A PhD student has the impression he must find significant results if he wants to defend his dissertation successfully. He wants to show a difference in social awareness, as measured by his own scale,...

A PhD student has the impression he must find significant results if he wants to defend his dissertation successfully. He wants to show a difference in social awareness, as measured by his own scale, between a normal group and a group of ex-delinquents. He has a problem, however. He has data to suggest that the normal group has a true mean of 38, and he has 50 of those participants. The student has access to either 100 high-school graduates who have been classed as delinquent in the past, or to 25 high-school dropouts who have a history of delinquency. He suspects that the high-school graduates come from a population with a mean of approximately 35, whereas the dropout group comes from a population with a mean of approximately 30. He can use only one of these groups. Which should he use? Assume the standard deviation is the same for all groups.