Prepare an 800-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?
Additional Guidance on This Assignment
Here are the descriptive numbers for the assignment at the 95% confidence level. These values below represent all that you need for step #1. You may use my values for the 95% confidence level (step #1).
When you compute/identify the values for Step 2, the only values that will change are the confidence level (99%), the z-Value, and the upper and lower bounds of the confidence level.
Step 1.
Confidence interval – mean
95% confidence level
18.1077 Mean
4.2 std. dev.
65 N
1.960 Z
1.0210 half-width
19.1287 upper confidence limit
17.0867 lower confidence limit
Review the upper confidence limit and determine if the upper confidence limit is less than or equal to the required return time of 19.5 days
Step 2.
Compute/identify values for the 99% confidence level (the z score, and the confidence interval). Review the upper confidence limit and determine if the upper confidence limit is less than or equal to the required return time of 19.5 days.