Thursday, November 21, 2019

Skittles Statistic Project

                This my reflection of my Skittles project for my Math 1040 Statistics class.  This project has been very fascinating for several reasons.  Statistics has some actual, real-world implications.  The purpose of statistics is to figure out a desired proportion of data to answer several questions.  For this project, two questions were ultimately asked: “What is the expected mean number of Skittles for the population?” and “What is the expected mean proportion of yellow Skittles for the population?
                The process wasn’t very much at all what I expected, and that’s a good thing.  Probably the most useful thing I learned is the implication of confidence intervals.  This presents the fact that no statistical question is ever going to be answered to the utmost accuracy.  Therefore, when dealing with the population, it’s never answered in an absolute.  Even though the samples can be dealt with extreme accuracy, it is impossible to find out the actual answers for an entire population, especially since the population in this case is the world.  Therefore, population answers are always responded with “we expect.”  Hence the use of the confidence interval.  To staple a confidence percentage to a population prediction shows humanity in these studies, and with enough accuracy to allow a margin of error to stay somewhat accurate.
                These statistics skills can be incredibly useful for other classes that require math skills.  It was also incredibly useful to learn how create the different kind of charts needed to visually convey different data sets.  I think another lesson that the instructor was trying to get us to learn is that when working with statistics, it would be discouraged to go through the entire process all by yourself.  Which is why he assigned us into groups.  Getting different outlooks and opinions on statistical definitions, as well as how the data is turning out so far.
                With all of that being said, here’s how my project report turned out.  Enjoy!
          


          We were asked to buy a 2.17-ounce bag of Original Skittles.  The purpose of this was to have a varying amount of samples from each of the classmates in an attempt to figure out the mean population proportion of yellow Skittles found in said bags.
          Obviously, the first thing I did was buy a bag of Skittles with the limits set.  The data turned out something like this:


Count Red
Count Orange
Count Yellow
Count Green
Count Purple
Total
My Bag
10
8
17
17
7
59













          The next thing we were asked to do was to make a prediction about what the overall proportions for each bag.  Here were my predictions:


Red
Orange
Yellow
Green
Purple
Predicted proportion for each color
0.15
0.14
0.30
0.30
0.11


          I tried to keep my prediction as close to my original count in my personal bag as possible.  I figured that would be a great place to start hypothesizing.  After receiving the data of the other student's here's how the results turned out:


Red
Orange
Yellow
Green
Purple
Total Count
Counts for my bag
10
8
17
17
7
59
Counts for the entire class sample
1206
1171
1196
1125
1094
5792
Actual Proportions for my bag
0.17
0.14
0.29
0.29
0.12
1
Actual Proportions for the entire class sample
0.21
0.20
0.21
0.19
0.19
1


          Then I turned the data into a pie chart and a pareto chart.  Here's what those look like:







          And then I made my statement on the project up to this point:

          "This study so far has been surprisingly informative.  I wasn’t very surprised by how random the color of skittles was in my personal bag.  I figured it would be like that.  And looking at other class member’s personal skittles confirmed to me just how random theirs were as well.  That didn’t surprise me either.  What did surprise me, however, was how close to equal portions the colors became once everyone’s bags of skittles all came together.  With the entire class sample, every color turned up to somewhere around 20%.  I didn’t think those results would be so uniform.  I thought the overall number would be as random as any ordinary bag of skittles.  I’m looking forward to learning more about these statistics."


          As part of this project, we were also assigned into different groups.  The instructor asked us specific questions throughout the semester and we as a group would determine our group answer and respond.  We were asked, "Does the class data represent a random sample? Why or why not? What population are we sampling from?"  Here was our response:

"As a group we discussed and whether the class data was a random sample or not. We concluded that it is a random sample because each bag of skittles was purchased by individual people at different places and at different times.
We were unsure of what defined the population but concluded that it could be all of the 2.17oz bags of skittles in the US."


          The next thing I did was calculate what the mean number, standard deviation, and the 5-number summary was for the data thus far.  Here are those results:

-    Mean Number of Candies Per Bag:  63.6

-    Standard Deviation of the Number of Candies Per Bag:  34.5

-    5-Number Summary for the Number of Candies Per Bag:  47, 57, 59, 60, 382


          Then I turned the bag count into a histogram and into a boxplot.  Here's what those look like:




          If this data looks incredibly skewed, it's because there was a student who, for some reason, didn't stick to the rules and decided to buy a Skittles bag with 382 Skittles in it.  And wanting to be as fiercely loyal to the instructor's instructions as possible (and the fact that he gave us the data for this enormous bag), I put the data in.  Here was my summary after making these graphs:

          "The difficult part about this graph is the random skittles bag filled with 382 skittles.  It sort of messes up the overall look of both graphs.  But it was in the class sample, so it’s here.  As far as the shape of the distribution is concerned, it’s sort of bizarre.  It looks more skewed to the right, but it doesn’t gradually disperse either way.  Most bags are in the 55-60 range and then it drops significantly to both sides.  But there are much more candies above the 60 range, which leads to me conclude that the shape is skewed right.  I expected this too happen, considering that most of the numbers upon initial viewing were all clustered around 55-60.  As far as outliers are concerned, there are quite a few that exceed the upper fence.  Those outliers are 65, 66, 86, 89, 91, both 95’s, and, of course, 382.  Again, everything would look fine and be presented in an orderly manner, but the 382 bag really jacks things up."


Our next group discussion, we were asked these three questions.  Here are the responses to each question:
What is the difference between qualitative and quantitative data?  "Quantitative data is data that can be literally counted or measured can be determined through the use of numbers. Qualitative data is descriptive and based on traits and characteristics."
What types of graphs make sense and what types of graphs do not make sense for qualitative data? For quantitative data? Explain why.  "Pie and bar charts are best for qualitative data because you can split off for specific characteristics effectively. For quantitative data, histograms and dot plots are best because they show the desired numerical value."
What types of calculations (eg. summary statistics) make sense and what types do not make sense for qualitative data? For quantitative data? Explain why. "The relative frequency calculation is good for both qualitative and quantitative data because it proports the data to make it better to read."


          The last thing I did was construct a confidence interval of 99% for the population proportion of yellow Skittles, as well as population mean number of overall Skittles with a 95% confidence interval.  The equations didn't transfer over as well from Microsoft Word as I would have liked them to, but they did well enough for these purposes.  Here's what that looks like:

          1) According to the equation below (using both plus and minus versions and including the misplaced giant bag of skittles), we can be 99% confident that the proportion of yellow skittles in a typical bag of skittles population is in between 0.196 and 0.224 (19.6% and 22.4%).
𝟎.𝟐𝟏 ± 𝟐.𝟓𝟖(√ 𝟎.𝟐𝟏(𝟏 − 𝟎.𝟐𝟏)/𝟓𝟕𝟗𝟐 )

          2) According to this equation down below (using both plus and minus versions and including the misplaced giant bag of candy), we can be 95% confident that mean number of skittles in a typical bag of skittles population is in between 62 and 65 skittles.
𝟔𝟑.𝟔 ± 𝟏.𝟗𝟔𝟐(𝟑𝟒.𝟓/√𝟓𝟕𝟗𝟐 )


          For our last group discussion, we were asked two questions.  Here they are, as well as are responses to them:
Explain in general the purpose and meaning of a confidence interval.  "How well a statistic model estimates the underling population can have issues. Confidence intervals address these issues by giving a range of values which are likely to contain the population parameter in question."
What factors affect the width of a confidence interval? Why?  "A factor that can affect the width of a confidence interval is if the standard deviation is known or needs to be estimated. In most real world situations the standard deviation is unknown so the confidence interval width would need to be adjusted to accommodate the estimation.
Another factor would be sample size. The larger the sample size means the closer the data will be to the population parameter, so the confidence interval width can be smaller."
 

          This was a very fascinating study.  This was a good project to really teach us how to take sample statistics and construct a confidence interval to try and figure out a desired, specific proportion.  I feel much more confident that if I wanted to conduct another study of attempting to find a mean or proportion of something, I have the necessary tools and knowledge to do so.

Tuesday, May 1, 2018

Ethics Term Paper Reflection

     Business bluffing has been a subject I've been very fascinated with over the past few years.  I've always believed that lying is wrong.  I still do believe that it's wrong.  It's unethical  But what if you were technically not lying?  What if you were explaining only some of the truth, but not all of it?  Is it still ethical at that point?  It was interesting for me to research this subject and learn what several other people though.  These types of people included journal writers, university professors, former businessmen, etc.
     Some thought that it was okay to bluff.  After all, business is only a game.  Carr is famous for referencing it to a game of poker.  The goal is to bluff your way to winning and fooling everyone else.  I believe this way of thinking is completely unethical.  Business is not a game.  In a game of poker, everybody has to willingly lay down money and compete to fool each other and win it all.  And while there are some people like that in the world of business, not everyone is like that.  In poker, you really only lose money (if you're not foolish about it).  In business, you could lose so much more than money.  You could lose careers and even lifestyles.  Plus, it's truly an awful thing to purposely screw someone over to benefit yourself.  Yes, I understand that you do need to take care of yourself.  But if you're actions are intended to hurt other people, a reconsideration is necessary.  I would much rather be a good person than a rich person. Other people I've researched have shared this sediment too.
     However, as paradoxical as this may initially sound, I don't believe all business bluffing is bad.  Researching this paper actually helped me come to this conclusion.  Before I started writing, I wrote off the notion that all business bluffing is bad.  I've learned that that's not true.  Only when purposely bluffing knowing full well that it'll hurt people is it considered bad.  There may be times when you have to keep the whole truth from someone solely because it will hurt them and you.  Obviously, this is a sticky situation.  You can easily say, "isn't everyone entitled to the whole truth?"  Possibly.  But business is tricky.  I presented a great example given by Jeffrey Seglin in my paper about an instance where business bluffing was probably the smart thing to do.  It would have saved the business and the employees a whole deal of trouble (you can read it in my paper on the next post).
     The general conclusion I came to is that people are generally pretty split on the issue.  But at the end of the day, it's my opinion on the matter that counts to me.  And my opinion is that business bluffing is only ethical depending on how it affects you and others.  If it affects others in a negative way, then the obvious answer to me is not to do it.  But if you are bluffing to save others and yourself, then I think it's acceptable.

Is Business Bluffing Morally Acceptable?

Landon Bangerter
Business 1040
Professor Matt Hatcher
1 May 2018

Is Business Bluffing Morally Acceptable?
    One of the more interesting and controversial topics of ethical discussion is whether or not business bluffing is morally acceptable.  In the world of business, to bluff means to present your company and anything that is affiliated with it on a higher level than it probably is.  Basically, to be deceptive.  And while that sounds like a dirty action, many would argue that business bluffing is a good thing since it can not only help you but possibly those with whom you are transactioning with.  But at the same time, bluffing is still, essentially, a form of lying, and many others would argue that this is inherently a bad thing.  The purpose of this assignment is to come to a general conclusion as to whether business bluffing is ethically appropriate or not.  My initial thought is that it is unethical and business leaders should be as honest as possible, but researching this topic could very well change my mind.  I will be researching the opinions of esteemed ethical-thinkers and examples of business bluffing.  As I write out the research, I will contrast opinions that have priorly been presented as we progress through this paper.  At the close of this paper, I will attempt to give a general conclusion from the research collected regarding business bluffing and I will also provide my personal opinion on the matter.
    We’ll start off with Albert Z. Carr, a man who’s explanation on the subject can be found in many books on ethics and who’s insight will basically serve as the basis of this paper.  This particular section of his thoughts is taken from “Ethics in the Workplace” compiled together by Robert A. Lamar.  This is perhaps the most popular explanation on business bluffing and is often used as the prime description on the subject in many ethics textbooks..  Carr argues that bluffing in business is only part of the game.  He likens the ideal to a game of poker.  He says the winner of the game “is the man who plays with steady skill.  In both games ultimate victory requires intimate knowledge of the rules, insight into the psychology of the other players, a bold front, a considerable amount of self-discipline, and the ability to respond swiftly and effectively to opportunities provided by chance.  In poker it is right and proper to bluff a friend out of the rewards of being dealt a good hand.” (Larmer, Carr, 2002, 4-5)
    Another textbook, “Honest Work: A Business Ethics Reader” contains some more explanation of Albert Z. Carr’s viewpoint.  In this textbook, he presents several examples of executives bluffing in business.  The justification here is that if it is in the legal confines of the law, then it is completely ethical, regardless of the outcome for any party.  One example Carr gives is of a firm that manufactures mouthwash.  This company was accused of selling products with a cheap form of alcohol that was possibly harmful to a buyer’s health.  In a private comment, the CEO stated that they had not broken any laws.  Their justification was that everything they did was perfectly legal.  He was clearly getting agitated that the general view of ethical treatment was frustrating his company.  The CEO says, “If the ethics aren’t embodied in the laws by the men who made them, you can’t expect businessmen to fill the lack.  Why, a sudden submission to Christian ethics by businessmen would bring about the greatest economic upheaval in history!” (Ciulla, et al., 2017, 46)
    Fritz Allhoff was an admirer of Carr’s concept of bluffing.  He too believes that the ethical implications associated with games like poker are comparable to the business world.  He claims that it is only human nature for people to bluff.  When given the opportunity to raise your sales price above your reservation price, it is only rational that you’d take it.  It is rational and human to want to have more money.  He says that it is “morally acceptable since business is governed by role differentiated morality” and “because the coherence of the idea of business negotiations itself presupposes that bluffing is accepted.” (Varelius, Allhoff, 2006, 163-164)
    However, with fans like Allhoff, there are also critics.  Professor Jerry Kilpatrick of California State Polytechnic University wrote an article citing his critiques of Carr’s views on bluffing, aptly titled “A Critique on ‘Is Business Bluffing Ethical?’”.  Kilpatrick states that there are three premises that are to be challenged.  One is Carr’s lack of including other ethical theories into his insight.  He is basically only including the Judeo-Christian religious theory of altruism.  According to Kilpatrick, there are many other views to consider when presenting such a statement on bluffing.  The second challenged premise is that business is a game.  Kilpatrick says that business is not only not a game, but that mindframe can be used to justify really distasteful acts, such as cowardice.  And the third premise to be challenged is Carr’s claim that deception is only part of the negotiation process, something that Allhoff greatly defended.  Kilpatrick then shares a piece of work from Gerard I. Nierenberg, who says, “In a successful negotiation, everybody wins. Negotiation is not a game—and it is not war. Its goal is not a dead competitor. A negotiator ignores this point at his own peril. The purpose of negotiation is to achieve agreement, not total victory. Both parties must feel that they have gained something. Even if one side has had to give up a great deal, the overall picture is one of gain.”  (Kilpatrick, Nierenberg, 2002, 1-10)
    In her book “Just Business,” Elaine Sternberg takes the side of Kilpatrick.  Business is not a game.  Not only that, but she explains that games themselves are not immune to moral judgement.  She explains that the best kind of games are the games that are fair and challenging.  We tend to not want to play games that are cheap or unfair.  And when someone is cheating at a game, the credibility and even dignity of that person (at least for the game) are uncredited.  The business world is viewed differently.  There aren’t a whole ton of rules to winning in the business world, but there’s still the morality of it all.  She exclaims, “Neither the nature of business nor the model of a game provides any justification for exempting business from moral judgement.” (Sternberg, 2000, 64-66)
    To compare with Carr’s thinking, Sternberg and Kilpatrick are both basically explaining that games and business are uncomparable.  Gamers play knowing full well the rules and what they are getting themselves into.  Most gamers participate with the intention to play fairly, abiding by the rules.  And if you lose, it’s no big deal.  It’s only a game.  Carr’s and Allhoff’s thoughts are interesting and relatable, but Sternberg and Kilpatrick share much more convincing cases.  Poker is only a game where every player abides by rules (usually).  The world of business has a significantly higher chance of moral consequences, especially when taking into consideration that everyone has at least a slightly different ethical standard than others.
    In his book “The Good, the Bad, and Your Business”, Jeffrey L. Seglin uses a different term to describe business bluffing.  He calls it posturing and essentially states that posturing is not a bad thing.  He doesn’t believe it’s dishonest nor does he believe that it lacks integrity.  When given the choice to say nothing or to disclose every truthful detail, there may be some cases where it is more generally beneficial for everyone.  An example of this he gives of this is someone he interviewed, a CEO of Inc. 500., to seek out examples of unsavory tactics.  “I called all of my people together and said: ‘Look, we’re handing out payroll checks, but we’re broke.  If you have to cash your check, I understand.  But this is where we are financially.  Could you guys just hold off cashing your checks for a week?’  All 40 employees ran to the bank that day.” (Seglin, 2000, 137-138)
It seems that Seglin takes sort of a middle ground between Carr and Allhoff, and Sternberg and Kilpatrick.  While he never really digs into the legalities of business bluffing (or posturing), his arguments tend to swing towards logical reasoning and determining what’s best for everyone.  In this sense, he stands with Sternberg and Kilpatrick a little bit.  But because he defines there to be nothing wrong with business posturing, he also takes a little bit of Carr’s side as well.  So here we have two polar opposite opinions, and a person who takes more of the median.
Determining a general conclusion is proving to be difficult.  It is fascinating to see how large of an influence Carr’s comments have had on thinkers everywhere, considering all of the opinions gathered in this paper are based on responding to Carr’s words.  There are people like Allhoff who unapologetically agree with Carr but then there are those who simply disagree with his claims like Kilpatrick and Sternberg.  And then there are those who take sort of a middle ground like Seglin.
Whatever the case may be, everything seems to circulate around the very fact that Carr stated that bluffing in business is only a game like poker.  When determining whether business bluffing is ethical or not, it always comes back to whether or not business should be treated as though it were a game.  The responses on this seem to be pretty mixed.  It wouldn’t be completely unreasonable to say that opinions on the matter are almost split at 50/50.  Although if I had to pick which side seemed more favorable, I would tip my hand towards those who largely disagreed with Carr.
As for my personal conclusion, my opinion has only been slightly swayed.  I actually tend to side more with Jeffrey Seglin than anyone else.  But it turns out to be more of a situational scenario.  You should allow yourself to bluff in certain situations.  I agree that you should generally be concerned for yourself and try to determine what is best for you and your company.  But you need to be aware of the price you could pay.  I’m not talking about physical price.  I’m talking about moral price.  How much of your soul are you willing to sell to ensure profits?
Carr has a point when he says business is like poker.  Business is not like any other game, but it is like poker.  It shouldn’t have to be, but it is.  It’s a bit more severe in business.  In poker, you usually only lose money (which is a lot for some people), but in business, careers and even lives are at stake when bluffing.  The main question here isn’t exactly how are you going to ensure that you don’t go under, but rather, who are you okay with deceiving and hurting in order to save yourself?
My conclusion ultimately ends up like this: bluffing is only okay if it seeks to not only help yourself, but not inflict dire consequences on those you are dealing with.  You owe it to those you interact to know as much of the truth as they can benefit (and possibly as much as they will take consequence from), if not only for the fact that you would probably want to know as much of the truth as you need also.  Even if they don’t know everything, they need to know enough.  Let’s be frank, it is very selfish to justify bluffing that really hurts someone else.  When your bluffing is being set up to hurt someone else, you need to reconsider your actions.  The question I would like to pose is: when given the choice to be a rich man or a good man, which will you choose?  Any day of the week, I would much rather be a good man than a rich man.

















References
  • Larmer, Robert A., and Albert Z. Carr. Ethics in the Workplace: Selected Readings in Business Ethics. West, 2002.
  • Ciulla, Joanne B., et al. Honest Work: a Business Ethics Reader. Oxford University Press, 2017.
  • Varelius, Jukka, and Fritz Allhoff. “Allhoff on Business Bluffing.” SpringerLink, Kluwer Academic Publishers, May 2006, link.springer.com/article/10.1007/s10551-005-4665-4.
  • Kilpatrick, Jerry. “A Critique of ‘Is Business Bluffing Ethical?".” Cal Poly Pomona, 2002, www.cpp.edu/~jkirkpatrick/Papers/CritBluff.pdf.
  • Sternberg, Elaine.  Just Business: Business Ethics in Action.  2nd ed., Oxford University Press, 2000.
  • Seglin, Jeffrey L. Good, the Bad, and Your Business. Orient Paperbacks, 2011.