On Statistics

Qu1. Statistics Problem "Alternative"

You have just been transferred!! Your company has offered you either one of two opportunities. (Staying put is not an option). Because of the poor present economic climate for people in your line of work and your wish to become vested in the company’s pension plan, you feel you must accept one of these two positions. Pertinent details of each position are tabled below. Use the Analytical Hierarchy Process and your personal feelings about the attributes of each job to make a selection. Rework if necessary until your consistency ratio is less than 0.1 for all matrices. Give the priority vector .i.e., the list of weights and final consistency ratios for all matrices.  (For 2x2 preference matrices the consistency ration is always 0) Assume that the cost of living does not differ appreciably between your present location and either of the two new locations.

Alternative
Attribute	Dry Gulch	Rapid Creek
Salary	Your present plus 20%	Your Present plus 10%
Proximity to Relatives	2000 miles	500 miles
Promotion Potential	Fair	Good
Total Daily Commuting Time	40 minutes	90 minutes

Qu2. Statistics Problem "Decision Maker"

A decision maker is faced with the problem shown. Assume that the decision maker is risk neutral.

a)      A test is available that will provide information about the possible outcomes associated with A. Add a branch called “do the test” to the decisions below. Show how the test can be used to guide the selection of A or B. Previous evaluations of the test’s performance indicate that when the outcome was “good” the test indicated “good” 90% of the time. Given that the outcome was “bad”, the test predicted “bad” 40% of the time. What is the value of the information in the test? What is the optimal strategy for the decision maker to follow?

b)      Suppose the test results in the past show that the test predicted “good” 50% of the time when the outcome was “good” and predicted “bad” 50% of the time when the outcome was “bad.” What is now the value of the information in the test? Why? What is the optimal strategy when this test is used?

c)      What is the value of perfect information about outcome A?

Qu3. Statistics Problem - "Orange Computers"

The management of Orange Computers was considering launching a new product called the whopper101. The problem was that if a certain competitor had developed a new technology as had been rumored, they would quickly blow the whopper101 out of the water resulting in a loss of $500K. The board of directors assessed the chance that the competitor had this technology at 70%. If the competitor did not have this technology the board anticipated profits of $2,000,000.

 The chair, Steve Tasks, the company founder, was not happy making a launch/no launch decision with such a high degree of uncertainty and asked “ how can we get information about whether they have this technology or not? “There are a few ways we can go about it” said his slimeball assistant Will Cheet. “As you know, we have used one of their ex-employees, Barbara Bayes, to assist us in making assessments before. I think she’ll have an 85% chance of getting it right if we ask her. Let’s incorporate that possibility in our decision tree. She’ll probably want about $5000 for supplying her expert opinion. I wonder if it’s worth it because even after we get her view there will still be some uncertainty. You know, I’m sure that for $50,000 we could hire someone inside their company to tell us for sure. “

 Draw the tree for Orange’s Decision problem and determine the optimum decision based on expected values. Include the possibility of launching or not 1) without information, 2) with Barbara’s input and 3) using the industrial spy.

 Repeat using an exponential utility function with R=$1000.

Qu4.

A particular fast food restaurant is located near a University. 40% of the customers are students. Students prefer the spicier items. For example, a student customer will ask for extra hot sauce 75% of the time whereas a non-student will ask for extra hot sauce only 30% of the time. While waiting in line you observe a customer ask for extra hot sauce. What is the probability that this customer is not a student? The manager claims that about half the customers ask for extra hot sauce. Do you agree?