The Payment Time Case Study

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timer Asked: Sep 8th, 2017
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Question description

The Payment Time Case Study- The Excel has been posted and completed just need paper

Purpose of Assignment

The purpose of the assignment is to develop students' abilities in using datasets 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?

Format your assignment consistent with APA format.

Click the Assignment Files tab to submit your assignment.

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. Purpose of Assignment The purpose of the assignment is to develop students' abilities in using datasets 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? Copyright © 2017 by University of Phoenix. All rights reserved. 1 Case Study – Payment Time Case Study QNT/561 Version 9 Format your assignment consistent with APA format. Click the Assignment Files tab to submit your assignment. Copyright © 2017 by University of Phoenix. All rights reserved. 2
Difference PayTime from Mean 22 3,8923 19 0,8923 16 -2,1077 18 -0,1077 13 -5,1077 16 -2,1077 29 10,8923 17 -1,1077 15 -3,1077 23 4,8923 18 -0,1077 21 2,8923 16 -2,1077 10 -8,1077 16 -2,1077 22 3,8923 17 -1,1077 25 6,8923 15 -3,1077 21 2,8923 20 1,8923 16 -2,1077 15 -3,1077 19 0,8923 18 -0,1077 15 -3,1077 22 3,8923 16 -2,1077 24 5,8923 20 1,8923 17 -1,1077 14 -4,1077 14 -4,1077 19 0,8923 15 -3,1077 27 8,8923 12 -6,1077 17 -1,1077 25 6,8923 13 -5,1077 Arithmetic mean 18,1077 Difference Squared 15,1501 0,7962 4,4424 0,0116 26,0885 4,4424 118,6424 1,2270 9,6578 23,9347 0,0116 8,3654 4,4424 65,7347 4,4424 15,1501 1,2270 47,5039 9,6578 8,3654 3,5808 4,4424 9,6578 0,7962 0,0116 9,6578 15,1501 4,4424 34,7193 3,5808 1,2270 16,8731 16,8731 0,7962 9,6578 79,0731 37,3039 1,2270 47,5039 26,0885 Variance 15,6913 Std Deviation (sample) 3,96123 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 -1,1077 -2,1077 -5,1077 -0,1077 0,8923 -0,1077 -4,1077 -1,1077 -1,1077 -6,1077 4,8923 5,8923 -0,1077 -2,1077 -2,1077 1,8923 -3,1077 5,8923 -1,1077 2,8923 -3,1077 -4,1077 0,8923 7,8923 2,8923 1,2270 4,4424 26,0885 0,0116 0,7962 0,0116 16,8731 1,2270 1,2270 37,3039 23,9347 34,7193 0,0116 4,4424 4,4424 3,5808 9,6578 34,7193 1,2270 8,3654 9,6578 16,8731 0,7962 62,2885 8,3654 1004,2462 Sum of Squares

Tutor Answer

strongboss5
School: Cornell University

Kindly see attached file with the requested analysis together with the corresponding plagiarism report.I haven't done any editions to the excel worksheet you had uploaded. The rest of calculations needed are shown in the word file. However, if you believe you need to include them as well in the excel let me know to do it

Running head: THE PAYMENT TIME CASE STUDY

THE PAYMENT TIME CASE STUDY
(NAME)
(PROFESSOR’S NAME)
(COURSE)
(DATE)

1

THE PAYMENT TIME CASE STUDY

2

Confidence intervals are a commonly used statistical tool to provide a rapid idea of both
the average value, located in the middle of the interval, and of the variability of the results,
indicated by the limits of the confidence interval (O’Hagan, 2009). Taking this into account, both
the average and the variation of the results need to be calculated when attempting to build a
confidence interval. Another important parameter necessary when establishing the confidence
interval is the desired confidence level. This represents the minimum probability that the
statistician is willing to accept of finding the real population mean within the limits of the
confidence interval (Johnson, 2000).
In this report, different confidence intervals are being used to evaluate if the payment
time of the customers of a hypothetical trucking company is affected by the new company
strategy. In this regard, the managers of the company hope that the new strategy motivates
customers to pay their bills earlier, such that the payment time is decreased to at least 19.5 days.

Evaluation of the descriptive statistics of the payment time case data set
As has been previously indicated, one of the necessary steps to build a confidence
interval for a series of data is to calculate both their mean value and their standard deviation.
Another critical parameter is the sample size being considered, since it is expected that the
broader the sample, the higher the variability of the results within it.
Taking this into account, the first step towards the construction of the necessary
confidence intervals requested to answer the manager’s questions has been the calculation of the
average, standard deviation and sample size of the data provided in the payment time case study
dataset. The obtained results from such analysis are summarized in table 1.
Table 1. Summary of the results obtained from the descriptive analysis of the dataset

THE PAYMENT TIME CASE STUDY

3

Statistic

Value

Average payment time

𝑥̅ =

Sample standard deviation
𝑠=√
Sample size

∑𝑥
= 18.11
𝑛

∑(𝑥 − 𝑥̅ )2
= 3.96
𝑛−1

n = 65 customers

Analysis
In order to build the confidence intervals of the payment time with the gathered data, it
has been assumed that they follow a normal distribution. This assumption is considere...

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Review

Anonymous
Good stuff. Would use again.

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