Simulating an opinion poll. A recent opinion poll showed that about 59% of the American public approve of labor unions.3 Suppose that this is exactly true. Choosing a person at random then has probability 0.59 of getting one who approves of labor unions. Use the Probability applet or your statistical software to simulate choosing many people independently.

(In most software, the key phrase to look for is

“Bernoulli trials.” This is the technical term for independent trials with Yes/No outcomes. Our outcomes here are “favorable”

or not.)

(a) Simulate drawing 20 people, then 80 people, then 320 people.

What proportion approve of labor unions in each case? We expect (but because of chance variation we can’t be sure) that the proportion will be closer to 0.59 in larger runs.

(b) Simulate drawing 20 people 10 times and record the percents in each trial who approve of labor unions. Then simulate drawing 320 people 10 times and again record the 10 percents. Which set of 10 results is less variable?We expect the results of larger trials to be more predictable (less variable) than the results of smaller trials. That is “long-run regularity” showing itself.