UBLOGO1

MGQ 606: PROBABILITY AND STATISTICS FOR MANAGEMENT

Instructor:	Teaching Assistant:
Frank Krzystofiak Ph.D.	Nisha Lakshminarayanan
271 Jacobs Management Center	275 Jacobs Management Center
Hours: 2:30 – 3:30 M. & W.	Hours:
Phone: (716) 645 – 3230	Phone: (716) 645 - 5236
E-mail: fk@buffalo.edu	E-mail: nl24@buffalo.edu
Web: http://ublearns.buffalo.edu

Orientation and Objective:

Managerial activity revolves around the making of decisions. One essential aspect of decision making involves organizing and evaluating relevant data. Given the amount of data accessible to today’s managers there is an increasing need to rely on quantitative methods as a means of extracting significant information and giving it meaning. In this way, Quantitative Methods means making facts speak clearly by turning facts into information, so that information can be turned into decisions, and decisions into results.

Good managerial judgment requires an understanding of the numbers combined with an appreciation for what the numbers mean (and what they don't mean!). Managers find simple models and ideas provide powerful and sometimes surprising qualitative insights about common problems. The course aims to give you a feeling for the kinds of problems that are amenable to quantitative analysis, the methods available for performing such analysis, and the difficulties involved in gathering the relevant data.

Third the course reflects my belief that managers do more than make decisions; managers communicate to others their understanding of situations, including the issues to be considered, objectives, action alternatives, contingencies, and uncertainties. One emphasis of this course will be placed on: development of abilities to approach problems by using a systematic, analytical process; implementation of mathematical models on a computer; understanding of the resulting output; and communication of relevant information.

Rather than survey all of the techniques I stress those fundamental concepts and tools that I believe are most important for the practical analysis of management decisions, presenting the material as much as possible in the context of realistic business situations from a variety of settings. The implementation of these tools has been facilitated considerably by the development of spreadsheet-based software packages, and so I make liberal use of spreadsheet models. My goal is to enable you to become intelligent users of quantitative techniques, not experts in statistics or computer software.

You may find that much of the action in the course has to do with the mechanics of the formulation and solution of simple problems. That is not the purpose of the course, but I believe that at time it is the best way to accomplish course objectives. The simple exercises are complemented by a case assignment that captures more realistically the complexity of managerial problems.

Skill Orientation

Numeracy skills: The ability to reason logically, especially with numbers, making rough estimates or a back-of-the-envelope calculation, checking for consistency of units.

Design skills: The skills necessary to build and use a simple spreadsheet. Basic ability: to identify key data, to summarize that data, to display results both tabularly and graphically, to debug a spreadsheet effectively, and to draw useful inferences from the outputs.

Interpretation skills: Interpretation skills include the ability to recognize a problem in a complex mess of symptoms, causes, solutions, and data; the ability to infer patterns and meanings from data; and the ability to translate these patterns into layman’s language to communicate clearly to decision makers or employees who will have to implement proposed changes

Course Mechanics:

1. Reading, assignments and cases are completed prior to the period for which they are assigned.

2. In general, attendance is voluntary.

3. Side conversations, late arrivals and early departures, reading the newspaper, and the like are disruptive. The role of enforcer is one that I neither desire nor enjoy, so I will count on all of you to uphold and enforce appropriate standards of classroom conduct. Thank You.

4. Pictures and Name Cards: All students will be asked to provide a current photograph. The photograph must look like you and be clear!

5. The lectures are used to present the basic ideas. Although the textbook will be followed fairly closely, it is the students' responsibility to keep informed and current in regard to day-to-day coverage.

Text:

Grades:

◦ Final grades will be based on cumulative points earned in examinations, cases, and evaluations.

◦ Final Examination 25%

◦ Quizzes 30%

◦ Individual Homework 20%

◦ Group Cases/Homework 25%

◦ Peer Evaluations (part of group case homework 25%)

◦ Class Participation (part of individual & group homework 45%)

Homework:

◦ Six Individual Homework exercises provide opportunities to practice statistical analysis introduced in the course. Homework emphasizes the quantitative aspects of the course material and provides feedback on how well the analytic techniques are being mastered. Students are encouraged to go over these assignments in-group. Each of you is expected to seriously attempt each homework problem individually, and only to use the group to help resolve open issues. Ultimately, each student is responsible for all the material covered on the homework.

◦ Homework is to be submitted as an electronic file (Excel, Word, Power Point, PDF, or RFT) via the U B Learns digital drop box.

1. Log into U B Learns,

2. Select Tools,

3. Select Digital Drop box

4. Select Send File Note: if you select Add File the file is uploaded but not sent to the instructor.)

5. Enter your name,

6. Browse to find and attach your file, and

7. Click Submit.

◦ Homework Grading Policy:

• Five questions from each homework will be graded

• 1 point: for each of the 5 graded questions that is completed

• 0-3: for each of the 5 graded questions, based on the accuracy of the answer

◦ The lowest completed homework score will be dropped when calculating the total homework score

◦ All homework assignments are due by 9:00 am on the scheduled date. Late work will neither be accepted nor graded if we erroneously accept it.

◦ These assignments will count towards your final grade, and hence you each must submit your own homework solution. Though homework only accounts for 20% of the final grade, it is important to do the assignments for practice. Similar problems are likely to appear in the quizzes and exams.

◦ File Naming convention: Last Name_ Person Number _ Assignment (e.g. Krzystofiak 55559999 H1.xls or Krzystofiak 55559999 H1.doc). Each homework assignment should be headed in the upper left corner with your last name, first name, and student ID number. Homework without proper student identification will be discarded.

Group Cases

Group Homework provides a description of practical situations where statistics analysis can play an important role. The cases provide opportunities to practice translating situations into problem structures and, in doing so, to adapt the general concepts of modeling to particular circumstances. The group will submit one solution.

• The lowest Case score will be dropped when calculating the group case score

• Peer & Instructor evaluations will be used as a multiplier to adjust your individual case score from 0% (yes that is zero 0%) to 110% of the group case score

2. Case 2: Rugged Client Computers (Description & Display): Prepared for his class by Frank Krzystofiak

3. Case 3: Rugged Client Computers: Quality Control (Probability) Prepared for his class by Frank Krzystofiak

Exams and Quizzes:

◦ There will be two quizzes and a cumulative final exam for this class.

◦ All students must use a pen to write midterm and final exams. Use of pencil voids the student's right to request a re-grade of the exam.

◦ The quizzes and exams will be closed book. One 8.5 x 11.5" note sheet will be allowed on the quizzes and two 8.5 x 11" note sheets will be allowed on the final exam. You may use any portable calculator for the quizzes or the exam (so long as it is not capable of wireless communication). Necessary tables and Excel output or data sets required to solve problems will be provided.

◦ Makeup quizzes and examinations will not be given. The only excuses for missing an exam are: a serious illness or a major family crisis. You must provide proof in the form of an official document. A note from a family member is not sufficient. To be clear -- To prove that you are seriously ill, you need to have a note from a physician documenting that you could not take the particular exam. A note from a physician saying that you were seen for a problem is not sufficient. Colds, sinus problems, upset-stomach, slight fever, etc. are not valid reasons for missing an exam. If you miss a quiz or exam and do not have a valid excuse as described above, you will receive a zero.

Grading Policies:

◦ I do not give extra-credit work (even if you ask).

◦ (Re-grade) Any dispute arising in grading of homework and exams should be submitted in writing. This letter should clearly state the question(s) where you think there has been a grading error and what you think that error is. Note that upon resubmission the entire exam or homework may be re-graded and not just the disputed question.

◦ (Re-grade) No re-grades will be accepted for quizzes and exams written in pencil.

◦ (Re-grade) There is a one-week time limit for submission of disputes for quizzes, exams and homework. The one-week limit starts from the day the homework/exam have been returned in class.

Comments

The Course is structured to promote learning by a combination of individual and group efforts. Group interaction is encouraged to enable you to use time efficiently and to improve your understanding of the material. Group collaboration is always encouraged. However, each student is responsible for learning all the material on the assignment.

The group is responsible for allocating group work equitably among its members and for disciplining free riders. Remember, at the end of semester every group member will be required to submit Peer Evaluation forms to indicate the percentage contribution by each group member. The cumulative score of peer evaluation will count toward the final grade.

With respect to exams, group preparation is permissible, but the work during the exam must be done without the help of other students. Conversations with second-year students or alumni about specific assignments or exams before their due-dates are prohibited.

Class Participation and Preparation:

Class participation is evaluated subjectively and will be employed to make marginal adjustments to final grades.

I value attendance, punctuality, familiarity with the required readings, and classroom questions or comments that are relevant and insightful. In general, I evaluate your classroom participation based on the extent to which you contribute to a positive and effective learning environment (for yourself and others). Demonstration of mastery of advanced topics at inappropriate times does not contribute to a positive learning environment! Correcting me, when I am in error, or asking what may appear to be a dumb question, does contribute positively. (Dumb questions are rarely ridiculous. If it is an issue for you, it is likely an issue for many. Asking can keep the class on track.)

Academic Integrity

In the case of written homework assignments, your assignment must represent your own individual work. Although you may discuss homework problems with other students, assignments must represent your own work. It may be confusing to draw a line between individual and group work when groups are allowed to "discuss" problems. For this course, groups may discuss the overall nature of a problem, the various ways to approach each problem, and talk through strategies for solving a problem. Groups are not permitted to work at solving the problem, i.e., they may not start building spreadsheets, analyzing data, and producing results. Those activities must be done individually.

Copying or otherwise using the work of other students on an assignment constitutes a violation of the Policy on Individual Work. Copying or otherwise using any other outside materials on an assignment (including last year's solutions of homework assignments and cases) constitutes a violation of the Policy on Individual Work. Any student who copies or knowingly allows his/her work to be copied or who uses outside materials in the preparation of assignments will receive an 0 grade for the assignment.

All students should familiarize themselves with the School's Code of Ethics and Standards of Academic Integrity (MBA Handbook). Unless otherwise specified, cases, papers, and examinations are to be your work and only your work. In other words, you are to be the sole creator of that work (it is to be developed without the assistance of other individuals and without the aid of cases, papers, and examinations from prior semesters). If you are in doubt about the information sources and/or support that may be used, please ask!

1. Cheating. Obtaining information from another student or other unauthorized source, or giving information to another student, in connection with an examination or assignment

2. Plagiarism. Copying material from a source or sources and submitting this material as one's own without acknowledging, through specific footnoting and quotation marks, the particular debt to the source

3. Falsification of Academic Materials. Fabricating data or other information, forging an instructor's name or initials for any purpose, changing entries in an instructor's record or official University records, taking an examination under another student's name or engaging any person to take an examination under your name, or submitting an assignment of any kind, prepared in whole or part, by any person other than the person responsible for the assignment.

4. Failing to Fulfill Teamwork Requirements. MBA students are expected to contribute as full members of study teams. Failing to meet commonly accepted team standards includes but is not limited to: not attending team meetings, not completing a fair share of team assignments, and not valuing the contributions of all team members.

Cases Deliverables

Group Homework provides a description of practical situations where statistics analysis can play a role. For each case your deliverables will include hardcopy submission of a PowerPoint presentation (handout view) along with Electronic Submission of the PowerPoint presentation and an associated Excel file containing relevant analysis.

PowerPoint should address the following (Don’t answer the questions that I have suggested, rather use the question to guide preparation of a business presentation)

· Introduction (What is the purpose of the presentation? Why are making it?)

· Objective / Question (What is / are the issue (s) or Question (s) ?)

· Analytical setup (What is the nature of the sample, data, etc.? If there are any key assumptions this might be the place to point them out.)

· Analysis (What are your key findings?)

· Interpretations / Implications (What does it mean?)

· Conclusion (Your recommendations? Any limitations)

The Excel file should contain the backup detail of your analysis

· The data

· Analytical calculations and results

· Calculations for interpretations

About cases, I am frequently asked a question along the following lines, “Why did we only get a B or B- on this case? After all, we answered the question!” My answer tends to make a distinction between homework assignments and cases. In homework assignments there is invariably a correct answer, and the grading considerations are only that you found the correct answer and used an appropriate method to get it. In cases the answers are not merely right or wrong. Rather, they can be arrayed along a better to worse continuum in terms of the extent to which they would add value to the organization. Better cases tend to push the interpretations, implications, and conclusions to find ways to add value to the organization in question. Worse cases tend to do little more than answer the question.

Case 1: Lanco Catalogue Sales (Introduction)

1. What is the returns problem? Identify possible source (s) of the problem. Assemble and present the evidence relating your source (s) to order returns.

2. What assumption have you made in your analysis?

3. What options could / should be considered to rectify the problem.

4. Make recommendations to Lanco’s directors on how to deal with the “product returns” issue. Support your recommendations.

Don’t worry about coming up with the single best answer! As far as I am concerned, there probably isn’t a best answer (although there are many bad answers). Make a reasonable set of assumptions and analyze accordingly. From your analysis, make a decision or recommendation. If you need assistance feel free to ask any question that you have and / or use me as a consultant.

Case 2: Rugged Client Computers (Description & Display)

The point of this exercise is to link your data analysis and presentation to managerial decision making. Developing analysis and presentation skills will make the models that you build useful. We build models in order to facilitate evidence based decision making.

Start with Rugged_Computer.xls (completed model with Scenarios). Develop tables and/or charts that summarize the results of the model. The focus should be to assist in selection of an optimal entry price for the computers. Again this involves two tasks: analysis of the data preparation of a graphical exhibit that communicate.

Through analysis and presentation you market the results or products of your efforts. As a manager you gather information and build models to facilitate evidence based decision making.

An essential analytic task in making decisions based on evidence is to understand how things work – mechanism, trade - offs, process and dynamics, cause and effect. That is, intervention - thinking and policy - thinking demand causality - thinking.

Making decisions based on evidence requires the appropriate display of that evidence. Good display of data helps to reveal knowledge relevant to understanding mechanism, process and dynamics, cause and effect. That is, display of statistical data should directly serve the analytic task at hand. (Tufte, 1997)

Tufte’s point is simple: just because something is reasonable or obvious in theory, just because is clear in the data, doesn’t mean that it will implemented in the actual practice of assessing the data and making decisions.

Case 3: Rugged Client Computers: Quality Control (Probability)

1. Under the assumption that component failures are independent, prepare an analysis to explain who is correct and what the proper order of testing is.

a. Does order really matter?

b. What determines the proper order, cost, the probability of failure, both, or neither?

2. Should Rachel just send all of the systems to rework?

a. It currently cost $50.00 to send a system to rework. Rachel Mel the founder of Rugged Client computers believes that that this could be brought down to $36.00 or perhaps even $35.50 if all systems were sent to rework.

b. On the plus side this would save the $19.50 that is costs to test every certified system as well as $50.00 rework plus some or all of the $19.50 for any system that experiences a failure for 1 or more components.

3. Based on the 100 system tested does it seem as though component failures are independent?

4. The Data file Rugged Sample of 2500.xls contains complete test results for 2500 system builds. Are component failures independent? What implications does this have for the optimal testing procedure?

Case 4: Amore Foods (Normal Distribution)

1. If the fill target is lowered to 8.22 ounces, how many 20-minute batches will fail to meet the FDA-approved standard because the five sample pies average less than 8 ounces per pie?

2. Prepare a recommendation to Mr. Jenkins regarding lowering the target to 8.22 ounces.

Analysis: The following assumptions may be made to facilitate your analysis.

◦ The mechanical filler fills to target with a standard deviation of 0.22 ounces.

◦ The five sample pies’ weights are independent.

◦ The production rate is 1,000 dozen every 20 minutes.

◦ The monthly production is 60 20-minute batches, or 60,000 dozen pies. Yearly production is 720 batches.

◦ Rejected batches are first sold at the Thrift Store and then donated to charity once the Thrift Store demand has been filled.

◦ The Thrift Store demand is 240 dozen (4 X 60) per month.

Case 5: Home Education Inc. (Point Estimation)

1. What financial reserve should be set aside for TV kits?

2. After presenting your estimates to the auditors, you are surprised to find that the auditors don’t think the estimate is accurate enough. In particular, the auditors insist that the financial reserve be within $10,000 of the actual liability.

a. What sample would be required to provide this level of accuracy?

b. What do you do now?

Case 6: Bamberger’s Department Store (Hypothesis test)

Harry Lev was reviewing the recent sales report for Bamberger’s Department store in an effort to assess whether or not the newly implemented Wednesday evening late openings had had a positive overall effect on sales. Lev was under some pressure to demonstrate that the sales during the extended hours were more than covering the added cost to the store of the late opening, since he had been instrumental in initiating this change despite strong employee resistance. If he could not clear show a financial benefit, he could expect pressure to discontinue the experiment.

Starting with the spreadsheet data file (Bamberger.xlsx) prepare an analysis that can be used to assess the impact of the “Wednesday experiment”. In other words is there a real difference in the level of sales or has the hours expansion merely resulted in a redistribution of sales during the week? Within a hypothesis testing framework address the following:

1. Prior to the hour’s expansion were Wednesday sales different from the sales for other weekday’s sales (Monday, Tuesday, Thursday, and Friday)?

2. Prior to the hour’s expansion were Saturday sales different from the sales for weekdays (Monday, Tuesday, Thursday, and Friday)?

3. Following the hour’s expansion were Wednesday sales different from the sales for other weekday’s sales (Monday, Tuesday, Thursday, and Friday)?

4. Following the hour’s expansion were Saturday sales different from the sales for weekdays (Monday, Tuesday, Thursday, and Friday)?

5. When comparing the pre and post hour’s expansion period did Wednesday sales differ?

6. When comparing the pre and post hour’s expansion period did non-Wednesday weekday sales differ?

7. When comparing the pre and post hour’s expansion period did Saturday sales differ?

8. When comparing the pre and post hour’s expansion period weekly sales differ?

If the evidence supports expansion of sales estimate the magnitude of the increment in sales associated with Wednesday evening hours. The following questions and hints may be helpful. What implications would the change in sales have for income? To assist you Harry put together some weekly information from the pre-extended hour period. Sales average about $3.8 million per week. Since the cost of goods sold were 72% of sales, the gross margin was slightly more than $1 million per week. With operating expenses of $115,000 plus $14,500 for every hour of operation the Earnings before interest and taxes amounted to $167,000. After the 35% tax the resulting income was slightly over $100,000 (see below).

Average Weekly Data (for 54 hour week)

Sales	3,801,000	Norman weekly sales
Cost of Goods Sold	2,736,000	at 72% of Sales
Gross Margin	1,065,000
Selling General & Administrative	783,000	at 14,500 / hour of operation
Depreciation	115,000	fixed
Earnings Before Interest & Taxes	167,000
Taxes	58,000	at 35% of EBIT
Net Income	109,000

Prepare an analysis of the Wednesday experiment.

1. In analyzing the sales data what was the proper unit of analysis: hourly sales, daily sales, weekly sales?

2. What proportion of Wednesday’s increased sales represents a net increase as opposed to cannibalization from other days of the week? Was Harry justified in expanding the store’s Wednesday hours? What would you expect the quarterly report to show in terms of the impact on sales and income?

3. Should the store revert to a 54 hour Week? Should they consider opening a second evening?

4. Why?

Case 7: Alfonso’s Department Store

Run a regression to estimate the impact of Alfonso’s advertising on Alfonso’s sales? Interpret the regression results. If this was all the information available should Alfonso’s advertise?
Determine the impact of the market on Alfonso’s Sales. Plot Alfonso’s sales and total market sales over time? What do you see? Run a regression to estimate the impact of Total market sales on Alfonso’s sales? Interpret the regression results.
Run a regression to estimate the impact of Total market sales and Alfonso’s advertising on Alfonso’s sales? Interpret the regression results.
Run a regression to estimate the impact of Total market sales and Alfonso’s advertising and other’s advertising on Alfonso’s sales? Interpret the regression results.
How effective is Alfonso’s newspaper advertising? Feel free to make recommendations for future newspaper advertising.

Case 8: Springbank Drive

The City of London was expropriating a portion of Sprinbank Drive as part of a project to widen the road between Wharncliffe Road and Wonderland Road. George Canning owner of Canning Consultants Inc., was retained by the City of London to assess the resultant property value loss for the affected residents. Canning had assembled a database of residential sales along with various property attributes, and he now had to determine how to proceed in calculating appropriate compensation for the "taking."

1. Compare Canning's multiple linear regression approach to this problem with the more traditional sales comparison approach. Which one is more appropriate?

2. Are there any concerns with using the attribute variables in Canning's database as it is currently presented?

3. What first steps should be taken prior to developing the regression model?

4. Develop a multiple regression model for calculating appropriate compensation for the affected residents along Springbank Drive.

Week of	Topic	Reading Assignment	Individual Homework	Group Homework
08 / 27 / 2007	Introduction	ASW: Chapter 1	Information Sheet & Survey 2	- - - - - - -
09 / 03 / 2007	Graphics: Descriptive Statistics	ASW: Chapter 2	- - - - - - -	Lanco Catalogue 3
09 / 10 / 2007	Numerical: Descriptive Statistics	ASW: Chapter 3	- - - - - - -	Rugged Client Part 1
09 / 17 / 2007	Probability	ASW: Chapter 4	Homework 1	- - - - - - -
09 / 24 / 2007	Probability & Distributions	ASW: Chapter 5	- - - - - - -	Rugged Client Part 2
10 / 01 / 2007	Distributions	ASW: Chapter 6	Homework 2	- - - - - - -
10 / 08 / 2007	Exam 1	Exam 1	- - - - - - -	Amore Foods
10 / 15 / 2007	Sampling Distributions	ASW: Chapter 7 & 8	Homework 3	- - - - - - -
10 / 22 / 2007	Interval Estimation	ASW: Chapter 8 & 9	- - - - - - -	Home Education Inc.
10 / 29 / 2007	Hypothesis Testing	ASW: Chapter 9 & 10	Homework 4	- - - - - - -
11 / 05 / 2007	Exam 2	Exam 2	- - - - - - -	The Sophomore Jinx
11 / 12 / 2007	Linear Regression	ASW: Chapter 14	- - - - - - -	Alfonso's Department Store
11 / 19 / 2007	Linear Regression	ASW: Chapter 15	Homework 5	- - - - - - -
11 / 26 / 2007	Multiple Regression	ASW: Chapter 16	- - - - - - -	Lansink Appraisals
12 / 03 / 2007	Model Building	Review	Homework 6	- - - - - - -
Notes:	ASW: Statistics for Business and Economics, 10^th Anderson, David R., Sweeney, Dennis J., Williams, Thomas A.
	All Topics & Assignments are tentative and may be revised as needed

Note: The instructor reserves the right to make any changes he considers academically advisable.

Sun	Mon	Tue	Wed	Thu	Fri	Sat
8/26	8/27	8/28	8/29	8/30	8/31	9/1
	1		Information Sheet & Survey 2
9/2	9/3	9/4	9/5	9/6	9/7	9/8
	Labor Day		Lanco Catalogue 3
9/9	9/10	9/11	9/12	9/13	9/14	9/15
	4		5	Rosh Hashanah	Rugged Client Part 1
9/16	9/17	9/18	9/19	9/20	9/21	9/22
	6		7		*Homework 1*	YK
9/23	9/24	9/25	9/26	9/27	9/28	9/29
	8		9
9/30	10/1	10/2	10/3	10/4	10/5	10/6
	10	Rugged Client Part 2	11		*Homework 2*
10/7	10/8	10/9	10/10	10/11	10/12	10/13
	Exam 1 12		13
10/14	10/15	10/16	10/17	10/18	10/19	10/20
	14		15		Amore Foods
10/21	10/22	10/23	10/24	10/25	10/26	10/27
	*Homework 3* 16		17
10/28	10/29	10/30	10/31	11/1	11/2	11/3
	*Home Education Inc.* 18		19		*Homework 4*
11/4	11/5	11/6	11/7	11/8	11/9	11/10
	Exam 2 20		21
11/11	11/12	11/13	11/14	11/15	11/16	11/17
	*Bamberger’s Department Store* 22		23		Alfonso's Department Store
11/18	11/19	11/20	11/21	11/22	11/23	11/24
	24	Homework 5	Fall Recess	Fall Recess	Fall Recess
11/25	11/26	11/27	11/28	11/29	11/30	12/1
	25		26		Homework 6a
12/2	12/3	12/4	12/5	12/6	12/7	12/8
	Springbank Drive 27		Homework 6b 28
Sun	Mon	Tue	Wed	Thu	Fri	Sat