Statistical analyses are essential especially when it comes to testing for the effectiveness of new processes, use of new technology or just employment of different strategies within firms. As time goes by, businesses evolve so as to meet different customer needs as well as ensure that there is better customer satisfaction. This evolution almost always leads to an increase in competition between companies exploring the same niche. In this case, a new electronic billing system for Stockton, CA, trucking company is being tested in the hopes that it will reduce the amount of time it takes customers to make payments. Essentially, the company aims at reducing the payment times from its current 39 days to below the industry standard payment time of 30 days. The system has already been implemented by other companies and it is estimated that it has cut the payment times to less than 19.5 days. The company now aims to use data from these companies to ascertain whether the information is true and make a decision on whether or not to invest on it. The calculations below are from sample of 65 cases that were obtained from these companies.
To determine both the 95% and 99% confidence interval, we use the formula:
For the 95% confidence interval:
For the 99% confidence interval:
From the results above, we can be 95% confident that the population mean is less than days as the upper boundary is while the lower boundary is We can also be 99% confident that the population mean is less than 19.5 days as the upper boundary in this case is and the lower boundary is .
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The probability or ) that mean payment time of the 65 invoices is less than or equal to is and is obtained from the Z table.
References
Gardner, M. J., & Altman, D. G. (1986). Confidence intervals rather than P values: estimation rather than hypothesis testing. Br Med J (Clin Res Ed) , 292 (6522), 746-750.
Bluman, A. G. (2009). Elementary statistics: A step by step approach . New York: McGraw-Hill Higher Education.
