Deck 19: Decision Theory

Question 1

When the maximin criterion is used,the decision maker assumes that for any alternative action,the state of nature with the maximum payoff will take place.

Answer 1

False

Question 2

Maximax is a criterion used when making decisions under uncertainty.

Answer 2

True

Question 3

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:

A)Certainty.
B)Uncertainty.
C)Risk.
D)Optimism.

Answer 3

B

Question 4

The maximax criterion finds the best possible payoff for each alternative,and then chooses the alternative that yields the maximum (best)possible payoff.

Question 5

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.

Question 6

When making a decision in an environment of ________________,the decision maker knows which of the states of nature will actually occur.

A)Certainty
B)Uncertainty
C)Risk
D)Optimism

Question 7

Maximin is a criterion used when making decisions under certainty.

Question 8

When we use the expected monetary value criterion,the expected payoff equals the actual payoff that will be realized.

Question 9

A decision maker's expected utility is based upon his/her attitude toward risk.

Question 10

Maximin is a criterion used when making decisions under _____________.

A)Uncertainty
B)Certainty
C)Risk
D)Alternatives

Question 11

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

Question 12

A tire manufacturer needs to make a decision about the amount of production for the coming month (high vs.low).The level of production largely depends on the level of demand.For this situation,the level of demand (high,medium,low)is the state of nature.

Question 13

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

Question 14

The maximax criterion is preferred by pessimistic decision makers.

Question 15

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. $\begin{array}{lccc} &&\underline{{\text { States of nature }}} \\& s_{1} & s_{2} & s_{3} \\\text { Alternative (strategy) } 1 & 110 & 80 & 70 \\\text { Alternative (strategy) } 2 & 60 & 120 & 50\end{array}$

The best alternative (course of action)for the EKA manufacturing company,using the maximax criterion,is alternative 1.

Question 16

The maximin criterion is preferred by optimistic decision makers.

Question 17

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.

A)Maximax criterion
B)Maximin criterion
C)Expected utility
D)Expected value of perfect information
E)Expected value of sample information

Question 18

In utility analysis,a utility curve that shows a rapid increase in utility for initial amounts of money followed by a gradual leveling off for larger amounts of money is appropriate for a risk-seeking decision maker.

Question 19

When making a decision in an environment of ________________,the likelihood of each state of nature can be estimated.

A)Certainty
B)Uncertainty
C)Risk
D)Alternatives

Question 20

The maximin criterion finds the best possible payoff for each alternative and then chooses the alternative that yields the maximum payoff.

Question 21

A pharmaceutical company manufacturing pregnancy test kits wants to determine the probability of a woman actually being pregnant when the test results indicate that she is not pregnant.It is estimated that the probability of pregnancy among potential users of the kit is 10 percent.According to the company laboratory test results,1 out of 100 nonpregnant women tested pregnant (false positive).On the other hand,1 out of 200 pregnant women tested nonpregnant (false negative).A woman has just used the pregnancy test kit manufactured by the company,and the results showed that she is not pregnant.What is the probability that she is pregnant?

A)1%
B)0.9%
C)0.05%
D)8.3%
E)0.056%

Question 22

An automobile insurance company is in the process of reviewing its policies.Currently,drivers under the age of 25 have to pay a premium.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 has 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?

A)35%
B)20.5%
C)65%
D)68.3%
E)79.5%

Question 23

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. $\begin{array}{lccc} &&\underline{{\text { States of nature }}} \\& s_{1} & s_{2} & s_{3} \\\text { Alternative (strategy) } 1 & 110 & 80 & 70 \\\text { Alternative (strategy) } 2 & 60 & 120 & 50\end{array}$


The best alternative (course of action)for the EKA manufacturing company using the maximin criterion is strategy _____ and the best possible payoff is __________.

A)1,$50,000
B)2,$120,000
C)1,$100,000
D)1,$70,000
E)2,$80,000

Question 24

A pharmaceutical company manufacturing pregnancy test kits wants to determine the probability of a woman not being pregnant when the test results indicate pregnancy.It is estimated that the probability of pregnancy among potential users of the kit is 10 percent.According to the company laboratory test results,1 out of 100 nonpregnant women tested pregnant (false positive).On the other hand,1 out of 200 pregnant women tested nonpregnant (false negative).A woman has just used the pregnancy test kit manufactured by the company and the results showed pregnancy.What is the probability that she is not pregnant?

A)90%
B)0.9%
C)8.3%
D)91.7%
E)10.85%

Question 25

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

A)Expected utility
B)Expected value
C)Maximin
D)Maximax
E)Decision theory

Question 26

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

A)Certainty
B)Uncertainty
C)Risk
D)Alternatives

Question 27

An automobile insurance company is in the process of reviewing its policies.Currently,drivers under the age of 25 have to pay a premium.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 1300 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?

A)35%
B)20.5%
C)14%
D)68.3%
E)40%

Question 28

The utility curve given below represents the preferences of a _________________ decision maker.

A)Risk averse
B)Risk neutral
C)Risk seeking
D)None of these

Question 29

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

A)Maximax criterion
B)Maximin criterion
C)Expected utility
D)Expected value of perfect information
E)Expected value of sample information

Question 30

The utility curve given below represents the preferences of a _________________ decision maker.

A)Risk averse
B)Risk neutral
C)Risk seeking
D)None of these

Question 31

In utility analysis,a utility curve that shows a rapid increase in utility for initial amounts of money followed by a gradual leveling off for larger amount of money is appropriate for a risk _________ decision maker.

A)Seeking
B)Averse
C)Neutral
D)None of these

Question 32

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

A)payoff of sampling
B)payoff of no sampling
C)value of sample information
D)value of perfect information
E)utility

Question 33

The utility curve given below represents the preferences of a _________________ decision maker.

A)Risk averse
B)Risk neutral
C)Risk seeking
D)None of these

Question 34

A person's utility is determined by the preferences he/she exhibits for decision choices involving __________.

A)Certainty
B)Uncertainty
C)Risk
D)Bayes' Theorem

Question 35

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

A)Prior analysis.
B)Preposterior analysis.
C)Posterior analysis.
D)Payoff analysis.
E)Utility analysis.

Question 36

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. $\begin{array}{lccc} &&\underline{{\text { States of nature }}} \\& s_{1} & s_{2} & s_{3} \\\text { Alternative (strategy) } 1 & 110 & 80 & 70 \\\text { Alternative (strategy) } 2 & 60 & 120 & 50\end{array}$


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. $$\text { P(Poor } \mid \text { High } ) = .2 , P ( \text { Poor } \mid \text { Medium } ) = .5 , P ( \text { Poor } \mid \text { Low } ) = .8$$
What is the probability of high demand given that the weather conditions are poor.

A).06
B).44
C).1371
D).12
E).1818

Question 37

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. $\begin{array}{lccc} &&\underline{{\text { States of nature }}} \\& s_{1} & s_{2} & s_{3} \\\text { Alternative (strategy) } 1 & 110 & 80 & 70 \\\text { Alternative (strategy) } 2 & 60 & 120 & 50\end{array}$

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)EMV₁ = $98,000,EMV₂ = $95,000,choose strategy 1
B)EMV₁ = $88,000,EMV₂ = $95,000,choose strategy 2
C)EMV₁ = $88,000,EMV₂ = $85,000,choose strategy 1
D)EMV₁ = $66,667,EMV₂ = $76,667,choose strategy 2
E)EMV₁ = $120,000,EMV₂ = $110,000,choose strategy 1

Question 38

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. $\begin{array}{lccc} &&\underline{{\text { States of nature }}} \\& s_{1} & s_{2} & s_{3} \\\text { Alternative (strategy) } 1 & 110 & 80 & 70 \\\text { Alternative (strategy) } 2 & 60 & 120 & 50\end{array}$


The management believes that the 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.What is the maximum amount that the company would be willing to pay for perfect information?

A)$95,000
B)$112,000
C)$7,000
D)$24,000
E)$17,000

Question 39

Maximax is a criterion used when making decisions under __________________.

A)Certainty
B)Uncertainty
C)Risk
D)Alternatives

Question 40

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. $\begin{array}{lccc} &&\underline{{\text { States of nature }}} \\& s_{1} & s_{2} & s_{3} \\\text { Alternative (strategy) } 1 & 110 & 80 & 70 \\\text { Alternative (strategy) } 2 & 60 & 120 & 50\end{array}$


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.What is the probability that weather conditions are poor,given that the demand is high?

A).2
B).5
C).8
D).25
E).75

Question 41

The _____________________ is the difference between the expected value of sampling and the cost of sampling.

A)expected monetary value
B)expected value of perfect information
C)expected value of sample information
D)expected net gain of sampling

Question 42

__________________ statistics is an area of statistics that uses Bayes' Theorem to update prior belief about a probability or population parameter to a posterior belief.

A)Bayesian
B)Utility theory
C)Preposterior analysis
D)Risk theory

Question 43

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

A)Risk
B)Utility
C)Certainty
D)Uncertainty

Question 44

When making a decision in an environment of ________________,the decision maker knows which of the states of nature will actually occur.

A)Risk
B)Utility
C)Certainty
D)Uncertainty

Question 45

The __________________ criterion is preferred by optimistic decision makers.

A)Maximax
B)Maximin
C)Utility theory
D)Risk theory

Question 46

In a decision-making situation,the maximum amount of money that should be spent to obtain perfect information is called the ______________________________.

A)expected monetary value
B)expected value of perfect information
C)expected value of sample information
D)expected net gain of sampling

Question 47

A tire manufacturer needs to determine the amount of production for the coming month (high vs.low).The level of production largely depends on the level of demand.For this situation,the amount of production constitutes the ___________________ actions.

A)Alternative
B)Utility
C)Certainty
D)Uncertainty

Question 48

_______________________ is a diagram that assists the decision maker in analyzing a decision problem.

A)Bayes' Theorem
B)A decision tree
C)A utility curve
D)Maximax

Question 49

The _____________ criterion finds the worst-possible payoff for each alternative and then chooses the alternative that yields the maximum worst-possible payoff.

A)Maximin
B)Certainty
C)Maximax
D)Decision

Question 50

Decision makers in business organizations make most decisions in environments that involve some degree of ___________________.

A)Risk
B)Utility
C)Certainty
D)Uncertainty

Question 51

A decision maker's expected _____________ is based upon his/her attitude toward risk.

A)Maximax
B)Maximin
C)Utility
D)Risk theory

Question 52

When we assess the worth of sample information in a decision-making problem,we are performing a(n)_____________ analysis.

A)Utility
B)Maximax
C)Posterior
D)Preposterior

Question 53

The __________________ criterion is preferred by pessimistic decision makers.

A)Maximax
B)Maximin
C)Utility theory
D)Risk theory

Question 54

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

A)expected monetary value
B)expected value of perfect information
C)expected value of sampling information
D)expected net gain of sampling

Question 55

A corn farmer has categorized the weather into three possible levels.The weather conditions will affect the timing of the harvest and the associated payoff.In this situation,the weather conditions are called the ____________________________.

A)Alternatives
B)States of nature
C)Payoffs
D)Perfect information

Question 56

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.

A)expected monetary value
B)expected value of perfect information
C)expected value of sample information
D)expected net gain of sampling

Question 57

The _____________ criterion finds the best-possible payoff for each alternative and then chooses the alternative that yields the maximum best-possible payoff.

A)Maximin
B)Certainty
C)Maximax
D)Decision

Question 58

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

A)Maximin
B)Certainty
C)Maximax
D)Decision

Question 59

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

A)Maximin
B)Certainty
C)Maximax
D)Decision

Question 60

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

A)Utility
B)Maximax
C)Posterior
D)Preposterior

Question 61

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.

Question 62

The quality control manager for NKA Inc.must decide whether to accept (alternative 1),further analyze (alternative 2),or reject (alternative 3)a shipment (lot)of incoming material.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.

Question 63

A pharmaceutical company manufacturing pregnancy test kits wants to determine the probability of a woman actually being pregnant when the test results indicate that she is not pregnant.It is estimated that the probability of pregnancy among potential users of the kit is 10 percent.According to the company laboratory test results,1 out of 100 nonpregnant women tested pregnant (false positive).On the other hand,1 out of 200 pregnant women tested nonpregnant (false negative).A woman has just used the pregnancy test kit manufactured by the company and the results showed that she is not pregnant.What is the probability that she is pregnant?

Question 64

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

A)expected monetary value
B)expected value of perfect information
C)expected value of sample information
D)expected net gain of sampling

Question 65

An automobile insurance company is in the process of reviewing its policies.Currently,drivers under the age of 25 have to pay a premium.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?

Question 66

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.

Question 67

In utility theory,a(n)__________________ decision maker is an individual who will choose the decision alternative having the highest expected profit.

A)high risk
B)low risk
C)risk neutral
D)posterior

Question 68

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.

Question 69

The quality control manager for NKA Inc.must decide whether to accept (alternative 1),further analyze (alternative 2),or reject (alternative 3)a shipment (lot)of incoming material.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.

Question 70

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.

Question 71

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.

Question 72

The _________ curve of an individual decision maker is a plot of the decision maker's utilities versus the profits.

A)Utility
B)Maximax
C)Posterior
D)Preposterior

Question 73

The 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.

Question 74

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.

Question 75

A pharmaceutical company manufacturing pregnancy test kits wants to determine the probability of a woman not being pregnant when the test results indicate pregnancy.It is estimated that the probability of pregnancy among potential users of the kit is 10 percent.According to the company laboratory test results,1 out of 100 nonpregnant women tested pregnant (false positive).On the other hand,1 out of 200 pregnant women tested nonpregnant (false negative).A woman has just used the pregnancy test kit manufactured by the company and the results showed pregnancy.What is the probability that she is not pregnant?

Question 76

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.

Question 77

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.

Question 78

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.

Question 79

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.

Question 80

An automobile insurance company is in the process of reviewing its policies.Currently,drivers under the age of 25 have to pay a premium.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.
An accident has just been reported.What is the probability that the insured driver is under the age of 25?