You need to drive the truck and get back to us.

If the gas pedal is being operated with considerable enthusiasm and gusto,
the transmission will not shift when expected. If the gas pedal is on the
floor, the transmission will hold the gear for as long as it can tolerate
it.

I don't mean to suggest that your son pushes the pedals too hard, but if he
does press them too hard, then the result can easily be that the
transmission holds the gear longer than you might like.

If there is a fault, the OBD II Scan Tool should be able to pull it for you.
Odds favor this would trip the Check Engine light, but maybe not. You can
use the scan tool for free from Autozone stores. Depending ou where you
live, either they will pull the codes for you, or they will give you the
scan tool and you pull the codes yourself. It's very easy to pull and reset
the codes.

You will find the data port along the bottom edge of the dash board. Plug
the scan tool in and set the ignition to ON but not START. The codes will be
displayed on the scan tool. Make a list of the codes that are present, then
reset the codes.

Drive the truck and see for yourself what the conditions are that make the
transmission hold the gear for too long. Then, pull codes again and see if
there are any that are on your list from earlier.

If the transmission holds a gear to 4k on the tach, then you have to
determine if it is related to a specific gear change or all of them.

I also have a 00 F150 and mine was doing the same type thing but what i
thought to be the tranny was in fact plugs needing to be changed. Also had a
problem like that but it turned out to be the fuel filter needing to be
changed. After those fixes, runs great and has 145,000mi on it.