I understand that a choked nozzle removes the dependance on the static pressure $p_a$ because if M>1 in a choked nozzle then waves cannot travel upstream in the nozzle (as explained in the paragraph below from Jet Propulsion, Cumpsty). By removing this dependance from the outside, one can perform dynamic scaling to get mass flow rate, etc. at other altitudes.
My question is the following: In the case of an engine on a static test bed, does the nozzle need to be choked both at cruise and on a static test bed? Why or why not? Is it even possible for the same engine to be choked at both?
ADDED EXAMPLES These problems in the book illustrate this paragraph, in both there's a choked nozzle at cruise, from which we can or cannot perform dimensional scaling at static conditions. I solved both of the exercises by following the instructions/using the equations. In 8.2, the dynamic scaling can be performed, but in 8.4, it cannot. I am unsure as to why that is the case.