Determine whether the new billing system has reduced the mean bill payment time

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. 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?

qnt561_r9_payment_time_case_dataset qnt561_r9_payment_time_case_week_4