Deck 9: Decision Analysis

Question 1

The maximax approach is an optimistic strategy.

Answer 1

True

Question 2

Payoffs always represent profits in decision analysis problems.

Answer 2

False

Question 3

States of nature are alternatives available to a decision maker.

Answer 3

False

Question 4

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

Question 5

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

Question 6

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

Question 7

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

Question 8

The maximin criterion is an optimistic criterion.

Question 9

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

Question 10

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

Question 11

Payoff tables may include only non-negative numbers.

Question 12

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

Question 13

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

Question 14

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

Question 15

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

Question 16

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

Question 17

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

Question 18

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

Question 19

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

Question 20

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

Question 21

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 22

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 answer choices is correct.

Question 23

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

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

Based on the following payoff table, answer the following:
$$\begin{array} { | l | r | r | } \hline { \text { Alternative } } & \text { High } & { \text { Low } } \\\hline \text { Buy } & 90 & - 10 \\\hline \text { Rent } & 70 & 40 \\\hline \text { Lease } & 60 & 55 \\\hline \text { Prior Probability } & 0.4 & 0.6 \\\hline\end{array}$$
The Bayes' decision rule strategy is:

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

Question 26

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

Question 27

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

Question 28

Based on the following payoff table, answer the following:
$$\begin{array} { | l | r | r | } \hline { \text { Alternative } } & \text { High } & { \text { Low } } \\\hline \text { Buy } & 90 & - 10 \\\hline \text { Rent } & 70 & 40 \\\hline \text { Lease } & 60 & 55 \\\hline \text { Prior Probability } & 0.4 & 0.6 \\\hline\end{array}$$
The maximin strategy is:

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

Question 29

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

Question 30

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

Question 31

Based on the following payoff table, answer the following:
$$\begin{array} { | l | r | r | } \hline { \text { Alternative } } & \text { High } & { \text { Low } } \\\hline \text { Buy } & 90 & - 10 \\\hline \text { Rent } & 70 & 40 \\\hline \text { Lease } & 60 & 55 \\\hline \text { Prior Probability } & 0.4 & 0.6 \\\hline\end{array}$$
The expected value of perfect information is:

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

Question 32

Based on the following payoff table, answer the following:
$$\begin{array} { | l | r | r | } \hline { \text { Alternative } } & \text { High } & { \text { Low } } \\\hline \text { Buy } & 90 & - 10 \\\hline \text { Rent } & 70 & 40 \\\hline \text { Lease } & 60 & 55 \\\hline \text { Prior Probability } & 0.4 & 0.6 \\\hline\end{array}$$
The maximax strategy is:

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

Question 33

The exponential utility function assumes a constant aversion to risk.

Question 34

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

Question 35

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 36

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

Question 37

Based on the following payoff table, answer the following:
$$\begin{array} { | l | r | r | } \hline { \text { Alternative } } & \text { High } & { \text { Low } } \\\hline \text { Buy } & 90 & - 10 \\\hline \text { Rent } & 70 & 40 \\\hline \text { Lease } & 60 & 55 \\\hline \text { Prior Probability } & 0.4 & 0.6 \\\hline\end{array}$$
The maximum likelihood strategy is:

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

Question 38

Based on the following payoff table, answer the following:
$$\begin{array} { | l | r | r | } \hline { \text { Alternative } } & { \text { Yes } } & { \text { No } } \\\hline \text { Brmall } & 10 & 30 \\\hline \text { Medium } & 20 & 40 \\\hline \text { Mediurn Large } & 30 & 45 \\\hline \text { Large } & 40 & 35 \\\hline \text { Extra Large } & 60 & 20 \\\hline \text { Prior Probability } & 0.3 & 0.7 \\\hline\end{array}$$
The maximax strategy is:

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

Question 39

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 40

A risk seeker has a decreasing marginal utility for money.

Question 41

Based on the following payoff table, answer the following:
$$\begin{array} { | l | r | r | r |} \hline { \text { Alternative } } & \text { High } & { \text { Medium } } & { \text { Low } } \\\hline \text { A } & 20 & 20 & 5 \\\hline \mathrm { B } & 25 & 30 & 11 \\\hline \mathrm { C } & 30 & 12 & 13 \\\hline \mathrm { D } & 10 & 12 & 12 \\\hline \mathrm { E } & 50 & 40 & - 28 \\\hline \text { Prior Probability } & 0.3 & 0.2 & 0.5 \\\hline\end{array}$$
The maximum likelihood strategy is:

A) A.
B) B.
C) C.
D) D.
E) E.

Question 42

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.
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

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 44

Based on the following payoff table, answer the following:
$$\begin{array} { | l | r | r | r |} \hline { \text { Alternative } } & \text { High } & { \text { Medium } } & { \text { Low } } \\\hline \text { A } & 20 & 20 & 5 \\\hline \mathrm { B } & 25 & 30 & 11 \\\hline \mathrm { C } & 30 & 12 & 13 \\\hline \mathrm { D } & 10 & 12 & 12 \\\hline \mathrm { E } & 50 & 40 & - 28 \\\hline \text { Prior Probability } & 0.3 & 0.2 & 0.5 \\\hline\end{array}$$
The maximax strategy is:

A) A.
B) B.
C) C.
D) D.
E) E.

Question 45

Based on the following payoff table, answer the following:
$$\begin{array} { | l | r | r | } \hline { \text { Alternative } } & { \text { Yes } } & { \text { No } } \\\hline \text { Brmall } & 10 & 30 \\\hline \text { Medium } & 20 & 40 \\\hline \text { Mediurn Large } & 30 & 45 \\\hline \text { Large } & 40 & 35 \\\hline \text { Extra Large } & 60 & 20 \\\hline \text { Prior Probability } & 0.3 & 0.7 \\\hline\end{array}$$
The maximin strategy is:

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

Question 46

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:

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 47

Based on the following payoff table, answer the following:
$$\begin{array} { | l | r | r | r |} \hline { \text { Alternative } } & \text { High } & { \text { Medium } } & { \text { Low } } \\\hline \text { A } & 20 & 20 & 5 \\\hline \mathrm { B } & 25 & 30 & 11 \\\hline \mathrm { C } & 30 & 12 & 13 \\\hline \mathrm { D } & 10 & 12 & 12 \\\hline \mathrm { E } & 50 & 40 & - 28 \\\hline \text { Prior Probability } & 0.3 & 0.2 & 0.5 \\\hline\end{array}$$
The Bayes' decision rule strategy is:

A) A.
B) B.
C) C.
D) D.
E) E.

Question 48

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.
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 49

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.

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 50

Based on the following payoff table, answer the following:
$$\begin{array} { | l | r | r | } \hline { \text { Alternative } } & { \text { Yes } } & { \text { No } } \\\hline \text { Brmall } & 10 & 30 \\\hline \text { Medium } & 20 & 40 \\\hline \text { Mediurn Large } & 30 & 45 \\\hline \text { Large } & 40 & 35 \\\hline \text { Extra Large } & 60 & 20 \\\hline \text { Prior Probability } & 0.3 & 0.7 \\\hline\end{array}$$
The maximum likelihood strategy is:

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

Question 51

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.

What is his expected value of perfect information?

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

Question 52

Based on the following payoff table, answer the following:
$$\begin{array} { | l | r | r | r |} \hline { \text { Alternative } } & \text { High } & { \text { Medium } } & { \text { Low } } \\\hline \text { A } & 20 & 20 & 5 \\\hline \mathrm { B } & 25 & 30 & 11 \\\hline \mathrm { C } & 30 & 12 & 13 \\\hline \mathrm { D } & 10 & 12 & 12 \\\hline \mathrm { E } & 50 & 40 & - 28 \\\hline \text { Prior Probability } & 0.3 & 0.2 & 0.5 \\\hline\end{array}$$
The maximin strategy is:

A) A.
B) B.
C) C.
D) D.
E) E.

Question 53

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 54

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.
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 55

Based on the following payoff table, answer the following:
$$\begin{array} { | l | r | r | } \hline { \text { Alternative } } & { \text { Yes } } & { \text { No } } \\\hline \text { Brmall } & 10 & 30 \\\hline \text { Medium } & 20 & 40 \\\hline \text { Mediurn Large } & 30 & 45 \\\hline \text { Large } & 40 & 35 \\\hline \text { Extra Large } & 60 & 20 \\\hline \text { Prior Probability } & 0.3 & 0.7 \\\hline\end{array}$$
The Bayes' decision rule strategy is:

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

Question 56

Based on the following payoff table, answer the following:
$$\begin{array} { | l | r | r | r |} \hline { \text { Alternative } } & \text { High } & { \text { Medium } } & { \text { Low } } \\\hline \text { A } & 20 & 20 & 5 \\\hline \mathrm { B } & 25 & 30 & 11 \\\hline \mathrm { C } & 30 & 12 & 13 \\\hline \mathrm { D } & 10 & 12 & 12 \\\hline \mathrm { E } & 50 & 40 & - 28 \\\hline \text { Prior Probability } & 0.3 & 0.2 & 0.5 \\\hline\end{array}$$
The expected value of perfect information is:

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

Question 57

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:

What is his expected value of perfect information?

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

Question 58

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 59

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

Based on the following payoff table, answer the following:
$$\begin{array} { | l | r | r | } \hline { \text { Alternative } } & { \text { Yes } } & { \text { No } } \\\hline \text { Brmall } & 10 & 30 \\\hline \text { Medium } & 20 & 40 \\\hline \text { Mediurn Large } & 30 & 45 \\\hline \text { Large } & 40 & 35 \\\hline \text { Extra Large } & 60 & 20 \\\hline \text { Prior Probability } & 0.3 & 0.7 \\\hline\end{array}$$
The expected value of perfect information is:

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

Question 61

Refer to the following payoff table:

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 62

Refer to the following payoff table:

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

Question 63

Refer to the following payoff table:

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 64

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.
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 65

Refer to the following payoff table:

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

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.
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 67

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.
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 68

Refer to the following payoff table:

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 69

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.
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

Question 70

Refer to the following payoff table:

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 71

Refer to the following payoff table:

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 72

Refer to the following payoff table:

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 73

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.
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 74

Refer to the following payoff table:

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 75

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.
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 76

Refer to the following payoff table:

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 77

Refer to the following payoff table:

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 78

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.
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 79

What is the role of the group facilitator in decision conferencing?

A) Lead the group to the desired outcome.
B) Structure and focus discussions.
C) Provide mathematical support for decision analysis.
D) Determine the states of nature.
E) Determine the payoffs for each alternative.

Question 80

A risk-averse decision maker is trying to decide which alternative to choose. The payoff table for the alternatives, given two possible states of nature, is shown below. Assuming that the decision makers risk tolerance (R) is 5, which decision should she choose based on the utility of each outcome? Assume the exponential utility function is applicable.
$$\begin{array} { | l | r | r | } \hline { \text { Alternative } } & \text { High } & { \text { Low } } \\\hline \text { A } & 20 & 5 \\\hline \mathrm { B } & 25 & 11 \\\hline \mathrm { C } & 30 & 15 \\\hline \mathrm { D } & 10 & 12 \\\hline \mathrm { E } & 50 & - 28 \\\hline \text { Prior Probability } & 0.3 & 0.7 \\\hline\end{array}$$

A) Alternative A
B) Alternative B
C) Alternative C
D) Alternative D
E) Alternative E