Question: Write a report The Payment Time Case Study, including the following calculations and using the information to determine whether the new billing system has reduced
•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?
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Payment Time Case Study Overview As mentioned in the Payment Time Case Study the consulting firms including Ernst Accenture and Young Consulting utilize statistical analysis in reviewing the effectiveness of the processes and systems designed towards serving their customers In this report we are analyzing an electronic billing system that was designed and developed for a trucking company by the name Stockton Ca According to the case study the billing system allows for the sending of invoices electronically and directly to the consumers computers Once the invoices are sent the consumers get an opportunity of checking and correcting errors that might be present in those invoices The primary goal of the billing system is basically to reduce the time taken by consumers in making their payments The time taken by the old system is 39 days or more This timing exceeds the industry standard which recommends no more than 30 days Due to the inefficiencies of the old system there is a need for adoption of the new electronic billing system With the new system a company will not have to calculate the payment time on the sent invoices since continued information will not be required as it used to be in the old system It is believed that a consulting firm that is using the billing system will reduce the time taken by customers to pay by 50 percent Since the old system takes 39 days for consumers to make payments it means that the new system should take 195 392 days For us to determine whether the electronic billing system will be effectiveefficient or not it is good we embark on several computations under several assumptions Assumptions The report under the computation section assumes that standard deviation std dev of the payment times is 42 days The 95 percent confidence interval is utilized to examine whether the electronic billing system is suitableeffective or not Using 95 percent confidence interval the report determines whether we will be 95 percent confident that 195 days It also uses 99 confidence interval to determine whether it is possible we be 99 percent confident that 195 days In the report the consulting firm selects a random sample of about 65 invoices from more than 7000 invoices that are processed on the new billing system Effectiveness of Billing System 1 95 Confidence Level Answer Formula CIX Z N Standard Deviation 42 The Mean 181077 Sample Size 65 The Confidence Level 95 Computations Standard Error Mean 05209 Z Value 19600 Interval Half Width 10210 Confidence Interval Lower Limit 170867 Interval Upper Limit 191287 Therefore 95 CI 170867 191287 less than 195 Comment Using 95 confidence interval we conclude that 195 days 2 99 Confidence Level Answer Formula CIX Z N Standard Deviation 42 The Mean 181077 Sample Size 65 The Confidence Level 99 Computations Standard Error Mean 05209 Z Value 25760 Interval Half Width 13419 Confidence Interval Lower Limit 167658 Interval Upper Limit 194496 Therefore 99 CI 167658 194496 less than 195 Comment Using 99 confident we conclude that 195 day 3 195 Days as Mean Payment Time Answer Z value 18107719505209 267 P mean x 181077 P z 267 00038 Conclusion From the step by step computations shown above we have proven that the new electronic billing system will be effective ... View full answer
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