Question

An auditor wants to estimate what proportion of a bank’s commercial loan files are incomplete. The auditor wants to be within 10% of the true proportion when using a 95% confidence level. How many files must the auditor sample? No estimate of the proportion is available, so use 0.5 for the population proportion.

Answer 1

Here is one formula you might use for this problem:

n = [(z-value)^2 * p * q]/E^2

With your data:
n = [(1.96)^2 * .5 * .5]/.10^2

I'll let you finish the calculation (round to the next highest whole number).

Note: n = sample size needed; .5 for best estimate of the population proportion; .5 for q, which is (1 - p). E = maximum error, which is 10% or .10 from the problem. Z-value is found using a z-table (for 95%, the value is 1.96).

I hope this helps.