Transcript Chapter 17

Chapter 17
Thinking About Chance
Chapter 17
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?
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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.
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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
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?
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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.
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Two Concepts of Probability
 Personal-Probability
– The degree to which a given individual
believes the event in question will happen
– Personal belief
 Relative-Frequency
– The proportion of time the event in
question occurs over the long run
– “Long-run relative frequency”
Chapter 17
Relative-Frequency Probabilities
 Two
ways to determine:
– Physical assumptions
(theoretical mathematical model)
– Repeated observations (empirical results)
 Experience
with many samples
 Simulation
Chapter 17
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
Personal or Relative Frequency
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
Risk and Relative Risk
Case Study
The following table gives results for whether
or not subjects were still smoking when given
a nicotine patch or a placebo:
Smoking after 8 weeks?
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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 times the
risk when using the nicotine patch.
Chapter 17
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
Chapter 17
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
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
Key Concepts
 Personal
 Long-run Relative Frequency
interpretation of probability
 Relative Risk and cautious interpretation
Chapter 17