Traditionally, auditors have relied to a great extent on sampling techniques, rather than 100% audits, to help them test and evaluate the financial records of a client firm. When sampling is used to obtain an estimate of the total dollar value of an account-the account balance-the examination is known as a substantive test (Audit Sampling-AICPA Audit Guide, 2015). In order to evaluate the reasonableness of a firm's stated total value of its parts inventory, an auditor randomly samples 100 of the total of 500 parts in stock, prices each part, and reports the results shown in the table.

a. Give a point estimate of the mean value of the parts inventory.
b. Find the estimated standard error of the point estimate of part a.
c. Construct an approximate 95% confidence interval for the mean value of the parts inventory.
d. The firm reported a mean parts inventory value of $300. What does your confidence interval of part c suggest about the reasonableness of the firm's reported figure? Explain.

Sample Size 3 Part Number Part Price $ 108 002 101 55 500 73 300 54 92 832 077 688 910 839 121 10 833 5 271 399 761 093 505 597 830 50 125 1,000 62 205 12 2 88 100 11 19