Importance of Confidence Interval

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Resources: Microsoft Excel®, The Payment Time Case Study, The Payment Time Case Data Set
Review the Payment Time Case Study and Data Set.
Write a 500 to 700-word paper including the following calculations and using the information to determine whether the new billing system has reduced the mean bill payment time:
Assuming the standard deviation of the payment times for all payments is 4.2 days, construct a 95% confidence interval estimate to determine whether the new billing system was effective. State the interpretation of 95% confidence interval and state whether or not the billing system was effective.
Using the 95% confidence interval, can we be 95% confident that µ ≤ 19.5 days?
Using the 99% confidence interval, can we be 99% confident that µ ≤ 19.5 days?
If the population mean payment time is 19.5 days, what is the probability of observing a sample mean payment time of 65 invoices less than or equal to 18.1077 days?

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Case Analysis – Time Payments
Your Name
Subject and Section
Professor’s Name
November 18, 2019

Understanding the importance of statistics in business is crucial in order to help formulate sound business decisions. This importance becomes even more apparent these days as information becomes readily available and accessible, while the demands of the market also increases significantly. Accordingly, one of the statistical tools that can be used to achieve this goal is the confidence interval (CI). The confidence interval is commonly used in order to have a general and objective estimate of the true value of the results derived from the study population. It reduces the risks of an ‘unrepresentative’ population that could lead to false results (University of Yale, n.d.). In line with the case at hand, the confidence interval would be set at 95%. This is in line with the acceptable interval used in the field of both statistics and business.
Accordingly, the CI stated above would be used to measure the efficiency of a new electronic billing incorporated into a Californian trucking company. By obtaining a sample of sixty-five (65) invoices as sample population from a total of 7,823, the company is hoping to understand how to increase the efficiency of the payments. To ensure that there is an increase in an overall efficiency (reduction in number of days), the author of this paper have also set the null hypothesis to 19.5 days, which is the time estimated for clearing payments. All in all, the author believes that the use of the new Electronic Time record would increase the efficiency of the company’s billing system.

Estimation of 95% Confidence Interval

Relying on the Time Data Sheet provided by the company, the mean of the sample population could be computed using the following equation.
Sample mean = n

Utilizing this formula in order to interpret the data in the time sheet, the sample mean would be equal to 0.52.
Sample mean = n
=4.2 / 65
=0.52

In interpreting the derived value in the CI presented above to reach the final ‘sample mean’, a 1.96 CI can be used for the computation by checking the table for z-value. This would then lead to a result of 18.11. Thus, the CI for the given sample set would be:

Following the line of computations above, it could be seen that both the upper and lower limits of the CI falls lower than the 19.5 days (null hypothesis). This means that the use of the new system could indeed lessen the payment time to less than or equal to 19.5 days with 95% certainty.

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