In a study comparing individual performance with group performance, groups consistently outperformed the best of the individuals. The task was a letters-to-numbers problem in which an arithmetic problem was presented, substituting a letter in place of each digit. Participants had to determine which letters corresponded to each number. Three-person groups competed with individuals and scores were compared for the groups and the best of the individuals. The dependent variable was the number of trials needed to solve each problem. The following data are similar to those obtained in the study.

Groups Individuals

n=15 n = 15

x bar = 3.8 x bar = 4.7

SS= 15.4 SS= 18.2

Provide suitable hypotheses for an independent-measures t-test.