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**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. **With Three references**

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.
Grading Guide
Content
Met
Partially
Met
Not Met
Total
Available
Total
Earned
Partially
Met
Not Met
Comments:
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?
Writing Guidelines
The paper—including tables and graphs,
headings, title page, and reference page—is
consistent with APA formatting guidelines and
meets course-level requirements.
Intellectual property is recognized with in-text
citations and a reference page.
Met
Comments:
Writing Guidelines
Met
Partially
Met
Not Met
Total
Available
Total
Earned
Paragraph and sentence transitions are
present, logical, and maintain the flow
throughout the paper.
Sentences are complete, clear, and concise.
Rules of grammar and usage are followed
including spelling and punctuation.
Assignment Total
Additional comments:
Comments:
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Purchase answer to see full attachment

Purchase answer to see full attachment

HiKindly see attached file with the requested 700 words statistical report regarding the use of confidence intervals in the payment time case study

Running head: THE PAYMENT TIME CASE STUDY: CONFIDENCE INTERVALS

THE PAYMENT TIME CASE STUDY: CONFIDENCE INTERVALS

(NAME)

(PROFESSOR’S NAME)

(COURSE)

(DATE)

1

ONE-SAMPLE HYPOTHESIS TEST CASE STUDIES

Confidence intervals give the statistics not only an idea of the average value, but also of

the variability of the results around such average value (Johnson & Kuby, 2000). In this regard,

the objective of building a confidence interval is to evaluate which are the limits between which

a given data can be said to be part of the analyzed sample (O’Hagan & Forster, 2009). This

confidence level is normally pre-established by the person carrying out the analysis. However,

the confidence level is typically fixed at either 95% or 99% for most application purposes

(Bernstein & Bernstein, 1999).

The present report explains how confidence intervals are built and analyzed. In this

regard, both the 95% and 99% confidence inte...

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