Deck 9: Decision Analysis

Question 1

Bayes' decision rule says to choose the alternative with the largest expected payoff.

Answer 1

True

Question 2

The equally likely criterion assigns a probability of 0.5 to each state of nature.

Answer 2

False

Question 3

Graphical analysis can only be used in sensitivity analysis for those problems that have two decision alternatives.

Answer 3

False

Question 4

The maximin approach involves choosing the alternative with the highest payoff.

Question 5

Prior probabilities refer to the relative likelihood of possible states of nature.

Question 6

In decision analysis,states of nature refer to possible future conditions.

Question 7

The maximin criterion is an optimistic criterion.

Question 8

States of nature are alternatives available to a decision maker.

Question 9

Payoffs always represent profits in decision analysis problems.

Question 10

Using Bayes' decision rule will always lead to larger payoffs.

Question 11

The maximum likelihood criterion ignores the payoffs for states of nature other than the most likely one.

Question 12

A decision tree branches out all of the possible decisions and all of the possible events.

Question 13

The maximum likelihood criterion says to focus on the largest payoff.

Question 14

A event node in a decision tree indicates that a decision needs to be made at that point.

Question 15

An example of maximax decision making is a person buying lottery tickets in hopes of a very big payoff.

Question 16

An advantage of payoff tables compared to decision trees is that they permit us to analyze situations involving sequential decisions.

Question 17

Sensitivity analysis may be useful in decision analysis since prior probabilities may be inaccurate.

Question 18

The maximin approach involves choosing the alternative that has the "best worst" payoff.

Question 19

The maximax approach is an optimistic strategy.

Question 20

Payoff tables may include only non-negative numbers.

Question 21

Figure
The maximin strategy is:

A)Buy.
B)Rent.
C)Lease.
D)High.
E)Low.

Question 22

An advantage of Sensit's Spider graph when compared to Sensit's Tornado chart is that it allows data values to be varied by different percentages.

Question 23

The exponential utility function assumes a constant aversion to risk.

Question 24

Determining the worst payoff for each alternative and choosing the alternative with the "best worst" is the criterion called:

A)minimin.
B)maximin.
C)maximax.
D)maximum likelihood.
E)Bayes decision rule.

Question 25

A posterior probability is a revised probability of a state of nature after doing a test or survey to refine the prior probability.

Question 26

The maximin criterion refers to:

A)minimizing the maximum return.
B)maximizing the minimum return.
C)choosing the alternative with the highest payoff.
D)choosing the alternative with the minimum payoff.
E)None of the above.

Question 27

Testing how a problem solution reacts to changes in one or more of the model parameters is called:

A)analysis of tradeoffs.
B)sensitivity analysis.
C)priority recognition.
D)analysis of variance.
E)decision analysis.

Question 28

Which one of the following statements is not correct when making decisions?

A)The sum of the state of nature probabilities must be 1.
B)Every probability must be greater than or equal to 0.
C)All probabilities are assumed to be equal.
D)Probabilities are used to compute expected values.
E)Perfect information assumes that the state of nature that will actually occur is known.

Question 29

The Sensit Spider graph is useful for examining the impact of changes in several data values at once.

Question 30

Figure
The maximum likelihood strategy is:

A)Buy.
B)Rent.
C)Lease.
D)High.
E)Low.

Question 31

Bayes' theorem is a formula for determining prior probabilities of a state of nature.

Question 32

Which of the following is not a criterion for decision making?

A)EVPI.
B)Maximin.
C)Maximax.
D)Bayes' decision rule.
E)Maximum likelihood.

Question 33

A utility function for money can be constructed by applying a lottery procedure.

Question 34

The EVPI indicates an upper limit in the amount a decision-maker should be willing to spend to obtain information.

Question 35

The Sensit Plot tool is useful for examining the impact of changes in several data values at once.

Question 36

Most people occupy a middle ground and are classified as risk neutral.

Question 37

Utilities can be useful when monetary values do not accurately reflect the true values of an outcome.

Question 38

A risk seeker has a decreasing marginal utility for money.

Question 39

Two people who face the same problem and use the same decision-making methodology must always arrive at the same decision.
Multiple Choice Questions

Question 40

Figure
The maximax strategy is:

A)Buy.
B)Rent.
C)Lease.
D)High.
E)Low.

Question 41

Figure
The construction manager for ABC Construction must decide whether to build single family homes,apartments,or condominiums.he estimates annual profits (in $000)will vary with the population trend as follows:
If he uses Bayes' decision rule,which kind of dwellings will he decide to build?

A)Single family.
B)Apartments.
C)Condos.
D)Either single family or apartments.
E)Either apartments or condos.

Question 42

What is the probability that script #1 will be a success,but its sequel will not?

A)0.8.
B)0.7.
C)0.56.
D)0.2.
E)0.14.

Question 43

What is the expected annual profit for the dwellings that he will decide to build using Bayes' decision rule?

A)$187,000.
B)$132,000.
C)$123,000.
D)$65,000.
E)$55,000.

Question 44

What is the expected annual profit for the bus that he will decide to purchase using Bayes' decision rule?

A)$15,000.
B)$61,000.
C)$69,000.
D)$72,000.
E)$87,000.

Question 45

Figure
The expected value of perfect information is:

A)12.
B)55.
C)57.
D)69.
E)90.

Question 46

Figure
The Bayes' decision rule strategy is:

A)Buy.
B)Rent.
C)Lease.
D)High.
E)Low.

Question 47

Figure
The maximum likelihood strategy is:

A)small.
B)medium.
C)medium large.
D)large.
E)extra large.

Question 48

Figure
The expected value of perfect information is:

A)-28.
B)0.
C)10.5.
D)19.
E)23.

Question 49

What is the expected payoff from selecting script #1?

A)$150 million.
B)$90.6 million.
C)$84 million.
D)$72 million.
E)$60 million.

Question 50

Figure
The Bayes' decision rule strategy is:

A)small.
B)medium.
C)medium large.
D)large.
E)extra large.

Question 51

Figure
The operations manager for a local bus company wants to decide whether he should purchase a small,medium,or large new bus for his company.He estimates that the annual profits (in $000)will vary depending upon whether passenger demand is low,moderate,or high,as follows.
If he uses the maximum likelihood criterion,which size bus will he decide to purchase?

A)Small.
B)Medium.
C)Large.
D)Either small or medium.
E)Either medium or large.

Question 52

What is his expected value of perfect information?

A)$187,000.
B)$132,000.
C)$123,000.
D)$65,000.
E)$55,000.
The head of operations for a movie studio wants to determine which of two new scripts they should select for their next major production.She feels that script #1 has a 70% chance of earning $100 million over the long run,but a 30% chance of losing $20 million.If this movie is successful,then a sequel could also be produced,with an 80% chance of earning $50 million,but a 20% chance of losing $10 million.On the other hand,she feels that script #2 has a 60 % chance of earning $120 million,but a 40% chance of losing $30 million.If successful,its sequel would have a 50% chance of earning $80 million and a 50% chance of losing $40 million.As with the first script,if the original movie is a "flop",then no sequel would be produced.

Question 53

What would be the total payoff is script #1 were a success,but its sequel were not?

A)$150 million.
B)$100 million.
C)$90 million.
D)$50 million.
E)$-10 million.

Question 54

Figure
The operations manager for a local bus company wants to decide whether he should purchase a small,medium,or large new bus for his company.He estimates that the annual profits (in $000)will vary depending upon whether passenger demand is low,moderate,or high,as follows.
If he uses Bayes' decision rule,which size bus will he decide to purchase?

A)Small.
B)Medium.
C)Large.
D)Either small or medium.
E)Either medium or large.

Question 55

Figure
The maximin strategy is:

A)small.
B)medium.
C)medium large.
D)large.
E)extra large.

Question 56

What is the expected payoff from selecting script #2?

A)$150 million.
B)$90.6 million.
C)$84 million.
D)$72 million.
E)$60 million.

Question 57

Figure
The maximax strategy is:

A)small.
B)medium.
C)medium large.
D)large.
E)extra large.

Question 58

Figure
The expected value of perfect information is:

A)4.5.
B)9.
C)40.5.
D)49.5.
E)60.

Question 59

Figure
The construction manager for ABC Construction must decide whether to build single family homes,apartments,or condominiums.he estimates annual profits (in $000)will vary with the population trend as follows:
If he uses the maximum likelihood criterion,which kind of dwellings will he decide to build?

A)Single family.
B)Apartments.
C)Condos.
D)Either single family or apartments.
E)Either apartments or condos.

Question 60

What is his expected value of perfect information?

A)$15,000.
B)$61,000.
C)$69,000.
D)$72,000.
E)$87,000.

Question 61

Figure There is an option of paying $100 to have research done to better predict which state of nature will occur.When the true state of nature is S1,the research will accurately predict S1 60% of the time.When the true state of nature is S2,the research will accurately predict S2 80% of the time.
Given that the research is done,what is the expected payoff using Bayes' decision rule?

A)-82.
B)-44.
C)0.
D)29.
E)40.

Question 62

What is the probability that the statistics book would wind up being placed with a smaller publisher?

A)0.6.
B)0.5.
C)0.4.
D)0.3.
E)0.

Question 63

Figure There is an option of paying $100 to have research done to better predict which state of nature will occur.When the true state of nature is S1,the research will accurately predict S1 60% of the time.When the true state of nature is S2,the research will accurately predict S2 80% of the time.
Given that the research is not done,what is the expected payoff using Bayes' decision rule?

A)0.
B)29.
C)40.
D)75.
E)100.

Question 64

Figure There is an option of paying $100 to have research done to better predict which state of nature will occur.When the true state of nature is S1,the research will accurately predict S1 60% of the time.When the true state of nature is S2,the research will accurately predict S2 80% of the time.
What is the posterior probability of S1 given that the research predicts S1?

A)0.18.
B)0.44.
C)0.57.
D)0.65.
E)0.82.

Question 65

Figure There is an option of paying $100 to have research done to better predict which state of nature will occur.When the true state of nature is S1,the research will accurately predict S1 60% of the time.When the true state of nature is S2,the research will accurately predict S2 80% of the time.
Given that the research is done,what is the joint probability that the state of nature is S1 and the research predicts S1?

A)0.08.
B)0.16.
C)0.24.
D)0.32.
E)0.36.

Question 66

What is the expected payoff for the optimum decision alternative?

A)$150 million.
B)$90.6 million.
C)$84 million.
D)$72 million.
E)$60 million.
Two professors at a nearby university want to co-author a new textbook in either economics or statistics.They feel that if they write an economics book they have a 50% chance of placing it with a major publisher where it should ultimately sell about 40,000 copies.If they can't get a major publisher to take it,then they feel they have an 80% chance of placing it with a smaller publisher,with sales of 30,000 copies.On the other hand if they write a statistics book,they feel they have a 40% chance of placing it with a major publisher,and it should result in ultimate sales of about 50,000 copies.If they can't get a major publisher to take it,they feel they have a 50% chance of placing it with a smaller publisher,with ultimate sales of 35,000 copies.

Question 67

What is the expected payoff for the optimum decision alternative?

A)50,000 copies.
B)40,000 copies.
C)32,000 copies.
D)30,500 copies.
E)10,500 copies.

Question 68

Figure There is an option of paying $100 to have research done to better predict which state of nature will occur.When the true state of nature is S1,the research will accurately predict S1 60% of the time.When the true state of nature is S2,the research will accurately predict S2 80% of the time.
Given that the research is done,what is the joint probability that the state of nature is S1 and the research predicts S2?

A)0.08.
B)0.16.
C)0.24.
D)0.32.
E)0.36.

Question 69

Figure There is an option of paying $100 to have research done to better predict which state of nature will occur.When the true state of nature is S1,the research will accurately predict S1 60% of the time.When the true state of nature is S2,the research will accurately predict S2 80% of the time.
What is the unconditional probability that the research predicts S1?

A)0.32.
B)0.4.
C)0.44.
D)0.56.
E)0.6.

Question 70

Figure There is an option of paying $100 to have research done to better predict which state of nature will occur.When the true state of nature is S1,the research will accurately predict S1 60% of the time.When the true state of nature is S2,the research will accurately predict S2 80% of the time.
What is the unconditional probability that the research predicts S2?

A)0.32.
B)0.4.
C)0.44.
D)0.56.
E)0.6.

Question 71

What is the expected payoff for the decision to write the economics book?

A)50,000 copies.
B)40,000 copies.
C)32,000 copies.
D)30,500 copies.
E)10,500 copies.

Question 72

Figure There is an option of paying $100 to have research done to better predict which state of nature will occur.When the true state of nature is S1,the research will accurately predict S1 60% of the time.When the true state of nature is S2,the research will accurately predict S2 80% of the time.
What is the expected value of perfect information?

A)40.
B)45.
C)75.
D)85.
E)100.

Question 73

Figure There is an option of paying $100 to have research done to better predict which state of nature will occur.When the true state of nature is S1,the research will accurately predict S1 60% of the time.When the true state of nature is S2,the research will accurately predict S2 80% of the time.
Given that the research is done,what is the joint probability that the state of nature is S2 and the research predicts S2?

A)0.08.
B)0.16.
C)0.24.
D)0.32.
E)0.36.

Question 74

What is the expected payoff for the decision to write the statistics book?

A)50,000 copies.
B)40,000 copies.
C)32,000 copies.
D)30,500 copies.
E)10,500 copies.

Question 75

What is the probability that the economics book would wind up being placed with a smaller publisher?

A)0.8.
B)0.5.
C)0.4.
D)0.2.
E)0.1.

Question 76

Figure There is an option of paying $100 to have research done to better predict which state of nature will occur.When the true state of nature is S1,the research will accurately predict S1 60% of the time.When the true state of nature is S2,the research will accurately predict S2 80% of the time.
What is the posterior probability of S2 given that the research predicts S2?

A)0.18.
B)0.44.
C)0.57.
D)0.65.
E)0.82.

Question 77

Figure There is an option of paying $100 to have research done to better predict which state of nature will occur.When the true state of nature is S1,the research will accurately predict S1 60% of the time.When the true state of nature is S2,the research will accurately predict S2 80% of the time.
Given that the research is done,what is the joint probability that the state of nature is S2 and the research predicts S1?

A)0.08.
B)0.16.
C)0.24.
D)0.32.
E)0.36.