[RichardJ]

Depress the pedal several times and then hold the pedal down. Start the engine. The pedal should go down as you are pushing with the same pressure. If the pedal does not move you could have a vacuum leak before the booster or the booster could be bad.

Second test.
Depress the brake pedal with the engine running. Turn the engine off. The pedal should stay the same. If the pedal moves up the booster is bad.