By my calculations regarding to the excel spreadsheet of the
case study, it is a 99% probability that the mean payment will fall equal to or
less than 18.1077, because the confidence interval is between 17.1736 to 18.418
therefore, we made the population mean of payment time to be observed as far
less during those sample mean invoices based on the data given to us.
If the population mean payment time came out to 19.5 days,
what would be the probability of observing the sample mean payment time of 65
invoices having a less than or equal to 18.1077 days?
For the 99% confident interval above, the Stockton trucking company
can conclude with a 99% confidence that the population mean payment time for
the new electronic trucking billing system will falls between 17.736 and
17.736< ?<18.418 = 18.077 + .341 = 18.418 Upper CI = MEAN + CI = 18.077 - .341 = 17.736 Lower CI = MEAN – CI = 18.077 + 1.341 = 18.077 + 2.575 (.5209) CI = MEAN + z (SE) SE = 4.2 / sqrt 65 = .5209 When we use the 99% confidence interval, can we be 99% confident that µ < 19.5 days? Well we can be confident with the 99% having a higher level of confidence interval but however, there can be a high level of uncertainty, we just have to make it a 100% confidence. It will be less likely that the values will fall between the ranges as asked. By using this important level of confidence interval, the interval gets wider, with the sample size and standard deviation remaining the same which can lead to some further complications. For a 99% confidence interval we used the formula provided below: We have assumed that the calculation of the average payment period, their primary purpose is to obtain the average period that can be taken by the target company by making payments to its creditors. In this case, the new billing system will be appropriately computing to determine the probability of the mean payment time. When asked to use the 95% confidence interval, can we be 95% confident that the µ < 19.5 days, then the answer is yes; We can be 95% confident that the mean number of payment days will fall equal or below 19.5 as indicated in the data by the Excel spreadsheet.