You are using difference estimation in the costing of inventory as part of the audit of the Rubber Products and Supply Company. The following data are available or have been developed by you:

Required :

a. What is the sample size necessary to achieve your audit objectives ?

b. What would be the necessary sample size if the allowable error had been SI0,000 and everything else the same as in the original data?

c. Why did the change in the allowable error have such a large effect on sample size ?

d. What would be the necessary sample size if the population size had been 4,000 and everything else the same as in the original data ?

e. Why is the effect of the change in d the same as the effect of the change in b?

f. Without regard to your answer to part a above, assume that a sample of 60 items is selected and the following differences between book and audited values are identified. (Understatements are in parentheses.)

For each of the other 51 items in the sample, there was no difference between the book and audited values.
Calculate the achieved confidence interval at the required confidence level based on this sample.
g. Given that the actual sample size in party was smaller than the required sample size in part a, explain why the confidence limits still fall within the materiality limits.

Population book value Population size (N) Materiality Estimated point estimate Required confidence level: Beta risk Estimated standard deviation (based on data contained in last year's work papers) $648,050 2,000 $ 16,000 $ 4,000 5% $30