CASE STUDY: JMP014
Kerrich - Is a Coin Fair?
by Dr. DeWayne Derryberry, Idaho State University, Department of Mathematics
Key Concepts: Bar charts, confidence intervals for proportions, hypothesis testing for proportions, likelihood ratio, simulating random data, scatterplot, fitting a regression line
Dr. DeWayne Derryberry
Idaho State University
Objective
Using outcomes for 10,000 flips of a coin, use descriptive statistics, confidence intervals and hypothesis tests to determine whether the coin is fair.
Background
John Kerrich was an English mathematician who found himself in a prison camp in Denmark during WW II. This freed up his calendar considerably. To help occupy his time, he performed a series of experiments in probability.
Most statisticians claim that coins are fair, and this gave Kerrich a chance to test this claim. He had the time to flip a coin 10,000 times, resulting in 5,067 heads and 4,933 tails (The Practice of Statistics in the Life Sciences, 2nd Edition, Baldi and Moore, Page 209).
The Task
Determine whether this is a fair coin. “Fair” means that heads and tails are equally likely to occur.