The Payment Time Case The Payment Time Case introduces a trucking company in Stockton, CA, that has implemented a new electronic billing system aimed at reducing the average payment period from 39 days to at most 19.5 days, representing a 50% improvement. The company sampled 65 invoices out of a total of 7,823 from the first three months of system use to assess whether the new process is effective. The analysis involves constructing confidence intervals to determine if the sample data support the claim that the mean payment time has decreased to or below the targeted 19.5 days, using population standard deviation estimates and statistical inference. Specifically, the company’s statistical analysis seeks to evaluate whether the actual mean payment time, based on the sample, falls within acceptable limits that confirm the system's effectiveness. The standard deviation of the population payment times is given as 4.2 days, and the sample mean recorded was approximately 18.11 days. The analysis employs confidence intervals at both 95% and 99% levels to estimate the true population mean and to assess the statistical significance of the observed reduction.
Paper For Above instruction The primary goal of this study is to validate whether the newly implemented electronic billing system effectively reduces the average customer payment time to the desired threshold of 19.5 days or fewer. This evaluation is undertaken through a rigorous statistical approach involving confidence interval estimation and hypothesis testing, which serve as tools to infer about the entire population based on the sampled data. Introduction to Confidence Intervals and Hypothesis Testing Confidence intervals are a range of values derived from sample data that are believed, with a certain level of confidence (e.g., 95% or 99%), to contain the true population parameter—in this case, the mean payment time. When constructing a confidence interval, statisticians consider sample mean, sample size, and known population standard deviation to estimate this range (Everitt & Hothorn, 2011). A narrower interval indicates a more precise estimate, often resulting from larger samples or smaller variability. Hypothesis testing complements this by assessing whether the observed data provide sufficient evidence to reject a specified null hypothesis in favor of an alternative. Here, the null hypothesis (H0) posits that the true mean payment time µ equals or exceeds 19.5 days, while the alternative hypothesis (H1) suggests µ is less than 19.5 days, aligning with the company's objective.