Powermwt & Mal H (and others), here the scoop with the alarm system as it was explained to me by a company representative when I called to complain ...
First off, the alarm is monitored by a central station however, that evening the alarm wasn't actually triggered. Instead, power went out. It seems that there is a feature when either telephone or power is cut, the alarm will sound in an attempt to fool the intruder into thinking that by cutting the phone line or shutting or the power, he has in fact triggered the alarm -- sort of a false alarm to scare somebody off.
I'm not sure if I like this feature not only because it woke us up in the middle of the night when power went out for less than a minute but if we lose power for an extended period of time, the back-up battery will be dead and if a break-in occurs them, the alarm will be worthless.