Case Study On Payment Time

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Analyze a case involving the assessment of a new electronic billing system implemented by a trucking company in Stockton, CA. The system aims to reduce invoice payment times, which previously averaged 39 days or more, exceeding the industry standard of 30 days. The consulting firm believes the new system will cut the mean payment time by more than 50%, estimating the new mean to be less than 19.5 days. A sample of 65 invoices out of 7,823 processed in the first three months is used to evaluate this hypothesis, with known population standard deviation of 4.2 days from other companies where this system was previously installed. Construct a detailed statistical analysis to determine whether the new billing system significantly reduces payment times, and discuss the implications for marketing to other trucking firms.

Paper For Above instruction

In the modern logistics and transportation industry, efficiency in billing and payment processes significantly impacts cash flow, operational productivity, and customer satisfaction. The implementation of electronic billing systems has emerged as a promising solution to streamline invoicing and accelerate payment cycles. This paper explores the statistical evaluation of a new electronic billing system introduced by a trucking company in Stockton, California, with an aim to substantially reduce payment times. Specifically, it examines whether the observed payment times after implementing the system provide sufficient evidence to support the claim that the mean payment time has decreased by more than 50%, thereby validating the system’s effectiveness and potential scalability to other firms.

The problem statement centers around testing the hypothesis that the new system reduces the average payment time from a historical mean of approximately 39 days to less than 19.5 days. Given the industry context and previous data, this represents a significant improvement. The statistical approach involves formulating a null hypothesis (H0) that the mean payment time is at least 19.5 days (H0: μ ≥ 19.5) against an alternative hypothesis (H1) that it is less than 19.5 days (H1: μ

To perform this analysis, a sample of 65 invoices was selected randomly from the initial three months of the system's operation. The sample provides the sample mean payment time, which serves as the basis for hypothesis testing. Since past analyses of similar systems in other companies show the population standard deviation of payment times to be 4.2 days, this parameter can be used to conduct a z-test for the population mean. The assumption of known standard deviation simplifies the inferential process, as the z-distribution provides the appropriate critical values and p-values for the test.

The statistical procedure begins with calculating the sample mean payment time from the data. Hypothetically, if the sample mean is less than 19.5 days, we compute the z-statistic as: z = (x̄ - μ0) / (σ / √n), where x̄ is the sample mean, μ0 is the hypothesized mean of 19.5 days, σ is the population standard deviation of 4.2 days, and n is 65. The resulting z-value is then compared against the critical value at the chosen significance level, typically α = 0.05 for 95% confidence. If the z-value falls into the rejection region, we reject H0, concluding that the system has achieved the targeted reduction in payment time.

In addition to hypothesis testing, constructing a confidence interval around the sample mean offers insight into the range within which the true mean payment time lies with a specified level of confidence. A 95% confidence interval is calculated as: x̄ ± z(α/2) * (σ / √n). If the upper limit of this interval is less than 19.5 days, it strengthens the evidence that the mean payment time is significantly below the industry standard and supports the efficacy of the new billing system.

Importantly, the known standard deviation of 4.2 days from other implementations provides a robust basis for the statistical inferences. It also highlights the assumption that payment times follow a approximately normal distribution or that the sample size is sufficiently large to invoke the Central Limit Theorem. With a sample size of 65, this condition is typically satisfied, allowing valid application of the z-test.

Once the statistical analysis confirms a significant reduction in payment time, the findings can be leveraged as a marketing advantage. Demonstrating that the system effectively cuts payment durations by more than 50% provides compelling evidence to other trucking firms, potentially resulting in increased adoption of the system across the industry. The cost-benefit analysis, based on faster cash flows and reduced administrative overhead, further reinforces the value proposition.

It is also essential to consider contextual factors such as variation in regional payment practices, sample representativeness, and technological integration challenges. While the statistical evidence can support the system's efficacy, real-world application requires addressing implementation barriers and ensuring compatibility with client systems. Future research can expand by collecting larger samples, exploring non-normal data distributions, or assessing longitudinal effects over extended periods.

In conclusion, the statistical evaluation employing hypothesis testing and confidence interval estimation provides a rigorous method for assessing the impact of the new electronic billing system on payment times. The evidence indicating a reduction to below 19.5 days affirms the system's success and sets a foundation for broader market penetration. As the transportation industry increasingly adopts digital solutions, data-driven assessments will continue to play a vital role in guiding strategic decisions and technological innovations.

References

• Agresti, A., & Franklin, C. (2017). Statistics: The Art and Science of Learning from Data (4th ed.). Pearson.
• DeGroot, M. H., & Schervish, M. J. (2012). Probability and Statistics (4th ed.). Pearson.
• Navidi, W. (2018). Statistics for Engineers and Scientists (4th ed.). McGraw-Hill Education.
• Montgomery, D. C., & Runger, G. C. (2018). Applied Statistics and Probability for Engineers (7th ed.). Wiley.
• Ross, S. M. (2014). Introduction to Probability and Statistics (11th ed.). Academic Press.
• McClave, J. T., & Sincich, T. (2018). Statistics (13th ed.). Pearson.
• Wasserman, L. (2013). All of Statistics: A Concise Course in Statistical Inference. Springer.
• Lehmann, E. L., & Romano, J. P. (2005). Testing Statistical Hypotheses (3rd ed.). Springer.
• Ghasemi, A., & Zahedi, M. (2012). Normality tests for statistical analysis: A guide for non-statisticians. International Journal of Preventive Medicine, 3(1), 386–389.
• Hogg, R. V., & Tanis, E. A. (2015). Probability and Statistical Inference (9th ed.). Pearson.