As auditor for the Court Company, you decide to use variables sampling to estimate the total cost of an inventory of 1,150 items which has a net book value of \(\$ 260,400\). The auditor decides to use a sampling plan that will provide assurance that a fairly stated book value is not rejected as being materially misstated. Based on past experience, it is believed that the standard deviation of the population is \(\$ 120\). The audit estimate is to be made with a precision range of \(\pm \$ 25,000\) and a reliability level of 95 percent.

Required:

a. Calculate the required sample size, assuming sampling without replacement.

b. Without prejudice to your answer in (a), assume a sample of 130 with a total audited value of \(\$ 28,600\) and a standard deviation of \(\$ 120\). Compute the achieved precision interval.

c. Is the book value fairly stated? Explain.