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Copyright © 2010 Pearson Education, Inc. Slide 11 - 1 A small town employs 34 salaried, nonunion employees. Each employee receives an annual salary increase of between $500 and $2,000 based on a performance review by the mayors staff. Some employees are members of the mayors political party, and the rest are not. Students at the local high school form two lists, A and B, one for the raises granted to employees who are in the mayors party, and the other for raises granted to employees who are not. They want to display a graph (or graphs) of the salary increases in the student newspaper that readers can use to judge whether the two groups of employees have been treated in a reasonably equitable manner. Which of the following displays is least likely to be useful to readers for this purpose? a. Back-to-back stemplots of A and B b. Scatterplot of B versus A c. Parallel boxplots of A and B d. Histogram of A and B that are drawn to the same scale e. Dotplots of A and B that are drawn to the same scale.

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Copyright © 2010 Pearson Education, Inc. Slide 11 - 2 A small town employs 34 salaried, nonunion employees. Each employee receives an annual salary increase of between $500 and $2,000 based on a performance review by the mayors staff. Some employees are members of the mayors political party, and the rest are not. Students at the local high school form two lists, A and B, one for the raises granted to employees who are in the mayors party, and the other for raises granted to employees who are not. They want to display a graph (or graphs) of the salary increases in the student newspaper that readers can use to judge whether the two groups of employees have been treated in a reasonably equitable manner. Which of the following displays is least likely to be useful to readers for this purpose? a. Back-to-back stemplots of A and B b. Scatterplot of B versus A c. Parallel boxplots of A and B d. Histogram of A and B that are drawn to the same scale e. Dotplots of A and B that are drawn to the same scale.

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Copyright © 2010 Pearson Education, Inc. Chapter 11 Understanding Randomness

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Copyright © 2010 Pearson Education, Inc. Slide 11 - 4 Why Be Random? What is it about chance outcomes being random that makes random selection seem fair? Nobody can guess the outcome before it happens. When we want things to be fair, usually some underlying set of outcomes will be equally likely (although in many games some combinations of outcomes are more likely than others).

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Copyright © 2010 Pearson Education, Inc. Slide 11 - 5 Why Be Random? (cont.) Example: Pick heads or tails. Flip a fair coin. Does the outcome match your choice? Did you know before flipping the coin whether or not it would match?

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Copyright © 2010 Pearson Education, Inc. Slide 11 - 6 Its Not Easy Being Random Computers have become a popular way to generate random numbers. Since computers follow programs, the random numbers we get from computers are really pseudorandom. Pseudorandom values are good enough for most purposes.

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Copyright © 2010 Pearson Education, Inc. Slide 11 - 7 TI – Tips Generating Random Numbers MATH PRB 5:randInt(first integer, last integer, number of integers)

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Copyright © 2010 Pearson Education, Inc. Slide 11 - 8 Examples: 1. Simulate rolling two dice. Roll the dice 10 times. 2. Cereal boxes contain three different sports cards. 20% of the cards are Tiger Woods, 30% are David Beckham and the rest are Serena Williams. Simulate opening a box of cereal to find out what type of sports card was inside. 3. Using the cereal box example, find out how many boxes of cereal you would have to open to get one card of each type. 4. Repeat example 3, 20 times and find the average number of boxes of cereal you would have to open to find all three sports cards.

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Copyright © 2010 Pearson Education, Inc. Slide 11 - 9 A Simulation We are going to use random numbers to simulate reality. The sequence of events we want to investigate is called a trial. The basic building block of a simulation is called a component. Trials usually involve several components. After the trial, we record what happenedour response variable. There are seven steps to a simulation…

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Copyright © 2010 Pearson Education, Inc. Slide 11 - 10 Simulation Steps 1.Identify the component to be repeated. 2.Explain how you will model the components outcome. 3.Explain how you will combine the components to model a trial. 4.State clearly what the response variable is. 5.Run several trials. 6.Collect and summarize the results of all the trials. 7.State your conclusion.

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Copyright © 2010 Pearson Education, Inc. Slide 11 - 11 Example: You take a quiz with 5 multiple choice questions. After you studied, you estimated that you would have about a 75% chance of getting any individual question right. What are your chances of getting them all right? Use at least 20 trials. Plan: State the problem. Identify the important parts of your simulation. Components: Identify the components. Outcomes: State how you will model each component using equally likely random digits. Trial: Explain how you will combine the components to simulate a trial. Response Variable: Define your response variable. Mechanics: Run at least 20 trials. Analyze: Summarize the results across all trials to answer the initial question.

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Copyright © 2010 Pearson Education, Inc. Slide 11 - 12 What Can Go Wrong? Dont overstate your case. Beware of confusing what really happens with what a simulation suggests might happen. Model outcome chances accurately. A common mistake in constructing a simulation is to adopt a strategy that may appear to produce the right kind of results. Run enough trials. Simulation is cheap and fairly easy to do.

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Copyright © 2010 Pearson Education, Inc. Slide 11 - 13 What have we learned? How to harness the power of randomness. A simulation model can help us investigate a question when we cant (or dont want to) collect data, and a mathematical answer is hard to calculate. How to base our simulation on random values generated by a computer, generated by a randomizing device, or found on the Internet. Simulations can provide us with useful insights about the real world.

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Copyright © 2010 Pearson Education, Inc. Slide 11 - 14 Homework: Pg. 265 1-27 odd 17, 19, and 23, I expect to see your trials!!!

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