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Chapter 17

Chapter 17. Thinking About Chance. Thought Question 1. Here are two very different probability questions: If you roll a 6-sided die and do it fairly, what is the probability that it will land with “3” showing?

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Chapter 17

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  1. Chapter 17 Thinking About Chance Chapter 17

  2. Thought Question 1 • Here are two very different probability questions: • If you roll a 6-sided die and do it fairly, what is the probability that it will land with “3” showing? • What is the probability that in your lifetime you will travel to a foreign country other than one you have already visited? • For which question was it easier to provide a precise answer? Why? For which one could we all agree? Chapter 17

  3. Thought Question 2(from Seeing Through Statistics, 1st Edition, by J. M. Utts, p. 253) • Which of the following more closely describes what it means to say that the probability a tossed coin lands with heads up is 1/2? • As the number of tosses increases, the fraction of heads will get closer and closer to 1/2. • The number of heads tossed will always be close to half of the number of tosses. Chapter 17

  4. Thought Question 3 What is wrong with the following partial answer to TQ #1: “The probability that I will eventually travel to another foreign country (or of any other particular event happening) is 1/2, because either it will happen or it won’t.” Chapter 17

  5. Thought Question 4 A news article claimed that the risk of a relapse when quitting smoking “cold turkey” is five times the risk when using a nicotine patch to quit. Assume this statistic was based on legitimate, well-conducted research. What additional information would you want about the risks before deciding which of the two methods to use to quit smoking? Chapter 17

  6. Thought Question 5 A study of past semesters shows that the relative risk of failing this class if you do not do your homework, as compared to if you do, is 13.5. What is meant by the term relative risk? Hint: (TQ #4) The relative risk of a relapse when quitting smoking “cold turkey” as compared to using the nicotine patch is 5. Chapter 17

  7. Two Concepts of Probability • Personal-Probability Interpretation • The degree to which a given individual believes the event in question will happen • Personal belief • Relative-Frequency Interpretation • The proportion of time the event in question occurs over the long run • “Long-run relative frequency” Chapter 17

  8. Relative-Frequency Probabilities • Two ways to determine: • Physical assumptions (theoretical mathematical model) • Repeated observations (empirical results) • Experience with many samples • Simulation Chapter 17

  9. Relative-Frequency Probabilities: Summary • Can be applied when the situation can be repeated numerous times (conceptually) and the outcome can be observed each time. • Relative frequency (proportion of occurrences) of an outcome settles down to one value over the long run. That one value is then defined to be the probability of that outcome. • The probability cannot be used to determine whether or not the outcome will occur on a single occasion, or in a single sample (it is a long-run phenomenon). Chapter 17

  10. Personal or Relative Frequency Probabilities? • The probability that a lottery ticket will be a winner. • The probability that you will get a B in this course. • The probability that a randomly selected student in one of your professor’s classes will get a B. • The probability that the 7 a.m. flight from San Francisco to New York will be on time on a randomly selected day. • The probability that the Atlanta Braves professional baseball team will win the World Series in the year 2015. Chapter 17

  11. Risk and Relative RiskCase Study The following table gives results for whether or not subjects were still smoking when given a nicotine patch or a placebo: Chapter 17

  12. Relative Risk • Risk of continuing to smoke • Nicotine: .533 (just the proportion from the table) • Placebo: .800 • Relative risk of continuing to smoke when using the placebo patch compared with when using the nicotine patch is 1.5 (.800/.533 = 1.5). • The risk of continuing to smoke when using the placebo patch is 1.5 timesthe risk when using the nicotine patch. Chapter 17

  13. Cautions about Risk • What if the baseline risk is missing? • The relative risk means “relative” to what? • The reported risk is not necessarily your risk. • Are the subjects and the setting of the study representative of you and your situation? Chapter 17

  14. Baseline Risk is Missing Case Study Premature-birth Risk Found Higher for Teens (reported in the Sacramento Bee, April 27, 1995, p. A7) • “The youngest girls [in the study] , those aged 13 to 17, were 90 percent more likely than the women in their early 20’s to deliver prematurely.” • The relative risk was 1.9. • But what is the absolute risk for women in their 20’s which is used as the baseline? Chapter 17

  15. Reported Risk May Not Be Your Risk Case Study Premature-birth Risk Found Higher for Teens (reported in the Sacramento Bee, April 27, 1995, p. A7) • The greater risk may be due to lack of support from the father rather than the age of the girl. • If you are a pregnant teenage girl with plenty of support from the father, this risk may not apply to you. Chapter 17

  16. Key Concepts • Personal probability • Long-run Relative Frequency interpretation of probability • Relative Risk and cautious interpretation Chapter 17

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