By my calculations regarding to the excel spreadsheet of thecase study, it is a 99% probability that the mean payment will fall equal to orless than 18.1077, because the confidence interval is between 17.1736 to 18.418therefore, we made the population mean of payment time to be observed as farless 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 65invoices having a less than or equal to 18.1077 days?For the 99% confident interval above, the Stockton trucking companycan conclude with a 99% confidence that the population mean payment time forthe new electronic trucking billing system will falls between 17.736 and18.418.17.736< ?<18.
418= 18.077 + .341 = 18.418Upper CI = MEAN + CI= 18.077 – .341 = 17.
736Lower CI = MEAN – CI= 18.077 + 1.341= 18.077 + 2.575 (.
5209)CI = MEAN + z (SE)SE = 4.2 / sqrt 65 = .5209When we use the 99% confidence interval, can we be 99%confident that µ < 19.5 days? Well we can beconfident 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 rangesas asked.
By using this important level of confidence interval, the intervalgets wider, with the sample size and standard deviation remaining the samewhich can lead to some further complications. For a 99% confidence interval weused the formula provided below:We have assumed that the calculation of the average paymentperiod, their primary purpose is to obtain the average period that can be takenby the target company by making payments to its creditors. In this case, thenew billing system will be appropriately computing to determine the probabilityof the mean payment time. When asked to use the 95% confidence interval, can webe 95% confident that the µ < 19.5 days, then the answeris yes; We can be 95% confident that the mean number of payment days will fallequal or below 19.
5 as indicated in the data by the Excel spreadsheet.