1. Section 2.2 How Samples Vary

2. CNN / USA Today / Gallup Poll Jan. 20-22, 2006 www.poll.gallup.com
Which comes closest to your view -- [ROTATED: Iran poses an immediate threat to the United States, Iran poses a long-term threat to the U.S., but not an immediate threat, or Iran does not pose a threat to the United States at all]?

3. Results based on telephone interviews with 1,006 national adults, aged 18 and older:
The poll finds that 19% of Americans view Iran as an "immediate" threat to the United States (this question was asked before any mention of a possible nuclear weapons program in Iran), with another 65% seeing that Middle Eastern country as a "long-term" threat. Just 12% of Americans believe Iran poses no threat.

4. How can we be sure that the sample proportions from ONE sample reflect the views of all Americans?
Because we know (or will shortly know) that although sample proportions vary, they vary according to a predictable pattern.

5. Back to the Penny Example
Last week we were interested in estimating the proportion of heads that would land “heads up” if we flipped a coin many, many times.
To estimate this population proportion, , we each randomly sampled 25 pennies from the population of all pennies and individually computed the proportion of heads, , in our own particular sample.

6. How did our values vary?
Did all of the student get the same sample proportion after flipping the coin 25 times?
Show of hands
How many students got a value under 30%?
Between 30%-70%?
Greater than 70%?

7. So although we didn’t ALL get the same sample proportion there does seem to be some similarities in each of our values.
Let’s look for patterns in the sample proportion values.

8. Histogram of 58 students’ values Each is based on flipping a coin 25 times and finding the proportion of heads in the sample.