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Chapter 6: Q61E (page 338)
Answer
4 1.28
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U.S. Postal Service鈥檚 performance. The U.S. Postal Service (USPS) reports that 95% of first-class mail within the same city is delivered on time (i.e., within 2 days of the time of mailing). To gauge the USPS performance, Price Waterhouse monitored the delivery of first-class mail items between Dec. 10 and Mar. 3鈥攖he most difficult delivery season due to bad weather conditions and holidays. In a sample of 332,000 items, Price Waterhouse determined that 282,200 were delivered on time. Comment on the performance of USPS first-class mail service over this time period.
Question: Auditing sampling methods. 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鈥攖he account balance鈥攖he examination is known as a substantive test (Audit Sampling鈥擜ICPA Audit Guide, 2015). In order to evaluate the reasonableness of a firm鈥檚 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鈥檚 reported figure?
Question: Furniture brand familiarity. A brand name that consumers recognize is a highly valued commodity in any industry. To assess brand familiarity in the furniture industry, NPD (a market research firm) surveyed 1,333 women who head U.S. households that have incomes of $25,000 or more. The sample was drawn from a database of 25,000 households that match the criteria listed above. Of the 10 furniture brands evaluated, La-Z-Boy was the most recognized brand; 70.8% of the respondents indicated they were 鈥渧ery familiar鈥� with La-Z-Boy.
a. Describe the population being investigated by NPD.
b. In constructing a confidence interval to estimate the proportion of households that are very familiar with the La-Z-Boy brand, is it necessary to use the finite population correction factor? Explain.
c. What estimate of the standard error of should be used in constructing the confidence interval of part b?
d. Construct a 90% confidence interval for the true proportion and interpret it in the context of the problem.
Are you really being served red snapper? Refer to the Nature (July 15, 2004) study of fish specimens labeled 鈥渞ed snapper,鈥� Exercise 3.75 (p. 196). Recall that federal law prohibits restaurants from serving a cheaper, look-alike variety of fish (e.g., vermillion snapper or lane snapper) to customers who order red snapper. A team of University of North Carolina (UNC) researchers analyzed the meat from each in a sample of 22 鈥渞ed snapper鈥� fish fillets purchased from vendors across the United States in an effort to estimate the true proportion of fillets that are really red snapper. DNA tests revealed that 17 of the 22 fillets (or 77%) were not red snapper but the cheaper, look-alike variety of fish.
a. Identify the parameter of interest to the UNC researchers.
b. Explain why a large-sample confidence interval is inappropriate to apply in this study.
c. Construct a 95% confidence interval for the parameter of interest using Wilson鈥檚 adjustment.
d. Give a practical interpretation of the confidence interval.
The following is a 90% confidence interval for p:(0.26, 0.54). How large was the sample used to construct thisinterval?
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