts were being ordered and the descriptions were just not matching up. Incidentally, my 150F is serial number 15061899 with a 9/4/65 ?birthday.? My 150 is 53 serial numbers and about 2 weeks after the 150/15X that is listed for sale. Wow, they were really cranking them out back then!