Chapter 2.3 Good For

This assignment is due 48 hours after the Chapter Test is given.

• Good Fors' solutions can be turned in anytime before 5:00 PM two days after the Chapter Test.
• Good Fors are worth 10 points of extra credit each.
• Answers must be accompanied by valid reasoning. Just like the tests, the answer alone isn't enough!
• Please enter your solution in the text area at the bottom of this page. DON'T FORGET TO GIVE YOUR NAME!

An important application of the use of sets is to determine how widespread a particular belief or opinion is among a group of people. An efficient method used by researchers to determine the extent of these beliefs is by sampling a small number people within the population. This sampling of the public is often done by polls of which the Gallup Poll, named after George Gallup, is the most famous.

The doctoral thesis of George Horace Gallup (1901 - 1984) investigated how the public reacts to advertisements and current events. After completing his Ph.D., George founded the American Institute of Public Opinion in 1935. The institute's mission was "to impartially measure and report public opinion on political and social issues of the day without regard to the rightness or wisdom of the views expressed."

Gallup's first triumph was his prediction of the winner of the 1936 presidential election between Franklin D. Roosevelt and Alfred Landon. While the majority of political insiders predicted Landon to win, Gallup correctly predicted the margin by which Roosevelt would upset Landon and win the election. The Gallup Polls have correctly predicted every presidential election since, with the exception of Harry S. Truman's victory over Thomas Dewey. Gallup had predicted that Truman would only receive 44.5% of the vote and lose, but he actually won the election with 49.9%.

The technique used by Gallup to poll the public was to take a stratified random sample of the American population. If correctly executed, he argued, a sample size of 1,500 people was sufficient to obtain reliable results.

Here is your problem. After the presidential debates of 2000, two hundred people were surveyed on who they would still consider voting for. Of these, 12 people were not considering any of the three candidates (i.e., Bush, Gore, or Nader). Seventy-eight said they were still considering Bush, 88 were still considering Gore, but 128 said they were not considering Nader. No person who was considering Gore was also considering Bush.

How many people surveyed had decided on exactly one of the three candidates?

How many people surveyed who were considering Perot were also considering either Bush or Clinton?

Don't forget to explain your answer as clearly as possible.

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