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# Expected Payoff, Spearman's Coefficient, Chi squared test

1. Coffee Time is considering selling juices along with its other products.

States of Natures

High Sales Med. Sales Low Sales
A(0.2) B(0.5) C(0.3)
A1 (sell juices) 3000 2000 -6000
A2 (don't sell juices) 0 0 0

a. The probabilities shown above represent the states of nature and the decision makers's (e.g., manager) degree of uncertainties and personal judgement on the occurrence of each state. What is the expected payoff for actions A1 and A2 above? What would be your recommendation? Interpret the results based on practical considerations.
b. Bayes and empirical Bayes (EB) methods structure combining information from similar components of information and produce efficient inferences for both individual components and shared model characteristics. For example, city-specific information on the profits involved in selling a particular brand of coffee in Mumbai might be unavailable. How could CoffeeTime "borrow information" from adjacent cities or other countries to employ Bayesian logic?

2. Far West University offers both day and evening classess in business administration. One question in a survey of students inquires how they perceive the pretige associated with certain careers. Each student was asked to rank the careers from 1 to 8, with 1 having the most prestige and 8 the least prestige. The results were:

Career Ranking Ranking Career Ranking Ranking
by by by by
Day Evening Day Evening
Students Students Students
Accountant 6 3 Statistician 1 7
Computer Programmer 7 2 Mkter 4 8
Branch Bank Manager 2 6 Analyst 3 5
Hospital Administrator 5 4 Manager 8 1
Find Spearman's coefficient of rank correlation.

3. A study regarding the relationship between age and the amount of pressure sales personnel feel in relation to their jobs revealed the following sample information. At the .01 significance level, is there a relationship between job pressure and age? Explain.

Degree of Job pressures
Age (years) Low Medium High

Less than 25 20 18 22
25 up to 40 50 46 44
40 up to 60 58 63 59
60 and older 34 43 43

#### Solution Summary

The solution provides answers to 3 questions:
1) use of probability in decision making related to CoffeeTime
2) calculation of Spearman's coefficient of rank correlation
3) use of chi squared test for testing the relationship between job pressure and age

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