This paper presents the analysis of whether the new electronic billing system that was developed for Stockton, CA, a trucking company, was effective or not in reducing the mean bill payment time of its customers. Using the old billing system, it takes 39 or more days on the average for customers to pay. With the new billing system, it is expected that the amount of time of customers’ payments would be reduced by 50%. The new billing system would be considered effective if this objective was achieved.
The assessment of the effectiveness of the new billing system in reducing the customers’ payment time, i.e. from the time they received the invoice up to the time they made the payment, was done using the confidence interval estimates. The confidence intervals provide a range of values that contain the population mean with a given confidence level (Lane, n.d.). For instance, 95% confidence interval suggests that there is a 95% probability that the interval contains the population mean.
There were two confidence intervals that were considered in the analysis: (1) 95% confidence interval and (2) 99% confidence interval. The confidence intervals were computed using the Data Analysis function of MS Excel. With the assumption that the standard deviation of the payment times is 4.2 days and the sample mean of 18.1077 days from a sample of 65 customers, the 95% confidence interval was found to be from 17.0867 to 19.1287 (Appendix 1). On the other hand, the 99% confidence interval is between 16.7658 and 19.4496 (Appendix 2).
The 95% confidence interval of 17.0867 to 19.1287 means that we can be 95% confident that the payment time of customers of Stockton, CA using the new billing system is between 17.0867 and 19.1287 days. If the new billing system would be considered effective if the new payment time would be 19.5 days on the average, then we can be 95% confident the new billing system is not effective. This is because 19.5 days is beyond the 95% confidence limits. It likewise means that the probability that the payment time using the new billing system to be 19.5 days is less than 95%.
On the other hand, the 95% confidence interval of 16.7658 and 19.4496 implies that the there is a 95% probability that the Stockton’s customers’ payment time using the new billing system is from 16.7658 to 19.4496 days. Since 19.5 days, i.e. the basis of the effectiveness of the new billing system, is beyond these confidence limits, then we can conclude that the new billing system is not effective with 99% confidence.
Based on the values of the 95% and 99% confidence intervals, we cannot be 95% confident nor 99% confident that the payment time of customers using the new billing system is 19.5 days. Hence, the probability that the customers’ payment time is 19.5 days is less than 95%. Furthermore, the values of the confidence intervals at both 95% and 99% confidence levels tell that the new billing system is ineffective in reducing the payment time of Stockton’s customers by 50% of the payment time using the old billing system. This means that we cannot be 95% confident nor 99% confident that the mean payment time was reduced from 39 days and above to 19.5 days.
If we will assume that the population mean payment time is 19.5 days, the probability that of observing a sample mean payment time of 65 invoices less than or equal to 18.1077 days is 0.3707 or 37.07% (Appendix 3). This value suggests that is the population mean payment time using the new billing system is indeed 19.5 days such that the new billing system is effective in reducing the payment time by at least 50% of the payment time using the old billing system, there is only a 37.07% chance that the sample mean obtained would be 18.1077 days. Hence, there is a very small probability that the sample mean would be 18.1077 days.
Lane, D. (n.d.). Confidence Intervals Introduction. Retrieved from http://onlinestatbook.com/2/estimation/confidence.html
95% Confidence Interval Computation using MS Excel
99% Confidence Interval Computation using MS Excel
Probability of obtaining a sample mean of 18.1077 days computation