Review the Payment Time Case Study and Data Set.

Develop a 700-word report 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. Present the confidence interval, state the interpretation of the confidence interval, and state whether or not the new billing system was effective.
• Using a 99% confidence interval, can we be 99% confident that µ ≤ 19.5 days? Justify your answer.
• 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? Justify your answer.