If someone is jumping up and down in the bedroom of a private jet will the pilot be able to tell without listening? In other words, will the plane noticeably move?
That depends on how much the weight of that person force shifting (as a result of changing the center of gravity (CG)) as a ratio to the total weight force of the aircraft. If it's a tiny ratio then it will not affect the CG and thus will not change the aircraft attitude.
Depends very much on the size of the plane and the position of the jumping passenger.
For example, a Cirrus SF50 has a maximum takeoff weight of 2722kg. An overweight passenger (let's take 150kg for the example) jumping really hard can probably exert a force similar to 300kg upon landing. That's more than 10% of the gross weight of the plane. If the plane is not fully loaded, the ratio will be even bigger. So, especially if the passenger is not jumping close to the Center of Gravity of the plane, this is definitively feelable.
Take the other extreme, an Airbus Airbus A380-800. This one has a maximum takeoff weight of 575 000kg. Here the 300kg of the passenger only represents around 0.05% of the weight of the plane. The only way the pilot might feel that is if the passenger is jumping directly onto the rudder and even then I'd be doubtful.
For the sake of the argument, let's say all passengers in an A380 jump at the same time (and in a coordinated fashion, since random jumping would equal out). The plane is certified for 853 passengers. Say, every one of them weights an average of 100kg, which is a lot, then we would have 85300kg of passengers. Double that weight to get a rough estimate for the jumping impulse and now you have 170600kg, which would come close to 30% of the gross weight. Again, very feelable.