Suppose you wish to test the hypothesis that the students at university A are, on the average, younger than students at university B. A random sample of 80 students is drawn from university A and it is found that their mean age is 22.1 with a standard deviation of 2.6, while a random sample of 64 students from university B is found to have a mean of 23.5 with a standard deviation of 2.3. The samples do indicate that university A's students are younger than university B's; but is the difference significant at the 1% level?