Press and release reset with the board plugged in, and look for a triple-blink pattern. The bootloader only runs after a reset, not at power on, so you won't see a blink from the bootloader if you just apply power, so the test others were recommending above is not conclusive.
(this is true of AVRs with hardware bootloader support, like all official boards and most third party boards based on atmega-series micros; third party boards that don't have hardware bootloader support, but do use a bootloader, like some ATTiny boards, will flash on power on)