23.24 Acceptance sampling. You are a consumer of potatoes in an acceptance sampling situation. Your acceptance sampling plan has probability 0.01 of passing a truckload of potatoes that does not meet quality standards. You might think that the truckloads that pass are almost all good. Alas, it is not so.

  1. (a) Explain why low probabilities of error cannot ensure that truckloads that pass are mostly good. (Hint: What happens if your supplier ships all bad truckloads?)

  2. (b) The paradox that most decisions can be correct (low error probabilities) and yet most truckloads that pass can be bad has important analogs in areas such as medical diagnosis. Explain why most conclusions that a patient has a rare disease can be false alarms even if the diagnostic system is correct 99% of the time.