This note explains the basics of sampling. It defines and discusses the concepts of random sampling, the law of averages, and the central limit theorem. It covers the sampling of both continuous uncertain quantities (where the sample is summarized by the sample average and sample standard deviation) and categorical variables (where the sample is summarized by the sample proportion). The note carefully explains that the results of random sampling from an infinite population are equivalent to repeated and independent outcomes of an underlying probability distribution.
The Pelayo family has been studying roulette wheels and collecting data on tens of thousands of spins. Now the Pelayos have identified a wheel that they want to bet on, which has six numbers that have a 1/30 probability of winning instead of 1/37. They have staked EUR1,000 on this wheel. The question is: How much should they bet in order to have the most capital after 200 rounds? Log utility is used to compare alternatives and find an optimal bet.
This note describes a method for adjusting uncertain future cash flows into a present certain equivalent. The use of net present value (NPV) to adjust a stream of future known cash flows into a single-value equivalent adjusted for the time value of money is common practice. The use of simulation to produce a risk profile of NPV values is also now common. While the expected net present value (ENPV) is often used to convert a risk profile of uncertain NPVs into a single-value equivalent, this approach ignores risk and the decision maker's attitude toward risk. Simply put, a 50% probability of receiving an NPV of $1 million is not as attractive as a 100% chance of receiving an NPV of $500,000. The general logarithmic utility model (GLUM) constructs a single certain equivalent from a risk profile (i.e., a "risk-adjusted NPV") which goes beyond ENPV to incorporate risk aversion into the decision-making criterion. The simplicity and many attractive properties of the GLUM prompt us to suggest it as more attractive than other ways to adjust an NPV risk profile for risk.
The case presents data from 70,340 spins of four roulette wheels: three of which are real ("imperfect") and one of which is simulated ("perfect"). The challenge posed is to identify which of the four is the simulated wheel. After weeks spent recording spin results at their local casino, the members of the Pelayo family think they have identified three imperfect wheels. Before they start betting, they want to be certain that the three wheels they identified as imperfect are easily distinguishable from a theoretically perfect wheel. This case has been used successfully in Darden's MBA elective about data analysis. That course introduced pivot tables and the chi-squared goodness-of-fit test using the case "The Roulette Wheel." Discussion of "The Pelayo Family Plays Roulette" probably will not require an entire class period. One option would be to hand out the case during the discussion of "The Roulette Wheel" as something of a follow-on.
Researchers at the University of Pennsylvania were interested in whether exposure to light early in life might affect eye growth and lead to an increased risk of myopia (nearsightedness). Eyes grew rapidly after birth, but myopia usually did not develop until later in life and arose from excessive postnatal eye growth. They knew that the duration of daily light had been shown to increase eye growth in chicks and wondered whether the same might be true for humans. The results startled researchers and might explain the increase in myopia rates over the last two centuries. The B case gives the results of a follow-on study conducted by the Ohio State University.
Movie-industry analyst David Fitzhugh must estimate the value of the sequel rights associated with Chance Encounters, a soon-to-be-produced movie. The producers intend to use the cash from the sale of the sequel rights to help fund production of the original movie. With the purchase of the sequel rights, the client fully intends to produce a sequel--should the original movie prove successful.
The case descirbes a wine-tasting competition held in Princeton, New Jersey, in 2012. The competition pitted the best wines from New Jersey (NJ) against the best wines from France in blind taste tests. The case stops after the scores of nine judges tasting 20 wines have been recorded. Students are asked to take these 180 scores and determine the best red and best white and to also compare the performance of the 12 NJ wines to the 8 French wines.