How does a scientist determine the alertness of a turtle?

Answer 1

i would imagine a scientist would do tests that show that a turtle is alert and able to respond, such as:

visual stimuli - put something near the turtle where it can see it - does it respond to the appearance of this item?
aural stimuli - make a noise that the turtle can hear - does it respond to hearing that noise?
scent stimuli - introduce a smell that the turtle can detect - does it respond?
tactile stimuli - if you touch the turtle, does it respond?
temperature stimuli - if you put something hot or cold next to it, does it respond?

there are probably standard tests based on one or more of those types - and different times associated with level of alertness. clearly a sleeping turtle might not be very alert of something placed next to it.

Answer 2

You give them the turtle agility test which is similiar to the testing given to Navy Seals, the turles excell in the water testing, are a little slow on land, do very well in underwater breathing but lay an egg in the reproduction area. They are slow but steady swimmers and make a hell of a soup.

Answer 3

Well, you expose them to different stimuli in a controlled environment.