Exam 19: Decision Theory

Alternatives 1 and 2 in the following payoff table represent the two possible manufacturing strategies that the EKA manufacturing company can adopt. The level of demand affects the success of both strategies. The states of nature (S_I) represent the levels of demand for the company products. S₁, S₂, and S₃ characterize high, medium, and low demand, with probabilities of .3, .6, and .1, respectively. The payoff values are in thousands of dollars. The management believes that weather conditions significantly affect the level of demand. 48 monthly sales reports are randomly selected. These monthly sales reports show 15 months with high demand, 28 months with medium demand, and 5 months with low demand. 12 of the 15 months with high demand had favorable weather conditions. 14 of the 28 months with medium demand had favorable weather conditions. Only 1 of the 5 months with low demand had favorable weather conditions. The estimated probabilities of poor weather conditions given different levels of demand are presented below. P(Poor |High) = .2, P(Poor |Medium) = .5, P(Poor |Low) = .8 What is the probability of high demand given that the weather conditions are poor?

The expected net gain of sampling equals the ________ minus the cost of sampling.

Alternatives 1 and 2 in the following payoff table represent the two possible manufacturing strategies that the EKA manufacturing company can adopt. The level of demand affects the success of both strategies. The states of nature (S_I) represent the levels of demand for the company products. s₁, s₂, and s₃ characterize high, medium, and low demand, respectively. The payoff values are in thousands of dollars. Prior probabilities are .3 for s₁; .6 for s₂, and .1 for s₃. What is the maximum amount that the company would be willing to pay for perfect information?

The maximin criterion is preferred by optimistic decision makers.

________ statistics is an area of statistics that uses a theorem to update prior belief about a probability or population parameter to a posterior belief.

The ________ criterion for choosing among alternative actions assumes that the state of nature with the worst payoff will be experienced.

Alternatives 1 and 2 in the following payoff table represent the two possible manufacturing strategies that the EKA manufacturing company can adopt. The level of demand affects the success of both strategies. The states of nature (S_I) represent the levels of demand for the company products. S₁, S₂, and S₃ characterize high, medium, and low demand, with probabilities of .3, .6, and .1, respectively. The payoff values are in thousands of dollars. Find the expected monetary value for each of the alternatives and determine the best alternative (course of action) for the EKA manufacturing company using the expected monetary value criterion.

A set of potential future conditions that will have an effect on the results of a decision is called the states of nature.

Alternatives 1 and 2 in the following payoff table represent the two possible manufacturing strategies that the EKA manufacturing company can adopt. The level of demand affects the success of both strategies. The states of nature (S_i) represent the levels of demand for the company products. S₁, S₂, and S₃ characterize high, medium, and low demand, respectively. The payoff values are in thousands of dollars. The best alternative (course of action) for the EKA manufacturing company using the maximin criterion is strategy ________ and the best possible payoff is ________.

A pharmaceutical company manufacturing flu test kits wants to determine the probability of a teenager not having the flu when the test results indicate that they do (false positive). It is estimated that the probability of positive test for flu among potential users of the kit is 10 percent. According to the company laboratory test results, 1 out of 100 noninfected teenagers tested as having the flu (false positive). On the other hand, 1 out of 200 teenagers with the flu tested as not having the active virus (false negative). A teenager has just used the flu test kit manufactured by the company, and the results showed she does not have the flu. What is the probability that she does have the flu?

An automobile insurance company is in the process of reviewing its policies. The company is considering increasing the premium charged to drivers under 25. According to company records, 35 percent of the insured drivers are under the age of 25. Company records also show that 280 of the 700 insured drivers under the age of 25 have been involved in at least one automobile accident. On the other hand, only 130 of the 1300 insured drivers 25 years or older have been involved in at least one automobile accident. What is the probability that an insured driver of any age will be involved in an accident?

The ________ is the difference between the expected payoff that would have been realized had the best alternative action been selected if we knew which state of nature would occur and the expected payoff under risk.

The ________ criterion is preferred by optimistic decision makers.

Alternatives 1 and 2 in the following payoff table represent the two possible manufacturing strategies that the EKA manufacturing company can adopt. The level of demand affects the success of both strategies. The states of nature (S_I) represent the levels of demand for the company products. S₁, S₂, and S₃ characterize high, medium, and low demand, respectively. The payoff values are in thousands of dollars. The best alternative (course of action) for the EKA manufacturing company, using the maximax criterion, is alternative 1.

The quality control manager for NKA Inc. must decide whether to accept (alternative 1), further analyze (alternative 2), or reject (alternative 3) an incoming shipment (lot) of microchips. The historical data indicate that there is a 30 percent chance that the lot is poor quality (S₁), 50 percent chance that the lot is fair quality (S₂), and 20 percent chance that the lot is good quality (S₃). Assume the following payoff table is available. The values in the payoff table are in thousands of dollars. What alternative action should be selected according to the maximax criterion?

The ________ criterion is attractive to those decision makers who exhibit a neutral approach toward decision choices involving risk.

Alternatives 1 and 2 in the following payoff table represent the two possible manufacturing strategies that the EKA manufacturing company can adopt. The level of demand affects the success of both strategies. The states of nature (S_I) represent the levels of demand for the company products. S₁, S₂, and S₃ characterize high, medium, and low demand, respectively. The payoff values are in thousands of dollars. Determine the best alternative (course of action) for the EKA manufacturing company using the maximin criterion.

The quality control manager for NKA Inc. must decide whether to accept (alternative 1), further analyze (alternative 2), or reject (alternative 3) an incoming shipment (lot) of microchips. The historical data indicate that there is a 30 percent chance that the lot is poor quality (S₁), 50 percent chance that the lot is fair quality (S₂), and 20 percent chance that the lot is good quality (S₃). Assume the following payoff table is available. The values in the payoff table are in thousands of dollars. Based on historical data, if the lot is poor quality, 40 percent of the items are defective. If the lot is fair quality, 22 percent of the items are defective. If the lot is good quality, 10 percent of the items are defective. The quality control manager inspects one unit from a recent shipment. After inspecting it, he determines that the unit is not defective. Given that the inspected item is not defective, determine which alternative action the quality control manager should choose.

The maximax criterion finds the worst possible payoff for each alternative and then chooses the alternative that yields the maximum of those worst possible payoffs.

The expected monetary value criterion is best used when a large number of similar decisions will be made.