A nine-year-old tested professional touch therapists. Using a cardboard partition, she held a hand above one of the therapist's hands, and the therapist was asked to identify the hand that was chosen. What type of study is this? What are the variables of interest?

Observational study.

The variable which is of interest is the result of either correct or incorrect for each trial.

Explanation:

In Observatory study, researchers observe or measure characteristics of the subjects, but do not attempt to influence or modify these characteristics. As in this case, the study type clearly points at observational study as the aim is only to bxerve the therapist with  no attempt to influence the outcome.