1. A bank audited 100 randomly selected transactions of a newly hired cashier and found that all 100 were done correctly. What is the 95% confidence interval for the cashier’s probability of an error?
2. In order to be 95% confident that the incidence of fraud among tax returns is less than 1 in 10,000, how many tax returns would the IRS need to audit at a minimum? 3. An exam has 50 multiple-choice questions. A student got the first 10 right and so claimed by the Rule of Three that his chance of getting a question wrong on the exam was less than 30%, and so he should be passed without having to do the rest. Is this a proper use of the Rule of Three?
4. A manufacturer of delicate electronic systems requires a very low defect rate. To meet its standards, it demands the defect rate among the parts it is ordering from a supplier to be less than 0.01%. If it is ordering 100 of these parts, can it using acceptance testing to decide if the parts meet its requirements?
5. Suppose you observe a sample with all successes. How could you get a 95% confidence interval for p?
6. The Rule of Three generates a 95% confidence interval. What rule would you recommend if you wanted to have a 99.75% confidence interval?
7. Does the Rule of Three work with small samples as well? In particular, if n = 20 does the argument leading to the 95% interval [0, 3 / n] still apply?