Statistics for Business and Economics (13th Edition)
Statistics for Business and Economics (13th Edition)
13th Edition
ISBN: 9780134506593
Author: James T. McClave, P. George Benson, Terry Sincich
Publisher: PEARSON
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Chapter 6, Problem 6.138CTC

A sampling dispute goes to court. Sampling of Medicare and Medicaid claims by the federal and state agencies who administer those programs has become common practice to determine whether providers of those services are submitting valid claims. (See the Statistics in Action for this chapter.) The reliability of inferences based on those samples depends on the methodology used to collect the sample of claims. Consider estimating the true proportion, p, of the population of claims that are invalid. (Invalid claims should not have been reimbursed by the agency.) Of course, to estimate a binomial parameter, p, within a given level of precision we use the formula provided in Section 6.5 to determine the necessary sample size. In a recent actual case, the statistician determined a sample size large enough to ensure that the bound on the error of the estimate would not exceed .05, using a 95% confidence interval. He did so by assuming that the true error rate was p = .5, which, as discussed in Section 6.5, provides the maximum sample size needed to achieve the desired bound on the error.

  1. a. Determine the sample size necessary to estimate p to within .05 of the true value using a 95% confidence interval.
  2. b. After the sample was selected and the sampled claims were audited, it was determined that the estimated error rate was p ^ = .20 and a 95% confidence interval for p was (.15, .25). Was the desired bound on the error of the estimate met?
  3. c. An economist hired by the Medicare provider noted that, since the desired bound on the error of .05 is equal to 25% of the estimated p ^ = .20 invalid claim rate, the “true” bound on the error was .25, not .05. He argued that a significantly larger sample would be necessary to meet the “relative error” (the bound on the error divided by the error rate) goal of .05, and that the statistician’s use of the “absolute error of .05 was inappropriate, and more sampling was required. The statistician argued that the relative error was a moving target, since it depends on the sample estimate of the invalid claim rate, which cannot be known prior to selecting the sample. He noted that if the estimated invalid claim rate turned out to be larger than .5, the relative error would then be lower than the absolute error bound. As a consequence, the case went to trial over the relative vs. absolute error dispute. Give your opinion on the matter.

[Note: The Court concluded that “absolute error was the fair and accurate measure of the margin of error.” As a result, a specified absolute bound on the error continues to be the accepted method for determining the sample size necessary to provide a reliable estimate of Medicare and Medicaid providers’ claim submission error rates.]

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Chapter 6 Solutions

Statistics for Business and Economics (13th Edition)

Ch. 6.2 - Will a large-sample confidence interval be valid...Ch. 6.2 - Heart rate variability of police officers. Are...Ch. 6.2 - Tipping points in daily deal transactions? Online...Ch. 6.2 - Corporate sustainability of CPA firms. Corporate...Ch. 6.2 - College dropout study. Refer to the American...Ch. 6.2 - Wear-out of used display panels. Refer to Exercise...Ch. 6.2 - Unethical corporate conduct. How complicit are...Ch. 6.2 - Shopping on Black Friday. The day after...Ch. 6.2 - 401 (k) Participation rates. Named for the section...Ch. 6.2 - Accounting and Machiavellianism. Refer to the...Ch. 6.2 - Facial structure of CEOs. In Psychological Science...Ch. 6.2 - Improving SAT scores. Refer to the Chance (Winter...Ch. 6.2 - The Raid test kitchen. According to scientists,...Ch. 6.3 - Suppose you have selected a random sample of n = 5...Ch. 6.3 - Use the applet Confidence Intervals for a Mean...Ch. 6.3 - Use the applet Confidence Intervals for a Mean...Ch. 6.3 - Explain the differences in the sampling...Ch. 6.3 - Let t0 be a specific value of t. Use Table III in...Ch. 6.3 - The following random sample was selected from a...Ch. 6.3 - The following sample of 16 measurements was...Ch. 6.3 - Lobster trap placement. An observational study of...Ch. 6.3 - Radon exposure in Egyptian tombs. Many ancient...Ch. 6.3 - Do social robots walk or roll? Refer to the...Ch. 6.3 - Hospital length of stay. Health insurers and the...Ch. 6.3 - Repair and replacement costs of water pipes. Refer...Ch. 6.3 - Prob. 6.34ACICh. 6.3 - Oxygen bubbles in molten salt. Molten salt is used...Ch. 6.3 - Performance of stock screeners. In Exercise 2.44...Ch. 6.3 - Minimizing tractor skidding distance. When...Ch. 6.3 - Crude oil biodegradation. Refer to the Journal of...Ch. 6.3 - Largest private companies. IPOsinitial public...Ch. 6.4 - Describe the sampling distribution of p based on...Ch. 6.4 - Use the applet Confidence Intervals for a...Ch. 6.4 - Prob. 6.6AECh. 6.4 - For the binomial sample information summarized in...Ch. 6.4 - A random sample of size n = 121 yielded p=.88. a....Ch. 6.4 - A random sample of size n = 225 yielded p=.46. a....Ch. 6.4 - A random sample of 50 consumers taste-tested a new...Ch. 6.4 - Customer participation in store loyalty card...Ch. 6.4 - Crash risk of using cell phones while driving....Ch. 6.4 - Zillow.com estimates of home values. Zillow.com is...Ch. 6.4 - Do social robots walk or roll? Refer to the...Ch. 6.4 - Is Starbucks coffee overpriced? The Minneapolis...Ch. 6.4 - Nannies who are INA certified. The International...Ch. 6.4 - Prob. 6.51ACICh. 6.4 - Prob. 6.52ACICh. 6.4 - Minority ownership of franchises. According to a...Ch. 6.4 - Study of aircraft bird-strikes. As worldwide air...Ch. 6.4 - Prob. 6.55ACICh. 6.4 - Diamonds sold on the open market. Refer to the...Ch. 6.4 - Are you really being served red snapper? Refer to...Ch. 6.4 - Eye shadow, mascara, and nickel allergies....Ch. 6.4 - Prob. 6.59ACACh. 6.5 - If you wish to estimate a population mean with a...Ch. 6.5 - Suppose you wish to estimate a population mean...Ch. 6.5 - In each case, find the approximate sample size...Ch. 6.5 - The following is a 90% confidence interval for p:...Ch. 6.5 - It costs you 10 to draw a sample of size n = 1 and...Ch. 6.5 - Suppose you wish to estimate the mean of a normal...Ch. 6.5 - If nothing is known about p. .5 can be substituted...Ch. 6.5 - Aluminum cans contaminated by fire. A gigantic...Ch. 6.5 - Accounting and Machiavellianism. Refer to the...Ch. 6.5 - Lobster trap placement. Refer to the Bulletin of...Ch. 6.5 - Evaporation from swimming pools. Refer to the...Ch. 6.5 - Do social robots walk or roll? Refer to the...Ch. 6.5 - Study of aircraft bird-strikes. Refer to the...Ch. 6.5 - Bacteria in bottled water. Is the bottled water...Ch. 6.5 - Shopping on Black Friday. Refer to the...Ch. 6.5 - Monitoring phone calls to a toll-free number. A...Ch. 6.5 - Eye shadow, mascara, and nickel allergies. Refer...Ch. 6.5 - Prob. 6.77ACICh. 6.5 - Is caffeine addictive? Does the caffeine in...Ch. 6.5 - Prob. 6.79ACACh. 6.6 - Calculate the percentage of the population sampled...Ch. 6.6 - Suppose the standard deviation of the population...Ch. 6.6 - Suppose N = 5,000, n = 64, and s = 24. a. Compare...Ch. 6.6 - Suppose N = 10,000, n = 2,000. and s = 50. a....Ch. 6.6 - Prob. 6.84LMCh. 6.6 - Prob. 6.85LMCh. 6.6 - Prob. 6.86LMCh. 6.6 - NFL player survey. Researchers at the University...Ch. 6.6 - Magazine subscriber salaries. Each year, the trade...Ch. 6.6 - Auditing sampling methods. Traditionally. auditors...Ch. 6.6 - Prob. 6.90ACICh. 6.6 - Invoice errors in a billing system In a study of...Ch. 6.6 - Prob. 6.92ACACh. 6.7 - For each of the following combinations of and...Ch. 6.7 - Given the following values of x, s, and n, form a...Ch. 6.7 - Prob. 6.95LMCh. 6.7 - A random sample of n = 6 observations from a...Ch. 6.7 - Oil content of fried sweet potato chips. The...Ch. 6.7 - Corporate sustainability of CPA firms. Refer to...Ch. 6.7 - Facial structure of CEOs. Refer to the...Ch. 6.7 - Radon exposure in Egyptian tombs. Refer to the...Ch. 6.7 - Drug content assessment. Refer to the Analytical...Ch. 6.7 - Jitter in a water power system. Jitter is a term...Ch. 6.7 - Lobster trap placement Refer to the Bulletin of...Ch. 6.7 - Phishing attacks on e-mail accounts. Refer to the...Ch. 6.7 - Is honey a cough remedy? Refer to the Archives of...Ch. 6 - In each of the following instances determine...Ch. 6 - In random Sample of 400 measurements, 227 of the...Ch. 6 - Prob. 6.109LMCh. 6 - Calculate the finite population correction factor...Ch. 6 - Find /22 and (1/2)2 from Table IV, Appendix D, for...Ch. 6 - Latex allergy in health care workers. Health care...Ch. 6 - Prob. 6.113ACBCh. 6 - Products Made in the USA. Refer to Exercise 2.154...Ch. 6 - Prob. 6.115ACBCh. 6 - Lead and copper in drinking water. Periodically,...Ch. 6 - Water pollution testing. The EPA wants to test a...Ch. 6 - Bankruptcy effect on U.S. airfares. Both Delta...Ch. 6 - Prob. 6.119ACBCh. 6 - Motivation of drug dealers. Refer to the Applied...Ch. 6 - Budget lapsing at army hospitals Budget lapsing...Ch. 6 - Size of diamonds sold at retail. Refer to Exercise...Ch. 6 - Prob. 6.123ACICh. 6 - Prob. 6.124ACICh. 6 - Surface roughness of pipe. Refer to the...Ch. 6 - Interviewing candidates for a job. The costs...Ch. 6 - Overbooking policies for major airlines. Airlines...Ch. 6 - Paying for music downloads if you use the...Ch. 6 - Accuracy of price scanners at Walmart. The...Ch. 6 - Contamination of New Jersey wells. Methyl t-butyl...Ch. 6 - Cell phone use by drivers. Studies have shown that...Ch. 6 - Salmonella poisoning from eating an ice cream bar....Ch. 6 - Prob. 6.133ACICh. 6 - Latex allergy in health care workers. Refer to the...Ch. 6 - Prob. 6.135ACACh. 6 - Accountants salary survey. Each year, Management...Ch. 6 - Prob. 6.137ACACh. 6 - A sampling dispute goes to court. Sampling of...Ch. 6 - Prob. 6.139CTC
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