Do dance coaches score students that they have previously taught higher at competitions due to bias? Two samples were randomly selected from the British Ballroom competitive circuit. The first sample consisted of 50 students that had been previously trained by a prominent dance coach and judge and the second sample were 50 students who had been trained at a rival dance studio. The total score for each student was calculated to find a mean for each group.

If µ1and µ2 represent the mean dance scores for each group respectively for self-coach vs. rival coached, which of the following is the appropriate pair of hypotheses in this case?