2. An inspector for the IRS is auditing a mid-sized firm. She only has half a da
ID: 3154569 • Letter: 2
Question
2. An inspector for the IRS is auditing a mid-sized firm. She only has half a day to go through all the books and decides to inspect a sample of the invoices to see if she should start a fraud investigation (which would free up additional auditing resources). As a first step, she pulls 300 invoices at random for further inspection. 12 of these show inaccuracies. Can she assume that the sample distribution is (approximately) normal? (Note: always show your calculation: 3. Let’s assume the IRS normally only launches a full scale investigation when they suspect more than 3% of all invoices contain errors. Given the 12 invoices she found in her sample, what is the probability that more than 3% of all invoices have inaccuracies? 4. The IRS agent wants to report the 99.5% confidence interval for the proportion of incorrect invoices. Should she use a z-table or t-table, and what z or t-value should she use? 5. Calculate the 99.5% confidence interval for the proportion of incorrect invoices
Explanation / Answer
2. An inspector for the IRS is auditing a mid-sized firm. She only has half a day to go through all the books and decides to inspect a sample of the invoices to see if she should start a fraud investigation (which would free up additional auditing resources). As a first step, she pulls 300 invoices at random for further inspection. 12 of these show inaccuracies. Can she assume that the sample distribution is (approximately) normal? (Note: always show your calculation:
p = 12 / 300 = 0.04
miu = 0.04 * 300 = 12
she can assue that is normal because miu > 5
3. Let’s assume the IRS normally only launches a full scale investigation when they suspect more than 3% of all invoices contain errors. Given the 12 invoices she found in her sample, what is the probability that more than 3% of all invoices have inaccuracies?
Probability = 0.04
4. The IRS agent wants to report the 99.5% confidence interval for the proportion of incorrect invoices. Should she use a z-table or t-table, and what z or t-value should she use?
Z value because is a confidence interval of proportion so it is assume that is normally distributed
5. Calculate the 99.5% confidence interval for the proportion of incorrect invoices
alpha / 2 = 0.0025 Z = 2.80
0.04 +/- 2.80 * SRQT ( 0.04*0.96 / 300 )
0.04 +/- 0.0317
0.0083 < P < 0.0717
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