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.
Answers
MathGuru
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.
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.