Exam 19: Decision Theory

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

When applying Bayes' Theorem, the sample information is combined with prior probabilities to obtain ________ probabilities.

Maximax is a criterion used when making decisions under uncertainty.

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. 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 has the flu. What is the probability that she does not have the flu?

If the decision maker has no knowledge about the likelihood of any of the states of nature occurring, then it can be stated that the decision maker is operating in an environment of

The ________ is the difference between the expected payoff of sampling and the expected payoff based on expected monetary criterion and prior probabilities.

The expected value criterion is used for decision making under ________.

The ________ criterion for choosing among alternative actions assumes that the state of nature with the best 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, 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. If the weather conditions are poor, determine which manufacturing strategy the company should implement.

The expected ________ of a decision maker is based upon his/her attitude toward risk.

An investor is looking at three possible investments: growth stock, blue chip stock, or municipal bonds. The investment performance will vary depending on the investment market condition of bull (market rising), flat, or bear (market falling). The investment return for each investment for the corresponding market conditions is given below. Which investment would the investor select if using the maximax 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. What is the maximum amount that the quality control manager would be willing to pay for perfect information?

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. The 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 1,300 insured drivers 25 years or older have been involved in at least one automobile accident. An accident has just been reported. What is the probability that the insured driver is under the age of 25?

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 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. Based on this information, the prior probabilities have been revised. If the weather conditions are favorable, P(S₁) = .4286, P(S₂) = .5357, and P(S₃) = .0357; and if the weather conditions are poor, P(S₁) = .1364, P(S₂) = .6818, and P(S₃) = .1818. It is also determined that the probability of favorable weather is .56 and the probability of poor weather is .44. Determine the expected value of sample information. What is the maximum amount that the company is willing to pay for the weather information and the additional analysis?

When we assess the worth of sample information in a decision-making problem, we are performing a

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 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. Construct the revised probability table for favorable weather conditions, and find the probability of high demand given that the weather conditions are favorable.

Maximin is a criterion used when making decisions under ________.

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

Maximax is a criterion used when making decisions under ________.

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 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. Construct the revised probability table for poor weather conditions, and find the probability of high demand given that the weather conditions are poor.