Purpose of Assignment

The purpose of the assignment is to develop students' abilitiesin using data sets to apply the concepts of sampling distributionsand confidence intervals to make management decisions.

Assignment Steps

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

Review the Payment Time Case Study and DataSet.

Develop a 700-word report including thefollowing calculations and using the information to determinewhether the new billing system has reduced the mean bill paymenttime:

• Assuming the standard deviation of the payment times for allpayments is 4.2 days, construct a 95% confidence interval estimateto determine whether the new billing system was effective. Statethe interpretation of 95% confidence interval and state whether ornot the billing system was effective.
• Using the 95% confidence interval, can we be 95% confident thatµ ≤ 19.5 days?
• Using the 99% confidence interval, can we be 99% confident thatµ ≤ 19.5 days?
• If the population mean payment time is 19.5 days, what is theprobability of observing a sample mean payment time of 65 invoicesless than or equal to 18.1077 days?

Case Study – Payment Time CaseStudy

Major consulting firms such as Accenture, Ernst &Young Consulting, and Deloitte & Touche Consulting employstatistical analysis to assess the effectiveness of the systemsthey design for their customers. In thiscase, a consulting firm hasdeveloped an electronic billing system for a Stockton, CA, truckingcompany. The system sends invoices electronically to eachcustomer’s computer and allows customers to easily check andcorrect errors. It is hoped the new billing system willsubstantially reduce the amount of time it takes customers to makepayments. Typical payment times—measured from the date on aninvoice to the date payment is received—using the truckingcompany’s old billing system had been 39 days or more. Thisexceeded the industry standard payment time of 30days.

The new billing system does not automatically computethe payment time for each invoice because there is no continuingneed for this information. The management consulting firm believesthe new system will reduce the mean bill payment time by more than50 percent. The mean payment time using the old billing system wasapproximately equal to, but no less than, 39 days. Therefore, if µdenotes the new mean payment time, the consulting firm believesthat µ will be less than 19.5 days. Therefore, to assess thesystem’s effectiveness (whether µ < 19.5 days), the consultingfirm selects a random sample of 65 invoices from the 7,823 invoicesprocessed during the first three months of the new system’soperation. Whereas this is the first time the consulting company hasinstalled an electronic billing system in a trucking company, thefirm has installed electronic billing systems in other types ofcompanies.

Analysis of results from these other companies show,although the population mean payment time varies from company tocompany, the population standard deviation of payment times is thesame for different companies and equals 4.2 days. The payment timesfor the 65 sample invoices are manually determined and are given inthe Excel^® spreadsheetnamed “The Payment Time Case”. If this sample can be used toestablish that new billing systemsubstantially reduces payment times, the consulting firm plans tomarket the system to other trucking firms.

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

I do not need help with the paper. I need to understand themath.