AT ABOUT 1458 PST, THE AIRCRAFT ENCOUNTERED MODERATE TO SEVERE CLEAR AIR TURBULENCE FOR A PERIOD OF 8 TO 10 SECONDS WHILE CLIMBING THROUGH 35,500 FT. SEVEN PASSENGERS AND SEVEN FLIGHT ATTENDANTS RECEIVED MINOR INJURIES. THE SEAT BELT SIGN HAD BEEN TURNED ON BEFORE TAKEOFF AND HAD REMAINED ON THROUGHOUT THE ENCOUNTER. OF THE PASSENGER WHO WERE INJURED, FOUR STATED THEIR SEAT BELTS WERE OFF, TWO STATED THEIR BELTS WERE LOOSE AND ONE HAD DISREGARDED THE SIGN AND WAS IN THE LAVATORY. THE INJURED FLIGHT ATTENDANTS WERE PREPARING FOR CABIN SERVICE AND WERE NOT RESTRAINED. A REVIEW OF THE AIRLINE'S COMPUTER GENERATED FLIGHT PLAN DATA REVEALED THAT THE MAXIMUM GENERATED TURBULENCE INDEX PREDICTED WAS LIGHT. THERE WAS A CAT SIGMET, VALID FOR THE PERIOD, WHICH REPORTED MODERATE TURBULENCE AT FLIGHT LEVEL 360 TO 370 OVER SOUTHERN CALIFORNIA IN THE HECTOR-THERMAL AREA.