1. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Chapter 11 Understanding Randomness

2. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 11- 2 Why Be Random? What is it about chance outcomes being random that makes random selection seem fair? Two things: Nobody can ____________ the outcome before it happens. When we want things to be fair, usually some underlying set of outcomes will be __________ ____________.

3. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 11- 3 Why Be Random? (cont.) Statisticians don’t think of __________________ as the annoying tendency of things to be ________________ or ________________. Statisticians use _________________ as a tool. But, truly random values are surprisingly hard to get…

4. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 11- 4 It’s Not Easy Being Random

5. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 11- 5 It’s Not Easy Being Random (cont.) It’s surprisingly difficult to generate random values even when they’re ____________ ____________. __________________ have become a popular way to generate random numbers. Even though they often do much better than humans, computers can’t generate truly ___________ _________________ either. Since computers follow programs, the “random” numbers we get from computers are really ____________________________.

6. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 11- 6 It’s Not Easy Being Random (cont.) There are ways to generate random numbers so that they are both ____________ ___________ and ___________ _______________. The best ways we know to generate data that give a ______ and ______________ picture of the world rely on randomness, and the ways in which we draw conclusions from those data depend on the randomness, too.

7. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 11- 7 Using a random number table Assign each outcome a ___________ _________ Select a _______________ ___________ in the list of random numbers _____________ the numbers to cover the range of values i.e. 2 digit numbers, 3 digit numbers, etc. Note the results. Be sure to distinguish whether __________ are allowed and what to do with numbers ____________ the range.

8. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 11- 8 2217726304387410092537086270581 Use the above chart to simulate A) B) C) Repeat using the calculator Store 25 into rand so we all have the same results

9. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 11- 9 Practice p. 266

10. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 11- 10 Assignment P.266 #1-3, 6-8, 10-11

11. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 11- 11 A Simulation A _________________ consists of a collection of things that happen at random. The most basic event is called a ___________ of the simulation. Each component has a set of ____________ _______________, one of which will occur at random.

12. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 11- 12 A Simulation (cont.) The sequence of events we want to investigate is called a _________. Trials usually involve ______________ _______________. After the trial, we record what happened—our ______________ _______________. There are seven steps to a simulation…

13. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 11- 13 Simulation Steps 1.Identify the component to be _____________. 2.Explain how you will __________ the ___________. 3.Explain how you will __________ the _______. 4.State clearly what the ___________ ______________ is. 5.Run several _________. 6.Analyze the ____________ ______________. 7.State your _________________ (in the context of the problem, as always).

14. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 11- 14 Just Checking The baseball World Series consists of up to seven games. The first two are played at one team’s home park, and the final two (if needed) are played back at the first park. Records over the past century show that there is a home field advantage; the home team has about a 55% chance of winning. Is it an advantage to play the first two games on you home field? Or would you rather have the middle three games at home with the opportunity to win it all? In other words, do the two teams have an equal chance to win the four games needed to win the World Series? 1. What is the component to be repeated? 2. How will you model the outcome? 3. How will you simulate the trial? 4. What is the response variable? 5. How will you analyze the response variable?

15. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 11- 15 Practice p. 267 #11

16. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 11- 16 What Can Go Wrong? Don’t overstate your case. Always be sure to indicate that future results will not ______________________________. Model the __________ ___________ accurately. Run enough __________.

17. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 11- 17 What have we learned? A simulation model can help us investigate a question for which: many _____________ are possible, we can’t (or don’t want to) collect ______, and a ___________________ ___________ is hard to calculate. We base our simulations on __________ values. Like all models, simulations can provide us with useful insights about ______________________.

18. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 11- 18 Assignment P. 267 #*19, 24, 28, 30, 33, *35