The Payment Time Case The Payment Time Case The Payment Time Case Introduction Many consulting firm hire statistical analysis to review their internal processes as well as the effectiveness of their systems in place. This study is based on a Stockton CA trucking company that hired a firm to develop an electronic billing system. This new and improved billing system has been developed with the hope that it can provide its customers their bills electronically with the hope that in turn the customer makes payments sooner. Currently, it is taking 39 days from the billing day to receive payment which is much higher than the 30 days net it has set on the accounts. The organization is hoping that this new billing systems will minimize the mean of the current billing amount of days it current has by at least 50%. This would dramatically change from the current 39 days mean to a hopeful 19.5 days, give or take. Sample Test The firm will take a sample of 65 invoices out of 7,823 invoices from the first three months of billing it accumulates with the new electronic billing system. The consulting firm has created billing systems for many companies, however, this is the first trucking company it develops a billing system. The population mean in other systems they have created varies, but the standard deviation normally stays around 4.2 days. For this same reason, this study has provided us with some analytic questions to review so that we can determine if the organization is on the right track. Effective New Billing 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 the billing system was effective ("How To Use Excel To Calculate Confidence Interval", 2010). Using the 95% confidence interval, can we be 95% confident that µ ≤ 19.5 days? Confidence Interval Estimate for the Mean FORMULA CI=X ± Z×α/√N 95% 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 Sample Size 65 Confidence Level 95% Confidence Interval Interval Lower Limit 17.0867 Interval Upper Limit 19.1287 95% CI = (17.0867, 19.1287) less than 19.5. ("Confidence Interval Calculator", 2017). Our results achieve a 95% confident that µ ≤ 19.5 days. Both the Internal lower and upper show results lower than the original 19.5 days promised by the firm. Using the 99% confidence interval, can we be 99% confident that µ ≤ 19.5 days? Confidence Interval Estimate for the Mean FORMULA CI=X ± Z×α/√N 99% Data Population Standard Deviation 4.2 Sample Mean 18.1077 Sample Size 65 Confidence Level 99% Intermediate Calculations St.