payment time (600 words including yellow marked)
payment time (600 words including yellow marked)
The Payment Time Case
The Payment Time Case
The Payment Time Case
Introduction
Many consulting firm hire statistical analysis to review their internal processes as well as the effectiveness of their systems in place. This study is based on a Stockton CA trucking company that hired a firm to develop an electronic billing system. This new and improved billing system has been developed with the hope that it can provide its customers their bills electronically with the hope that in turn the customer makes payments sooner. Currently, it is taking 39 days from the billing day to receive payment which is much higher than the 30 days net it has set on the accounts. The organization is hoping that this new billing systems will minimize the mean of the current billing amount of days it current has by at least 50%. This would dramatically change from the current 39 days mean to a hopeful 19.5 days, give or take.
Sample Test
The firm will take a sample of 65 invoices out of 7,823 invoices from the first three months of billing it accumulates with the new electronic billing system. The consulting firm has created billing systems for many companies, however, this is the first trucking company it develops a billing system. The population mean in other systems they have created varies, but the standard deviation normally stays around 4.2 days. For this same reason, this study has provided us with some analytic questions to review so that we can determine if the organization is on the right track.
Effective New Billing
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 the billing system was effective (“How To Use Excel To Calculate Confidence Interval”, 2010).
Using the 95% confidence interval, can we be 95% confident that µ ≤ 19.5 days?
Confidence Interval Estimate for the Mean FORMULA CI=X ± Z×α/√N
95%
Data
Population Standard Deviation
4.2
Sample Mean
18.1077
Sample Size
65
Confidence Level
95%
Intermediate Calculations
Standard Error of the Mean
0.5209
Z Value
1.9600
Interval Half Width
1.0210
Sample Size
65
Confidence Level
95%
Confidence Interval
Interval Lower Limit
17.0867
Interval Upper Limit
19.1287
95% CI = (17.0867, 19.1287) less than 19.5. (“Confidence Interval Calculator”, 2017).
Our results achieve a 95% confident that µ ≤ 19.5 days. Both the Internal lower and upper show results lower than the original 19.5 days promised by the firm.
Using the 99% confidence interval, can we be 99% confident that µ ≤ 19.5 days?
Confidence Interval Estimate for the Mean FORMULA CI=X ± Z×α/√N
99%
Data
Population Standard Deviation
4.2
Sample Mean
18.1077
Sample Size
65
Confidence Level
99%
Intermediate Calculations
Standard Error of the Mean
0.5209
Z Value
2.5760
Interval Half Width
1.3419
Sample Size
65
Confidence Level
99%
Confidence Interval
Interval Lower Limit
16.7658
Interval Upper Limit
19.4496
Our results achieve a 99% confident that µ ≤ 19.5 days. Both the Internal lower and upper show results lower than the original 19.5 days promised by the firm.
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?
Z value for 18.1077 is z = (18.1077-19.5)/0.5209 = -2.67
P (mean x <18.1077) = P (z < -2.67) =0.0038
(“Confidence Interval Calculator”, 2017).
Conclusion
The firm has created a faster and more reliable billing system. We have taken a sample of three months of billing for a total of 65 and our calculations show that under 95% and 99%, we are still under the 19.5 days requirement to reduce the billing period to more than 50%. This electronic billing system has proven to be effective given the results from the sample taken. Currently the sample sits at 65, but it can be increased if the error of margin needs to be minimized from a hypothesis perspective. But this sample has proven that it can accomplish the goal that the trucking company wants to accomplish when comparing to their current 39 days of invoices being paid.
References
Confidence Interval Calculator. (2017). Retrieved from
How to use Excel to Calculate Confidence Interval. (2010). Retrieved from
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