Is there a conclusion with Week 4 Payment Time Case?

A consulting company has developed an electronic billing system for a trucking company with the intent to reduce the amount of time it takes for customers to make payments by 50%. Measuring from the invoice date to the date payment is received, the general time it took to receive a payment from customers took 39 or more days, which exceeded the 30 day industry standard payment time. The management consulting firm believes that the new average amount of days it takes to receive customer payments will be less than 19.5 days with their new system. Using a random sample of 65 invoices from the 7,823 invoices processed during the first three months of the new system's operation, the firm wishes to conduct an analysis to determine if their theory if their new billing system substantially reduces payment times so that they can market the system to other trucking firms. The analysis will be performed using 95% and 99% confidence intervals and the findings will be discussed in the following sections.

Confidence Interval Analysis

For the 95% confidence interval analysis, alpha (), 1 - .95, is calculated to be .05. The mean of the payment times for the sample of 65 invoices is 18.11 days (rounded up from 18.107692) and the standard deviation is assumed to be 4.2 days. Using the CONFIDENCE (alpha, standard deviation, sample size) formula in Excel, the margin of error was calculated to be 1.021. To determine the upper and lower bounds of the confidence interval, the margin of error is added or subtracted from the sample mean. The upper bound of the confidence interval is calculated to be 19.129 (18.11 + 1.021) and the lower bound is 17.087 (18.11 - 1.021). The upper bound of the confidence interval is less than 19.5 days, indicating that the consulting firm can be 95% confident that the new mean payment time is less than 19.5 days.

For the 99% confidence interval, the sample size, sample mean, and standard deviation were the same. Alpha, however, was adjusted to reflect 1 - .99 and calculated as .01. Using the CONFIDENCE formula in Excel, the margin of error was calculated to be 1.342. The upper bound of the 99% confidence interval was 19.450, which was determined by adding the margin of error (1.342) to the sample mean (18.11). The lower bound was calculated at 16.766 by subtracting the margin of error from the sample mean. The 99% confidence interval analysis indicates that the consulting firm can be 99% confident that the new mean payment time is less than 19.5 days.

Conclusion

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