1. A consumer advocate wishes to know whether children are affected by Joe Camel cigarette ads. He designs a study of the reactions of 50 children to the ads. What is the sample and what is the population?
He wishes to know something about all children, and so this rather vaguely specified group is his population. The 50 children he studied are his population.
2. A polling agency samples 1000 "likely voters" and concludes that 40% of all voters will vote for Candidate A. What's the sample and what's the population?
This is actually a pretty vague population. It consists of all of those who are "likely" to vote. Not all registered voters, and not those who will actually vote. The sample consists of the 1000 people who were actually polled. The goal here is to predict the outcome of an election, and so you only wish to question people for whom you have good reason to believe they will vote.
3. There is currently a debate between the two main political parties and including the Executive Branch as to how the U.S. population Census should be carried out. Many Republicans say that the Constitution insists that the Census be an "enumeration", which they define as a headcount of all people in the U.S. and all U.S. citizens. If this were done, what would be the sample and what would be the population?
An enumeration as described above would produce a list of numbers that was both a sample and a population. The population here is all people living in the US and all US citizens. In practice, it is impossible to get a list that has everyone on it, so in reality the Census counts fewer people than are in the population, but is often assumed to be a close copy of the population. Just how close a copy is part of the debate going on now about Census 2000.