Simulating an opinion poll. A recent opinion poll showed that about 65% ofthe American

Chapter 0, Problem 10.56

(choose chapter or problem)

Simulating an opinion poll. A recent opinion poll showed that about 65% ofthe American public have a favorable opinion of the software companyMicrosoft. Suppose that this is exactly true. Choosing a person at random thenhas probability 0.65 of getting one who has a favorable opinion of Microsoft. Usethe Probability applet or your statistical software to simulate choosing many peopleat random. (In most software, the key phrase to look for is Bernoulli trials. Thisis the technical term for independent trials with Yes/No outcomes. Our outcomeshere are Favorable or not.)(a) Simulate drawing 20 people, then 80 people, then 320 people. Whatproportion has a favorable opinion of Microsoft in each case? We expect (butbecause of chance variation we cant be sure) that the proportion will be closer to0.65 in longer runs of trials.(b) Simulate drawing 20 people 10 times and record the percents in each samplewho have a favorable opinion of Microsoft. Then simulate drawing 320 people10 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.