QNT 561 The Payment Time Case

The Payment Time Case

QNT/561

The Payment Time Case

The following report will detail the case study of the electronic billing system that Davis Consulting developed for Stockton Trucking in order to significantly decrease the amount of time it takes the customers to make payments. The billing system was restructured to conduct invoices to the customers electronically to correct any errors and to save time in disbursing payments. Nevertheless, the billing system has a defect; since there is no ongoing need for information, it does not routinely compute the payment period for the invoices. The current billing system has a mean bill payment time of 39 days and it surpasses the average time of 30 days. It is projected that the new billing system will decrease the mean time of bill payment by more than 50%, under 19.5 days. In order for the firm to exam how the billing system is currently working, they took a sample of 65 invoices from a total of 7,823 invoices that were processed in the first three months while using the new billing system. The new mean of bill payment time was 18.11 days, 4.2 being the standard deviation and 40 of the invoices used as a sample had its’ bill paid in 18 days or less. The purpose of this assignment is to evaluate and utilize the data given to determine whether the new billing system has reduced the mean bill payment time.

By observing the data given, it can be said with 95% confidence the population mean falls between 17.087 and 19.129. With 99% confidence, the population mean falls between 16.766 and 19.449. This illustrates that the new system is working to provide the results expected. The numbers show with the new billing system, 40 of the 65 sampled invoices were paid in 18 days; and 60% of the invoices will be paid in 19.5 or less. By observing the data, the new system would help the firm in the long run and give the results that they expect.

The following equation was used to calculate the values:

By observing at the above values and by using the 95% confidence interval, it is proven that at 95% confidence µ ≤ 19.5 days. The lower interval is at 17.087 and the upper interval is at 19.129 with a z score of 1.96. The Z value seems to be lower than the initial billing system meaning that the new system is working competently and is reducing the payment time by almost 50%.

95% CI = (17.087, 19.129) less than 19.5 = µ ≤ 19.5 days.

By observing the values shown above and using the 99% confidence interval, the lower interval is at 16.766 and upper interval is at 19.449 with a marginal of error of 1.34 and a Z value of 2.576. Even with this, the Z score is less than the previous system meaning that it’s reducing the payment time in half.

99% CI =(16.766, 19.449) less than 19.5 = µ ≤ 19.5 days.

If the population mean payment time is 19.5 days, the probability of observing a sample mean payment time of 65 invoices less than or equal to 18.1077 days is 0.0038. The below calculation displays how the value was determined.

Z value for 18.1077 is z = (18.1077-19.5)/0.5209 = -2.67

P (mean x <18.1077) = P (z < -2.67) = 0.0038

By reviewing the values, the implementation of the new billing system will allow the customers to receive their invoices electronically and will also be useful in fast bill pay. This innovative system will save time for both the customers and the company as it was demonstrated in three months that the average bill payment time was decreased by 50%.

References

Black, K. (2017). Business Statistics: For Contemporary Decision Making, (9th Edition).

Hoboken, NJ: Wiley.