Case Study – Payment Time Case Study Major consulting firms such as Accenture, Ernst & Young Consulting, and Deloitte & Touche Consulting employ statistical analysis to assess the effectiveness of the systems they design for their customers. In this case, a consulting firm has developed an electronic billing system for a Stockton, CA, trucking company. The system sends invoices electronically to each customer’s computer and allows customers to easily check and correct errors. It is hoped the new billing system will substantially reduce the amount of time it takes customers to make payments. Typical payment times—measured from the date on an invoice to the date payment is received—using the trucking company’s old billing system had been 39 days or more. This exceeded the industry standard payment time of 30 days. The new billing system does not automatically compute the payment time for each invoice because there is no continuing need for this information. The management consulting firm believes the new system will reduce the mean bill payment time by more than 50 percent. The mean payment time using the old billing system was approximately equal to, but no less than, 39 days. Therefore, if µ denotes the new mean payment time, the consulting firm believes that µ will be less than 19.5 days. Therefore, to assess the system’s effectiveness (whether µ < 19.5 days), the consulting firm selects a random sample of 65 invoices from the 7,823 invoices processed during the first three months of the new system’s operation. Whereas this is the first time the consulting company has installed an electronic billing system in a trucking company, the firm has installed electronic billing systems in other types of companies. Analysis of results from these other companies show, although the population mean payment time varies from company to company, the population standard deviation of payment times is the same for different companies and equals 4.2 days. The payment times for the 65 sample invoices are manually determined and are given in the Excel® spreadsheet named “The Payment Time Case”. If this sample can be used to establish that new billing system substantially reduces payment times, the consulting firm plans to market the system to other trucking firms. Grading Guide Content Met Partially Met Not Met Total Available Total Earned Partially Met Not Met Comments: Review the Payment Time Case Study and Data Set. Develop a 700-word report including the following calculations and using the information to determine whether the new billing system has reduced the mean bill payment time: • Assuming the standard deviation of the payment times for all payments is 4.2 days, construct a 95% confidence interval estimate to determine whether the new billing system was effective. State the interpretation of 95% confidence interval AND state whether or not the billing system was effective. • Using the 95% confidence interval, can we be 95% confident that µ ≤ 19.5 days? • Using the 99% confidence interval, can we be 99% confident that µ ≤ 19.5 days? • If the population mean payment time is 19.5 days, what is the probability of observing a sample mean payment time of 65 invoices less than or equal to 18.1077 days? Writing Guidelines The paper—including tables and graphs, headings, title page, and reference page—is consistent with APA formatting guidelines and meets course-level requirements. Intellectual property is recognized with in-text citations and a reference page. Met Comments: Writing Guidelines Met Partially Met Not Met Total Available Total Earned Paragraph and sentence transitions are present, logical, and maintain the flow throughout the paper. Sentences are complete, clear, and concise. Rules of grammar and usage are followed including spelling and punctuation. Assignment Total Additional comments: Comments: PayTime 22 19 16 18 13 16 29 17 15 23 18 21 16 10 16 22 17 25 15 21 20 16 15 19 18 15 22 16 24 20 17 14 14 19 15 27 12 17 25 13 17 16 13 18 19 18 14 17 17 12 23 24 18 16 16 20 15 24 17 21 15 14 19 26 21
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