Question 1: An Application of Probability — Decision Trees
The readings are rather theoretical so I am including an application where knowing a probability value can be very helpful. There is a field in Management Science known as “Decision Theory”. We use probability to decide what the best course of action is given what we know. I attached some information showing a decision tree. It is a bit more complicated than the ice cream/soft drink problem but shows the structure of the tree with its paths or branches.
Try the first ice cream/soft drink problem. We must decide what is the best course of action knowing possible payoffs and probabilities. Here we need the probability that the day will be warm or cold. This is a simple probability. We can find it empirically by counting warm and cold days in the past and dividing by the total number of days observed. In this problem we arrive at the probability of a warm day to be 0.6. Since we only consider two outcomes, the probability of a cold day is 0.4.
Check out this snippet from Family Circle magazine (January, 2009, Liz Plosser):
Motorists who talk on a cell phone while driving are 9% slower to hit the brakes, 19% slower to resume normal speed after braking and four times more likely to crash.
Interesting, eh? Need more information? Sorry, that’s all the information this article provided. So, what can we conclude? How reliable are these results? Can you believe what the author tells you? Why or why not?
Pretend you’re a manager for one of the major cell phone service providers in the U.S. You’ve been asked by a major news magazine to speak to these “accusations.” What would you say? Use your knowledge of “statistics for managers” to level some well-founded criticisms of the conclusions above.
Careful! We cannot use personal opinions to battle statistics like these! Instead, you must explain why the numbers reported in Family Circle may, or may not, accurately represent the population of U.S. drivers. There are 100 possible answers to this conference topic.
You need only provide a single idea, to get the conversation rolling. Leave some material for others to contribute. Be sure that your contribution explicitly references what we’ve read and practiced this week. It is your classmates’ job to support or refute what you’ve said.
The title of this discussion topic comes from a quote often attributed to former British Prime Minister Benjamin Disraeli, who claimed that there are three types of lies: “Lies, Damned Lies, and Statistics”
The (entirely fictitious) University of South Central Maryland (USCM) is being sued for sexually discriminatory hiring practices. Last year, they hired two classes of employees, administrative staff and academic staff. They received 750 applications from women for administrative staff positions, of which they hired 250, and 250 applications from women for academic positions, of which they hired 200. In total, then, they had 1000 applications from women of which they hired 450, or 45%. They received 300 applications from men for the administrative positions, of which they hired 75, and 700 applications from men for the academic positions, of which they hired 550. In total, of the 1000 applications they received from men, they hired 625, or 62.5%.
Based on the numbers presented, what do you think of the discrimination claim?
Operations and production managers often use the normal distribution as a probability model to forecast demand in order to determine inventory levels; manage the supply chain; control production and service processes ; and perform quality assurance checks on products and services. The information gained from such statistical analyses help managers optimize resource allocation decisions and reduce process times, which in turn often improves contribution margins and customer satisfaction.
Based on your understanding of the characteristics of the normal distribution, examine the attached chart (assume that the process specifications have a low bound of 9 and an upper bound of 15), and contribute to our discussion by posting an response to ONE of the questions below, and by responding to a post of a classmate.
1. Does either of the processes below fit a normal distribution? Why or why not?
2. Which processes shows more variation? What does this mean?
I was reading a magazine and saw an advertisement claiming that a car had the best performance in the industry on maintenance. There was actually a footnote at the bottom giving the statistics and important information. It stated the sample size and how the results were calculated. That impressed me and you do not see these footnotes often. You may feel differently. How do you feel about this?
Listen to the Econtalk podcast on polling found here:http://www.econtalk.org/archives/2008/07/rivers_on_polli.html
It can also be found in the webliography.
What can we learn from the podcast about sampling issues? Can you think of an example from your business life where you have encountered gross errors in forecasting or estimations that you think may due the sort of issues mentioned in the podcast? Can you think of a place in your organization where polling would be a useful tool? Short of hiring Doug Rivers’ company, what sorts of issues do you need to keep in mind when designing a polling technique?