Under clause 40.2, the tests and inspections which either Party is to do have to be stated in the Works Information. Presumably, if allocated to the Employer then it is the Supervisor who does them on their behalf. So unless their is “may” or equivalent word, the Supervisor does not contractually have the option to cherry pick which tests and inpsections he is to do.
However, if the test or inspection is allocated to the Contractor, then under the last sentence of clause 40.3 “the Supervisor MAY watch any test done by the Contractor.” So in terms of observing any of the tests allocated to the Contractor, the Supervisor may indeed ‘cheery pick’.