Whenever Tommy has a babysitter and asks to stay up past his bedtime, the babysitter lets him. Whenever Tommy asks his parents to let him stay up past his bedtime, they do not let him. As a result, Tommy only asks the babysitter if he can stay up past his bedtime. The presence of the babysitter at bed time is referred to as a(an) for asking to stay up late:

discriminative stimulus        

Explanation:

In psychology, the discriminative stimulus is determined as one of the precursor stimuli that is supposed to have a stimulus control over a specific behavior due to the fact that the behavior was formerly reinforced in the presence of that particular stimulus in the past. In other words, it tends to set the event for specific behaviors that have already been reinforced in its presence in the "past".

As per the question, the mentioned statement represents the discriminative stimulus.

answer; utilitarian;