Week 2: Data-Driven Decision Making for healthcare Administration Practice

Probability and Probability Distributions

How is probability related to decision making? How might an appreciation for the likelihood of an event occurring versus not occurring affect how you might engage in decision making?

Although it might seem unclear right now, probability and probability distributions can aid healthcare administration leaders in determining those events that may or may not affect how healthcare delivery is practiced. In fact, the likelihood that certain events might occur could mean an increase in resource and staff costs. How might healthcare administration leaders leverage an understanding of probability to make sound business and healthcare decisions?

1. This week, you review the foundations of probability and probability distributions. You then apply probability distributions for informing how you might engage in data-driven decision making for business and healthcare delivery problems.

Learning Objectives

Students will:

· Apply the foundations of probability and probability distributions

· Apply probability distributions for data-driven decision-making problems.

Learning Resources

Note: To access this week’s required library resources, please click on the link to the Course Readings List, found in the Course Materials section of your Syllabus.

Required Readings

Albright, S. C., & Winston, W. L. (2017). Business analytics: Data analysis and decision making (6th ed.). Stamford, CT: Cengage Learning.

Chapter 4, “Probability and Probability Distributions”

Chapter 5, “Normal, Binomial, Poisson, and Exponential Distributions”

Fulton, L. V., Mendez, F. A., Bastian, N. D., & Musal, R. M. (2012). Confusion between odds and probability, a pandemic? Journal of Statistics Education, 20(3), 1–20.

Note: Retrieved from the Walden Library databases.

Microsoft. (2016). Statistical functions (reference). Retrieved from https://support.office.com/en-us/article/Statistical-functions-reference-624dac86-a375-4435-bc25-76d659719ffd

Required Media

ExcelIsFun. (2011, July 19). Excel 2010 statistics 63: Exponential probability EXPON.DIST function [Video file]. Retrieved from https://www.youtube.com/watch?v=RQ9VOaWxDFo&feature=youtu.be

Grande, T. [Todd Grande]. (2015, February 27). Calculating probabilities using the normal distribution function in Excel [Video file]. Retrieved from https://www.youtube.com/watch?v=MRxnYidPzlo&feature=youtu.be

Grande, T. [Todd Grande]. (2015, April 3). Binomial distribution function in Excel [Video file]. Retrieved from https://www.youtube.com/watch?v=i44hBz7pArE&feature=youtu.be

Hays, D. [David Hays]. (2012, April 12). Poisson distribution on Excel [Video file]. Retrieved from https://www.youtube.com/watch?v=jA_-PBGSMz4&feature=youtu.be.

Discussion Part

Utility of Probability Models in Healthcare Administration

1. You are the healthcare administration leader for a health services organization and are interested in achieving a standard, whereby 90% of all patients are screened within the initial 15 minutes of arriving for a family practice appointment. In a random sample of 30 patients, you find that 25 were screened within 15 minutes. The probability that this event (or one more extreme) would occur, might be modeled as a binomial with the following probability statement:

P(X?25 | N=30, p=0.9)

2. To solve, you use =binom.dist(25, 30, 0.9, TRUE) in Excel and find that you would expect 25 or fewer screenings in 30 trials when the success rate should be 0.9 about 17.5% of the time.

3. For this Discussion, review the resources for this week, and consider how one of the distributions presented might be useful for healthcare administration leaders.

By Day 3

4. an example of how one of the distributions presented might be used in your health services organization or one with which you are familiar. Then, generate a representative probability statement based on the scenario and solve using fictitious data. Be specific in your probability statement.

By Day 5

Continue the Discussion and respond to your colleagues in one or more of the following ways:

· Ask a probing question, substantiated with additional background information, evidence, or research.

· Share an insight from having read your colleagues’ postings, synthesizing the information to provide new perspectives.

· Offer and support an alternative perspective, using readings from the classroom or from your own research in the Walden Library.

· Validate an idea with your own experience and additional research.

· Make a suggestion based on additional evidence drawn from readings or after synthesizing multiple postings.

· Expand on your colleagues’ postings by providing additional insights or contrasting perspectives based on readings and evidence.

Submission and Grading Information

Grading Criteria

To access your rubric:

Week 2 Discussion Rubric

Post by Day 3 and Respond by Day 5

To participate in this Discussion: Week 2 Discussion.

Assignment Part (APA format 7th ed) 5 pages.

Medicare Overbilling Analysis

Your company is running a Medicare audit on Sleaze Hospital. Because Sleaze has a history of overbilling, the focus of your audit is on checking whether the billing amounts are correct. Assume that each invoice is for too high an amount with probability 0.06 and for too low an amount with probability 0.01 (so that the probability of a correct billing is 0.93). Also, assume that the outcome for any invoice is probabilistically independent of the outcomes for other invoices.

(A.) For this Assignment, reflect on the case presented. Think about what strategies you might use to calculate associated probabilities for Sleaze Hospital, and then address the series of questions for the completion of the Assignment.

The Assignment: (5 pages)

1. If you randomly sample 200 of Sleaze’s invoices, what is the probability that you will find at least 15 invoices that overcharge the customer? What is the probability you won’t find any that undercharge the customer?

2. Find an integer, k, such that the probability is at least 0.99 that you will find at least k invoices that overcharge the customer. (Hint: Use trial and error with the BINOMDIST function to find k.)

3. Suppose that when Sleaze overcharges Medicare, the distribution of the amount overcharged (expressed as a percentage of the correct billing amount) is normally distributed with mean 15% and standard deviation 4%.

4. What percentage of overbilled invoices are at least 10% more than the legal billing amount?

5. What percentage of all invoices are at least 10% more than the legal billing amount?

6. If your auditing company samples 200 randomly chosen invoices, what is the probability that it will find at least five where Medicare was overcharged by at least 10%?

By Day 7

Submit your answers and embedded Excel analysis as a Microsoft Word management report.

Submission and Grading Information

To submit your completed Assignment for review and grading, do the following:

Please save your Assignment using the naming convention “WK2Assgn+last name+first initial.(extension)” as the name.

Click the Week 2 Assignment Rubric to review the Grading Criteria for the Assignment.

Click the Week 2 Assignment link. You will also be able to “View Rubric” for grading criteria from this area.

Next, from the Attach File area, click on the Browse My Computer button. Find the document you saved as “WK2Assgn+last name+first initial.(extension)” and click Open.

If applicable: From the Plagiarism Tools area, click the checkbox for I agree to submit my paper(s) to the Global Reference Database.

Click on the Submit button to complete your submission.

Grading Criteria

To access your rubric:

Week 2 Assignment Rubric

Check Your Assignment Draft for Authenticity

To check your Assignment draft for authenticity:

Submit your Week 2 Assignment draft and review the originality report.

Submit Your Assignment by Day 7

To submit your Assignment: Week 2 Assignment