Do dance coaches score students that had been trained at a rival dance studio less at competitions due to bias? Two samples were randomly selected from the British Ballroom competitive circuit. The 1st sample were 50 students who had been trained at a rival dance studio and the 2nd sample consisted of 50 students that had been previously trained by a prominent dance coach and judge. The total score for each student was calculated to find a mean for each group.

If ₁and ₂ represent the mean dance scores for each group respectively for rival coached vs self-coached, which of the following is the appropriate pair of hypotheses in this case?