The Payment Time CaseJosie LoveThe Payment Time CaseQNT/561July 31, 2018

The Payment Time CaseAbstractMajor consulting firms such as, Accenture, Ernst & Young Consulting, and Deloitte & Touche Consulting employ statistical analysts to understand the effectivenessof systems designed for their customers[Uni181]. In this case, a system developed for a trucking company is being analyzed for a reduction in payment time. The analysis is included in this paper to determine if the system is effective and can be marketed to new firms.The Payment Time CaseA report was created to determine if the new billing system for consulting firms has decreased the average payment time[Uni181]. The calculations will assume that the standard deviation is 4.2 days for the current payment times. These calculations willhelp obtain a 95% confidence to see if the new system is working. The 95% confidenceinterval will be used to understand if the firms can be confident that µ ≤ 19.5 days. The 99% confidence interval will also be used to see if the confidence level that µ ≤ 19.5 days can be 99% reliable. This report will calculate if the mean payment time is 19.5 days and the probability of a sample mean payment time being 65 invoices less than or equal to 18.1077 days.

The Payment Time CaseIt will be assumed that the standard deviation of payment time is 4.2 days. A 95% confidence will be made to estimate whether the new billing system is effective or not. The interpretation of 95% confidence will be reviewed.Equation:CI=X ± Z×α/ √ N Confidence Interval Estimate for the Mean: Data:Population Standard Deviation 4.2 Sample Mean 18.1077 Sample Size 65 Confidence Level 95% Intermediate Calculations Standard Error of the Mean 0.5209 Z Value 1.9600 Interval Half Width 1.0210 Confidence Interval Interval Lower Limit 17.0867

The Payment Time CaseInterval Upper Limit 19.1287 (Using the 95% confidence interval, confidence is 95% that µ ≤ 19.5 days.)95% CI = (17.0867, 19.1287) or less than 19.5(It is concluded that confidence is 95% that µ ≤ 19.5 days. Using the 99% confidence interval, confidence is 99% that µ ≤ 19.5 days.)[Dav181]Confidence Interval Estimate for the Mean:DataPopulation Standard Deviation 4.2Sample Mean 18.1077 Sample Size 65 Confidence Level 99% Intermediate Calculations Standard Error of the Mean 0.5209 Z Value 2.5760 Interval Half Width 1.3419 Confidence Interval Interval Lower Limit 16.7658 Interval Upper Limit 19.449699% CI = (16.7658, 19.4496) less than 19.5

The Payment Time CaseIt is concluded that confidence is 99% that µ ≤ 19.5 per day. If the population mean payment time is 19.5 days, the probability of observing a sample mean payment time of 65 invoices is less than or equal to 18.1077 days.Z value for 18.1077 is z = (18.1077-19.5)/0.5209 = -2.67 P (mean x <18.1077) = P (z < -2.67) =0.0038The TestA null hypothesis or (Ho) says the mean is greater than or equal to 19.5 days, whereas, the alternate hypothesis or (Ha) is less than 19.5[UCD18]. The ‘alpha’ is set at .05 because a 95% level of confidence is desired. The sample is greater than 30, therefore, the z test is used. The fdr discards the null if z is less than the critical value (CRV) of 1.645. This CRV is used for a one-tail test. The calculations follow:z=´x−µσ√n=18.11−19.54.2/√65=−1.390.520946=−2.67265The null is excluded because the result is z is -2.67, which is less than the CRV of 1.645. It is assumed that the new billing system creates a large reduction in paymenttime. The recommendation would be to continue with the new system across all other firms.