The internal auditing staff of a local manufacturing company performs a sample audit each quarter to estimate the proportion of accounts that are current (between 0 and 60 days after billing).The historical records show that over the past 8 years 70 percent of the accounts have been current.Determine the sample size needed in order to be 99% confident that the sample proportion of the current customer accounts is within .03 of the true proportion of all current accounts for this company.
A)1842
B)1548
C)897
D)632
E)1267

Question

Quizplus · Accepted Answer

We can use the formula for sample size calculation for proportion:

n = (z^2 * p * q) / E^2

Where:
z = 2.576 (z-value for 99% confidence interval)
p = 0.7 (proportion of accounts that are current)
q = 0.3 (proportion of accounts that are not current)
E = 0.03 (margin of error)

Substituting the values, we get:

n = (2.576^2 * 0.7 * 0.3) / 0.03^2
n = 1547.89 (rounded up to the nearest whole number)
n = 1548

Therefore, the sample size needed is 1548 to be 99% confident that the sample proportion of the current customer accounts is within 0.03 of the true proportion of all current accounts for this company. Hence, the correct answer is B).

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