Probability and Statistics Made Interesting
Edition: 2
Copyright: 2023
Edition: 2
Copyright: 2023
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Based on years of experience teaching online and in-person, Probability and Statistics Made Interesting integrates the author’s classroom-tested and proven methods and examples to make probability and statistics interesting while still covering the necessary subject matter for a one semester, elementary course.
Probability and Statistics Made Interesting
- provides examples that introduce a variety of statistical concepts to motivate students. For example: What is randomness? What’s the point of taking a random sample? How do casino games demonstrate the law of averages?
- integrates chapters on the normal curve, conditional probability, and a chapter on “What’s Luck Got to do with it” that integrates challenging examples.
- examines both large and small sample tests for proportions and means, including Fisher’s Exact test, as well as a test to see if someone is accident prone or just unlucky.
- integrates technology such as smartphones, calculators, Excel, and Google Sheets.
- features discussion topics and problems at the end of each chapter
NEW - Examples from the Second Edition (available soon)
Simpson’s Paradox – Two drugs that treat mental illness – Which is better?
Berkson’s Paradox – Comparing restaurants: Does good bacon predict good eggs?
Inspection Paradox – Are average class sizes larger than average?
Random Lightning Strikes – Tragedy in Lafayette Park across from the White House
Predicting the Price of Ethereum (incorrectly)
Excess Deaths and the Covid Vaccine in England – Once again, correlation doesn’t mean causation
So-called psychics use inside information to fool their victims
The Prosecutor’s Fallacy – Fingerprint evidence may not be as strong as it seems
From the First Edition
Probability and gambling games – Can you win playing roulette?
Lotteries – If your chance is 1 in 303 million of winning the Mega Millions lottery jackpot, how come there are winners?
Stereotyping – Is the person described as shy more likely to be a farmer or a librarian? From “Thinking, Fast or Slow” by Daniel Kahneman
Clinical trials – Why is a clinical trial better than an observational study?
Zener Card Test for Psychic Powers – What can go wrong?
“Synchronicity” vs randomness – Which is it?
Acknowledgments
Preface
CHAPTER 1 Random Sampling and Describing Data
Spreadsheets
Randomness
Random Sampling
Using Excel to Select a Random Sample
Public Opinion Polls
The Inspection Paradox —Estimating Average Class Size
Train Arrival Times
Face-to-Face Surveys
Erroneous Data
Sample Size Matters
Summarizing the Results of a Random Sample
The Mean and the Median
Skewed Data
The Mode
Excel
Variation
Range
Standard Deviation
Excel
Shape
Excel
Bell-Shaped Data
CHAPTER 2 Probability
Measuring Randomness
A Brief History of Probability
The Basic Ingredients
Random Variation
The Law of Averages
The Gambler’s Fallacy
Cherry Picking
Casino Games
Craps
Roulette
The Addition Rule for Expectation-Multiple Bets
Pie Throwing
The Double-Down Strategy and the Karaoke Strategy
Bold Play
Watch the Wheel
Dr. Jarecki
That’s Entertainment
Blackjack and Simulations
Computer Simulations
The Kelly Betting System
Poker
The Mega Millions Lottery
Buy Many Tickets
Buy Every Ticket
Splitting the Jackpot Prize
The Station
A Tragic Strategy
The Impossible Lottery
Raffles
The Chance of Being Struck by Lightning
Lightning Strikes at Random
The Bad Luck Lottery
The Chance of Being Killed by a Hornet, Wasp, or Bee Sting
Probability Models
CHAPTER 3 Conditional Probability
Cards
Comparing Categorical Variables – Smoking versus Blood Pressure
Asthma and Diet
Astrology
Does Stepping on a Crack in the Sidewalk Really Bring You Bad Luck?
Multiplication Rule for Conditional Probability
Bayes’ Rule—Test For a Rare Disease
Stereotyping—Librarian or Farmer?
Raccoons and Rabies
A Guessing Game
Simpson’s Paradox
Student Admissions
The Nowhere Man
CHAPTER 4 Correlation and Regression
Relationships
Square Footage versus Selling Price
Smoking and Pregnancy
Predicting the Weather
The Correlation Coefficient
Random Variation, Sometimes Known as Random Error
Correlation versus Causation
The Regression Line
Using Excel for Regression
The Coefficient of Determination: r
Berkson’s Paradox – Bacon and Eggs
Some Things aren’t Linear
Fuel Efficiency
Two Half-Lives Do Not Make a Whole Life
Good Things (Like Regression) Don’t Last Forever
Predicting the Price of Ethereum (suggested by Katrina Uy)
Song of the Sirens
Excess Deaths and the Covid Vaccine in England
CHAPTER 5 The Normal Distribution
The Normal Curve and Probability Histograms
The Empirical Rule
Finding Normal Probabilities
Smooth Curves and Not-So-Precise Measurements
Using Z
Tails of Z
Other normal curves
Th is One’s a Turkey
And the Winner is . . .
“Reverse” Normal Computations
CHAPTER 6 Statistical Inference—Margin of Error and Confidence Intervals
Balls in a Box
Good Vibrations
Standard Error
The Central Limit Theorem
The Die is Cast . . . Numerous Times
How Large is Large?
Margin of Error
Confidence Intervals for Proportions
A Public Opinion Poll
Anthropology
The Cable Guy
Determining the Sample Size for Precision and Accuracy
Confidence Intervals for Means
Waiting in Line
Fire Control
CHAPTER 7 Hypothesis Tests and p-Values
Yes–No Decisions (Sorry, no “Maybe”)
A Market Research Problem
p-value
Significance Level
Excuse the Formality
Yet Another Guessing Game
Madam Zola
Psychics Sometimes Use Inside Information to Gain Confidence
Chance Needs Opportunity
More Zener Card Guessing
Cherry Picking
Meaningful and Meaningless
False Significance
The Bonferroni Correction
Predicting Stock Market Crashes
The Hamster Tout
Small Sample Test for a Proportion—the Binomial Test
Internet Advertising
Hypothesis Tests for Means
Small Sample Test for Means
Kicking the Tires (statistically speaking)
Two-Tailed Tests
Cloud Seeding and Rainfall
CHAPTER 8 Tests Comparing Proportions and Means
If You’re Happy and You Know It, Clap Your Hands
Clinical Trial to Test a New Vaccine
Blind and Double Blind
Efficacy
Relationships
Smoking and Blood Pressure
Asthma and Diet
She (He, They) Loves Me, She (He, They) Loves Me Not
The Experiment
Comparing Means for Two Independent Samples – Knee Replacement
The Not-So-Dumb Waiter
Small Sample Tests for Comparing Two Means—the Two-Sample t-test
Automobile Maintenance Costs—Gas Cars vs. Electric Cars
CHAPTER 9 The Hypergeometric, Binomial, and Geometric Distributions With Special Bonus – the Fisher Exact Test
The Multiplication Rule Revisited
Faces
Balls in Boxes
Getting Your Ducks in a Row
Combinations
The Mega Millions Lottery Revisited
The Impossible Lottery Revisited
Poker Hands
The Hypergeometric Distribution
Quality Control
Fisher’s Exact Test
Jury Selection
Again with the Coin Tossing
The Binomial Distribution
Internet Advertising Revisited
The Binomial Formula
Dogs and Fleas
Back to Coin Tossing
Betting on 7 in Craps Revisited
The Prosecutor’s Fallacy
Mean and Standard Deviation of the Binomial Distribution
Normal Approximation
The Hypergeometric Distribution Compared with the Binomial Distribution
The Geometric Distribution
The Assembly Line
Mean of the Geometric Distribution
CHAPTER 10 What’s Luck Got to Do With It?
What is Luck?
Luck Is All There Is
Roulette
Luck in Everyday Life
Prediction Games—What’s Luck Got to Do with It?
p-values
Multiple Comparisons
The Binomial Model
The Mega Millions Lottery Revisited
Lucky Winners
A Lucky Winner Needs Unlucky Losers
Accident Proneness—Give Chance a Chance
Run Over by a Bus . . . Twice
Using Data to Estimate a Probability
Bus Accidents in New York City
Finding the p-Value—Binomial and Poisson Distributions
Multiple Comparisons
Multiple Tickets
The Importance of Opportunity
A Statistician, an Insurance Agent, and Carl Jung Walk Into a Bar
On the Lookout
Statistics to the Rescue
Answers to Problems
Index
Dr. Michael Orkin is a professor, consultant, and author. He’s been an invited speaker at numerous events, including conferences, college graduations, rotary clubs, and technical venues such as Google Tech Talks (“Decision Making and Chance,” September 2006). He’s the author of several previous books, including “Can You Win? The Real Odds for Casino Gambling, Sports Betting, and Lotteries,” and “What are the Odds? Chance in Everyday Life.” Orkin has published numerous research articles in probability and statistics, including “Games of Chance and Games of Skill,” which appeared in a recent edition of Chance magazine. Dr. Orkin has a B.A. in Mathematics and Ph.D. in Statistics, both from the University of California at Berkeley. He is currently Professor of Mathematics at Berkeley City College in Berkeley, California and is Professor of Statistics, Emeritus, at California State University, East Bay.
Follow Dr. Michael Orkin
Probability and Statistics Made Interesting is really what the students need. May it be used everywhere. It’s really all they need.
Dr. Robert Pisani, Statistics Dept., University of California, Berkeley (ret.)
Co-Author of Statistics by Freedman, Pisani, and Purves