Simulating an opinion poll. A 2009 opinion poll showed that about 40% of the American public have very little or no confidence in big business. Suppose that this is exactly true. Choosing a person at random then has probability 0.40 of getting one who has very little or no confidence in big business. Use the Probability applet or statistical software to simulate choosing many people at random. (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.)

Required:

(i) Simulate drawing 20 people, then 80 people, then 320 people. What proportion have very little or no confidence in big business in each case? We expect (but because of chance variation we can't be sure) that the proportion will be closer to 0.40 in longer runs of trials.

(ii) Simulate drawing 20 people 10 times and record the percents in each sample who have very little or no confidence in big business. 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 samples of size 320 to be more predictable (less variable) than the results of samples of size 20. That is "long-run regularity" showing itself.