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Understanding Randomness

Understanding Randomness. Chapter 11. Multiple Choice Review Quiz. Number your paper from 1 – 20. 1. 11. 2. 12. 3. 13. 4. 14. 5. 15. 6. 16. 7. 17. 8. 18. 9. 19. 10. 20. Answer key: check your work.

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Understanding Randomness

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  1. Understanding Randomness Chapter 11

  2. Multiple Choice Review Quiz • Number your paper from 1 – 20. 1. 11. 2. 12. 3. 13. 4. 14. 5. 15. 6. 16. 7. 17. 8. 18. 9. 19. 10. 20.

  3. Answer key: check your work Record your number correct on the board, then determine the class mean for number correct

  4. Design a simulation: Ex. 1 • Plan a simulation using a die to estimate the number correct in the case of total guessing a 20 question quiz with 5 choices each.

  5. Design a simulation: example • Plan: Using 6-sided die, let • Rolling 1: correct answer • Rolling 2 – 5: incorrect answer • 6 : ignore

  6. Terminology for our simulation • A component of the simulation is one roll • The outcome is the individual result of a component (correct or incorrect in this case) • A trial will be complete when I have 20 “answers” • We need to perform multiple trials (repetition) for a simulation (at least 20 to 30). • The response variable will be the number correct for each trial • After we finish, we’ll calculate the response statistic (in this case the mean of our response variables)

  7. Demo of a trial • Now, each of you perform 2 entire trials. • Calculate response statistic for all our trials

  8. Ex. 2 • If someone told you this quarter is biased towards landing heads, you’d probably be skeptical. What would you do? • How many times of tossing it would be enough? • Would 3 times in a row of getting heads convince you it is biased? (Why or why not?) • Would 7 out of 10 be convincing? • We are looking for behavior that is inconsistent with our belief that heads should show up 50% of the time.

  9. Imagine 100 tosses . . . • Would 54 heads out of 100 convince you its biased? • 60 out of 100? • 95 out of 100? • 80 out of 100? • 70? • Make a personal decision rule: What would it take to convince you that the coin is unfair? (Write in down.) • Record your personal numbers on the board • Where should we draw the line between reasonable behavior and an outcome so strange that we think it proves something wrong?

  10. Simulate using calculators • As a one-time operation…”seed” your calculators • Last 4 digits of your phone number STO rand • randInt(0,1) is a way of simulating a coin toss (0 = tails 1=heads) • randInt(0,1,5) to simulate tossing 5 coins; try a few… • sum(randInt(0,1,100)) will give you the total heads in a simulation of 100 coin tosses • Record what you get for 5 or 6 sum(randInt(0,1,100)) • What’s the highest we’re seeing?

  11. We can now make a good decision rule for testing coins. Any coin that landed heads more than 65 (even 60?) times out of 100 would be suspect. • *Even after actually tossing the mystery coin 100 times and declaring it okay or biased, we wouldn’t know for sure. • A fair coin could show 75 heads. • A biased coin could come up 50-50.

  12. Such is the nature of statistics—that branch of mathematics in which we never know exactly what we are talking about or whether anything we say is true!

  13. Designing simulations – your turn to help

  14. Designing simulations – notes examples • Suppose a basketball player, Jessica, has an 80% free throw success rate. Design and conduct a simulation to estimate how many free throws she can make in a row without missing.

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