Final answer:
The appropriate design for testing the significance of the difference between the means in this scenario is a paired samples t-test.
Step-by-step explanation:
The appropriate design for testing the significance of the difference between the means in this scenario is a paired samples t-test. In a paired samples t-test, the subjects are matched in pairs and the differences between their measurements are calculated. These differences are then used to test the null hypothesis that there is no difference between the means of the two classes.