SlideServe
Télécharger Obtenir Pro
Menu
Accueil Pro
Préférences
ApparenceLight Aide et commentaires
© SlideServe · v2026

Understanding Randomness: Multiple Choice Review Quiz and Simulation Design

macaulay-peck avatar
macaulay-peck
14 diapositives · 280 Views · Nov 19, 2014

This chapter provides an engaging review quiz on multiple-choice scenarios, allowing students to assess their understanding of randomness in statistics. It includes a detailed simulation design using die rolls to estimate correct answers in a quiz and explores coin tosses to determine bias. The chapter encourages hands-on experimentation, demonstrating how to formulate personal decision rules based on simulated results. Engage with practical examples to deepen your grasp of statistical concepts and learn to embrace uncertainty through simulations.

Understanding Randomness: Multiple Choice Review Quiz and Simulation Design - slide 1
01 / 14Understanding Randomness: Multiple Choice Review Quiz and Simulation Design
1 / 17

Télécharger la présentation

Understanding Randomness: Multiple Choice Review Quiz and Simulation Design
Une image / un lien ci-dessous est fourni (tel quel) pour télécharger la présentation

Politique de téléchargement : le contenu du site vous est fourni TEL QUEL pour votre information et votre usage personnel ; il ne peut être vendu, concédé sous licence ni partagé sur d’autres sites sans l’accord de son auteur.Le contenu vous est fourni TEL QUEL, pour votre information et votre usage personnel uniquement. Téléchargez la présentation en cliquant sur ce lien. Lors du téléchargement, si vous ne parvenez pas à télécharger une présentation, l’éditeur a peut-être supprimé le fichier de son serveur.Pendant le téléchargement, si vous ne parvenez pas à obtenir une présentation, le fichier a peut-être été supprimé par l’éditeur.

F I N

Plus de contenu associé

Transcription de la présentation

  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.