Final answer:
The sampling in this scenario is dependent because the mental health of each patient is directly related to the category they belong to (with or without narcolepsy).
Step-by-step explanation:
The sampling in the given scenario is dependent. The researcher wants to compare the mental health of patients with and without narcolepsy. She obtains a random sample of 626 patients from each category and determines each patient's mental health. Since the mental health of each patient is directly related to the category (with or without narcolepsy) they belong to, the sampling is dependent.