1. A bank audited 100 randomly selected transac- tions of a newly hired cashier

Question

1. A bank audited 100 randomly selected transac- tions 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 stu- dent got the first 10 right and so claimed by the Rule of Three that his chance of getting a ques- tion 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? 3. An exam has 50 multiple-choice questions. A stu- dent got the first 10 right and so claimed by the Rule of Three that his chance of getting a ques- tion 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 suc- cesses. How could you get a 95% confidence interval for p? 5. Suppose you observe a sample with all suc- cesses. 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? 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?
CASE SUMMARY The Rule of Three provides a 95% confidence in quires Bernoulli trials: the data must define indepen- terval for the population proportion p when observ dent events with only two possible outcomes and a ing a sample with all failures (or all successes). The constant probability. interval for p is the range (0, 3/n]. The interval re- Key Terms Rule of Three Questions for Thought 1. A bank audited 100 randomly selected transac 3. An exam has 50 multiple-choice questions. A stu- tions of a newly hired cashier and found that dent got the first 10 right and so claimed by the Rule of Three that his chance of getting a ques- all 100 were done correctly. What is the 95% confidence interval for the cashier's probability tion wrong on the exam was less than 30%, and of an error? so he should be passed without having to do the rest. Is this a proper use of the Rule of Three? 2. In order to be 95% confident that the incidence of fraud among tax returns is less than 1 in 4. A manufacturer of delicate electronic systems requires a very low defect rate. To meet its 10,000, how many tax returns would the IRS need to audit at a minimum? standards, it demands the defect rate among the

Explanation / Answer

1:

Since here we have all suceesses in ranodm sample so according to rule of three the 95% confidence interval is

[0, 3/n] =[0, 3/100 ] = [0, 0.03]

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