All of Britain Must Be Stoned!

Distribution: To maintain the integrity and usefulness of cases published in INFORMS Transactions on Education (ITE), distribution of these teaching notes to any other party is prohibited. Please refer interested instructors to ITE for access to the teaching notes. Through an emphasis on data (its collection, analysis, and quality/meaning), this case provides students at the introductory (undergraduate or master’s) level with an opportunity to apply basic concepts of probability to a real problem taken from an actual newspaper article (Dodd 1999). To analyze this case, students must apply the following concepts from basic probability: • marginal probabilities (i.e., What is the probability of a low level of cocaine on a bank note?); • joint probabilities (i.e., What is the probability of both a low level of cocaine and a low level of Ecstasy on a bank note?); • conditional probabilities (i.e., What is the probability of a low level of cocaine on a bank note given the note has a low level of Ecstasy?); • methods of assigning probabilities to events (these probabilities are based on a sample of 500 bank notes and have been assigned to outcomes using the empirical relative frequency method); • statistical independence (i.e., Is the presence of a low level of cocaine on a bank note more likely/less likely if the bank note also is contaminated with a low level of Ecstasy? How is a bank note passed while in circulation?); • randomness (i.e., How were these 500 bank notes collected?); and • the binomial probability distribution (i.e., What is the probability a bank note will be passed 500 times and not be contaminated with a low level of cocaine? What is the probability that 496 or fewer bank notes from a sample of 500 will be contaminated with a low level of Ecstasy?). They must also consider the following issues in inference and the design of experiments: • model assumptions and their ramifications (i.e., Are the individuals who handle a bank note while it is in circulation independent? Is the probability of contamination constant for all individuals who could handle a bank note? How useful are the binomial models if these conditions are not met?); • sampling methods (Were the bank notes collected through probability or nonprobability/convenience sampling? If they were collected randomly, was the sample a simple random sample? A stratified random sample? A cluster sample? A systematic random sample? Are the bank notes collected independently? Could a single employee of the Bank of England’s Returned Note Centre be responsible for the contamination of many bank notes? Were all of the bank notes at the Returned Note Centre collected from the same neighborhood/area? What is the impact on the analysis of the answers to these questions?); • sampling error (What proportion of all circulating bank notes are contaminated? How reliable is a sample of 500 bank notes?); and • inference (confidence intervals and hypothesis testing) for qualitative data.