A common belief holds that the larger the population for which an estimate is being made, the larger the sample needs to be. By this logic, consider the statistics regarding the repeal of the U.S. "Don't Ask, Don't Tell" policy prohibiting homosexuals from serving in the military. A much larger sample would be needed to estimate the proportion of the U.S. Army's 2.4 million active duty and reserve personnel who approved the repeal than would be needed to estimate the proportion of the Marine Corp's 200,000 personnel who felt the same way. Is this correct? Why or why not?