Mathematics
QNT 561 University of Phoenix Billing System Effectiveness Case Study

Qnt 561

University of Phoenix

QNT

### Question Description

I’m trying to learn for my Statistics class and I’m stuck. Can you help?

urpose of Assignment

The purpose of the assignment is to develop students' abilities in using data sets to apply the concepts of sampling distributions and confidence intervals to make management decisions.

Assignment Steps

Resources: Microsoft Excel®, The Payment Time Case Study, The Payment Time Case Data Set

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. 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?

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PayTime 22 19 16 18 13 16 29 17 15 23 18 21 16 10 16 22 17 25 15 21 20 16 15 19 18 15 22 16 24 20 17 14 14 19 15 27 12 17 25 13 17 16 13 18 19 18 14 17 17 12 23 24 18 16 16 20 15 24 17 21 15 14 19 26 21 Case Study – Payment Time Case Study QNT/561 Version 9 University of Phoenix Material Case Study – Payment Time Case Study Major consulting firms such as Accenture, Ernst & Young Consulting, and Deloitte & Touche Consulting employ statistical analysis to assess the effectiveness of the systems they design for their customers. In this case, a consulting firm has developed an electronic billing system for a Stockton, CA, trucking company. The system sends invoices electronically to each customer’s computer and allows customers to easily check and correct errors. It is hoped the new billing system will substantially reduce the amount of time it takes customers to make payments. Typical payment times—measured from the date on an invoice to the date payment is received—using the trucking company’s old billing system had been 39 days or more. This exceeded the industry standard payment time of 30 days. The new billing system does not automatically compute the payment time for each invoice because there is no continuing need for this information. The management consulting firm believes the new system will reduce the mean bill payment time by more than 50 percent. The mean payment time using the old billing system was approximately equal to, but no less than, 39 days. Therefore, if µ denotes the new mean payment time, the consulting firm believes that µ will be less than 19.5 days. Therefore, to assess the system’s effectiveness (whether µ < 19.5 days), the consulting firm selects a random sample of 65 invoices from the 7,823 invoices processed during the first three months of the new system’s operation. Whereas this is the ﬁrst time the consulting company has installed an electronic billing system in a trucking company, the ﬁrm has installed electronic billing systems in other types of companies. Analysis of results from these other companies show, although the population mean payment time varies from company to company, the population standard deviation of payment times is the same for different companies and equals 4.2 days. The payment times for the 65 sample invoices are manually determined and are given in the Excel® spreadsheet named “The Payment Time Case”. If this sample can be used to establish that new billing system substantially reduces payment times, the consulting firm plans to market the system to other trucking firms. Copyright © 2017 by University of Phoenix. All rights reserved. 1 ...
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Billing system’s effectiveness
Name
Date
Institution.

BILLING SYSTEM’S EFFECTIVENESS

2

New Billing System effectiveness.
Introduction.
The management consulting group has recorded over seven thousand invoices for the
first three months. Out of those, our sample consists of only 65 observations. The management
consulting system believes that the new system will cut the invoice processing time by more
than half, which means that the current processing time of thirty-nine days is likely to reduce
to 19.5 days or less. To establish whether that is true, we could compute the mean for the
sample observations as well as the standard deviation to serve as an industry benchmark if
necessary. The other question, however, is if the metrics from the sample data is accurate for
the whole population, for this case, the 7832 invoices. To find whether this is true, we test the
estimates and find the confidence interval to assign Z scores to our evaluations.
Sample Data Metrics and Interpretation.
The mean for the sample data gets computed using the AVERAGE Excel functionality.
It calculates to be 18.11 as per the spreadsheet in the Appendix below. Subsequent variance is
calculated by subtracting the mean from each of the variables in the sample data. Conseque...

Carnegie Mellon University
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