Final answer:
A test of matched pairs is the appropriate design for testing the significance of the difference between the means when the freshmen competed with the sophomores to see who could raise the most money by recycling.
Step-by-step explanation:
The appropriate design for testing the significance of the difference between the means when the freshmen competed with the sophomores to see who could raise the most money by recycling and each freshman was paired with a sophomore of the same gender is a test of matched pairs.
In a test of matched pairs, subjects are matched in pairs and differences are calculated. The differences between the paired observations are used as the data for the hypothesis test. The population mean for the differences is then tested using a Student's-t test for a single population mean with n - 1 degrees of freedom, where n is the number of differences.
The test statistic (t-score) is used to determine the significance of the difference between the means. If the calculated t-score is greater than the critical value from the t-distribution at the desired level of significance, then the difference between the means is statistically significant.