Hypothesis

Case No.1 In the last few years, colleges and universities have signed exclusivity agreements with a variety of private companies. These agreements bind the university to sell that company’s products exclusively on the campus. Many of the agreements involved food and beverage firms. A large university with a total enrolment of about 50,000 students has offered Pepsi-Cola an exclusivity agreement, which would give Pepsi exclusive rights to sell their products at all university facilities for the next year and an option for future years. In return, the university would receive 35% of the on-campus revenues and an additional lump sum of $200,000 per year. Pepsi has been given 2 weeks to respond. The management at Pepsi quickly reviews what they know. The market for soft drinks is measured in terms of the equivalent of 10-ounce cans. Pepsi currently sells an average of 22,000 cans or their equivalents per week (over the 40 weeks of the year that the university operates). The cans sell for an average of 75 cents each. The costs, including labor, amount to 20 cents per can. Pepsi is unsure of its market share but suspects it is considerably less than 50%. A quick analysis reveals that if its current market share were 25%, then, with an exclusivity agreement, Pepsi would sell 88,000 cans per week or 3,520,000 cans per year (calculated as 88,000 cans per week * 40 weeks). The only problem is that Pepsi does not know how many soft drinks are sold weekly at the university. Coke is not likely to supply Pepsi with information about the sales of its brands, which together with Pepsi’s line of products constitutes virtually the entire market. A recent graduate of a business program volunteers that a survey of the university’s students can supply the missing information. Accordingly, she organizes a survey that asks 500 students to keep track of the number of soft drinks they purchase on campus over the next seven days. The responses are: 2 2 1 0 1 0 1 1 1 2 4 4 1 2 5 0 1 0

1 0 0 0 0 0 4 0 1 3 1 2 3 1 1 0 0 0

2 2 3 2 4 1 0 2 2 0 1 4 4 3 2 1 0 2

1 1 0 1 1 2 1 1 1 4 1 1 0 1 1 1 1 1

0 2 0 1 1 0 0 3 3 2 2 2 1 1 1 1 4 4

1 1 2 1 0 1 2 3 1 0 1 3 1 2 2 2 0 2

2 1 1 1 2 0 2 0 2 1 2 0 0 1 1 0 4 0

2 3 2 0 0 3 1 0 0 2 0 1 1 0 1 1 2 0

1 0 2 0 1 1 1 0 3 0 4 1 0 2 2 2 1 0

0 3 0 1 3 1 1 1 1 1 0 2 0 3 2 2 2 1

0 1 3 2 0 0 0 0 3 3 2 2 1 2 0 1 0 2 1 2 1 1 3 2 0 1 2 0 3 0 2 2

0 1 1 0 1 2 1 1 1 2 1 2 0 0 3 1 0 1 3 2 1 3 2 1 1 1 2 2 0 2 2 0

3 0 0 1 2 3 1 3 0 1 2 0 3 2 2 0 1 2 0 0 1 0 1 1 3 1 2 0 1 0 1 2

1 3 0 2 1 0 1 0 1 1 2 1 4 1 1 2 1 2 2 0 1 1 1 0 1 2 3 1 1 0 2 1

0 2 2 5 3 1 2 0 1 0 1 1 4 2 1 4 1 1 1 2 0 2 1 1 1 0 0 1 2 1 2 0

1 0 4 0 1 4 1 0 1 1 1 0 0 0 3 2 2 2 0 1 0 2 3 0 1 0 0 2 1 2 2 2

0 2 2 1 1 0 1 0 1 2 0 0 2 1 1 1 2 0 0 1 3 0 2 0 3 0 0 2 2 0 2 3

1 2 1 1 1 2 3 1 0 1 5 2 0 2 1 1 4 0 1 3 2 1 2 1 0 0 3 3 1 0 2 0

4 0 3 4 2 0 1 1 1 2 4 0 3 2 0 2 2 0 0 1 1 3 1 1 0 1 0 1 2 1 1 2

Perform a statistical analysis to extract the needed information from the data. Estimate with 95% confidence the parameter that is at the core of the decision problem. Use the estimate to compute estimates of annual profit. Assume that Coke and Pepsi drinkers would be willing to buy either product in the absence of their first choice. On the basis of maximizing profits from sales of soft drinks at the university, should Pepsi agree to the exclusivity agreement? While the executives of Pepsi-Cola are trying to decide what to do, the university informs them that a similar offer has gone out to the Coca-Cola Company. Furthermore, if both companies want exclusive rights, then bidding war will take place. The executives at Pepsi would like to know how likely is it that Coke will want exclusive rights under the conditions outlined by the university.

1 1 1 2 3 0 0 0 1 2 2 2 2 2 1 2 2 2 0 0 2 2 2 1 1 1 1 2 4 3 1 2

Perform a similar analysis to the one you did before, but this time from Coke’s point of view. Is it likely that Coke will want to conclude an exclusivity agreement with the university? Discuss the reasons for your conclusions.

Case No.2 A number of years ago, the Michigan legislature passed a law requiring insurance for all drivers. Prior to this event drivers did not have to be covered by insurance. The law was challenged on the grounds that it discriminated against poor people who would not be able legally to drive. At issue at the trial was the number of Michigan motorists who would be coerced by the law into buying insurance. To determine this, it was necessary to count the number of uninsured motorists. (These would be the people who would be forced by law to buy insurance.) There were a total of 4,505,665 license plates for passenger vehicles registered in Michigan at the time. An investigation of each one of these to determine whether the drivers had insurance coverage would be prohibitively expensive and time-consuming. It was decided that the state would draw a random sample of motorists and estimate the number of Michigan’s driving population who were uninsured from sample data. A random sample of 249 license plates was drawn using statistically sound sampling methods. Each was investigated to determine its insurance status. The license plates sampled were placed in one of three categories. The categories and the code on the disk are as follows: 1 Insured 2 Not Insured 3 Missing (License plates that were drawn for the sample but for which investigators were unable to find the car or its owner were classified as missing.) The data are: 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1

1 1 1 2 1 1 1 1 2 1 1 1 1 1 1

1 1 2 1 1 1 1 1 1 1 3 1 1 1 1

1 1 1 1 3 1 1 1 1 1 1 1 1 1 1

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

1 1 1 1 1 1 1 3 2 1 1 1 1 1 1 3 1 1 2 1 1 1 1 1 1 1 1 1 1 3 1 1 1 3 1

1 3 1 1 1 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 1 1 1 1 1 1 1 1 1 1 1

1 1 1 1 1 1 1 1 1 1 3 1 1 1 1 1 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 1

1 1 1 1 1 2 1 1 1 1 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 1 1 1 1 1 3 1

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 1 1 1 1 1 1 1 1 1 1 1 1

Your job is to estimate the proportion of all Michigan passenger vehicles that are not insured. Provide methods for dealing with the missing data. From each method, determine the upper and lower limits for the estimated number of motorists who would have been forced by law to buy insurance. Discuss which method is more reasonable.