Question 1

In most business situations, the choice of the best alternative will be made under conditions of risk and ignorance.

Accepted Answer

A) True 
 B)False  False

Question 2

The payoff table is a table in which the rows are states of nature, the columns are decision alternatives, and the entry at each intersection of a row and column is a numerical payoff such as a profit or loss.

Accepted Answer

A) True 
 B)False  True

Question 3

A payoff table, the prior probabilities for three states of nature and the likelihood probabilities are shown below.
Payoff Table: $\begin{array} { ccc  }
&\text { Alternative }\
\text { State of Nature }& a_{1} & a_{2} & a_{3}\
s_{1} & 80 & 120 & 90 \
s_{2} & 60 & 130 & 170 \
s_{3} & 200 & 140 & 100
\end{array}$
 Prior Probabilities:
P( $S _ { 1 }$ ) = 0.4, P( $S _ { 2 }$ ) = 0.5, P( $S _ { 3 }$ ) = 0.1.
Likelihood Probabilities: $\begin{array}{ccc} 
& I_{1} & I_{2}& I_{3} \
s_{1} & 0.5 & 0.3 & 0.2 \
s_{2} & 0.2 & 0.6 & 0.2 \
s_{3} & 0.1 & 0.2 & 0.7
\end{array}$ a. Determine the EMV decision.
b. Set up the opportunity loss table.
c. Determine the EOL decision.
d. What is the expected payoff with perfect information?
e. What is the expected value of perfect information?

Accepted Answer

a. EMV ( $a _ { 1 }$ ) = (0.4)(80) + (0.5)(60) + (0.1)(200) = 82.
EMV ( $a _ { 2 }$ ) = (0.4)(120) + (0.5)(130) + (0.1)(140) = 127.
EMV ( $a _ { 3 }$ ) = (0.4)(90) + (0.5)(170) + (0.1)(100) = 131.
The EMV decision is $a _ { 3 }$ . Hence EMV* = 131.
b. $\begin{array} { ccc  }
&\text { Alternative }\
\text { State of Nature }& a_{1} & a_{2} & a_{3}\
s_{1} & 40 & 0 & 30 \
s_{2} & 110 & 40 & 0 \
s_{3} & 0 & 60 & 100
\end{array}$
 c. EOL ( $a _ { 1 }$ ) = (0.4)(40) + (0.5)(110) + (0.1)(0) = 71.
EOL ( $a _ { 2 }$ ) = (0.4)(0) + (0.5)(40) + (0.1)(60) = 26.
EOL ( $a _ { 3 }$ ) = (0.4)(30) + (0.5)(0) + (0.1)(100) = 22.
The EOL decision is $a _ { 3 }$ . Hence EOL* = 22.
d. EPPI = (0.4)(120) + (0.5)(170) +(0.1)(200) = 153.
e. EVPI = EPPI - EMV* = 153 - 131 = 22, or
EVPI = EOL* = 22.

Question 4

Which of the following best describes a decision tree?

Accepted Answer

A)  A decision tree is a useful device for calculating probabilities. 
B)  A decision tree uses branches to represent both acts and states of nature. 
C)  The payoffs are shown at the end of branches of a decision tree. 
D)  All of these choices are correct. 
A)  A decision tree is a useful device for calculating probabilities. 
B)  A decision tree uses branches to represent both acts and states of nature. 
C)  The payoffs are shown at the end of branches of a decision tree. 
D)  All of these choices are correct.

Question 5

The expected monetary value (EMV) of a decision alternative is the sum of the products of the payoffs and the state-of-nature probabilities.

Accepted Answer

A) True 
 B)False

Question 6

A payoff table is shown below. $\begin{array} { ccc  }
&\text { Alternative }\
\text { State of Nature }& a_{1} & a_{2} & a_{3}\
s_{1} & 21 & 8 & -3 \
s_{2} & 12 & 12 & 7 \
s_{3} & -15 & 9 & 13
\end{array}$
 The following prior probabilities are assigned to the states of nature:
P( $S _ { 1 }$ ) = 0.2, P( $S _ { 2 }$ ) = 0.7, P( $S _ { 3 }$ ) = 0.1.
a. Determine the EMV decision.
b. Set up the opportunity loss table.
c. Determine the EOL decision.
d. What is the expected payoff with perfect information?
e. What is the expected value of perfect information?

Accepted Answer

a. EMV ( @#LAT-DLM& ) = (0.2)(21) + (0.7)(12) + (0

Question 7

Incentive programs for sales staff would be considered a state of nature for a business firm.

Accepted Answer

A) True 
 B)False

Question 8

A payoff table, the prior probabilities for two states of nature, and the likelihood probabilities are shown below.
Payoff Table: $\begin{array} { ccc  }
&\text { Alternative }\
\text { State of Nature }& a_{1} & a_{2} & a_{3}\
s_{1} & 20 & 28 & 33 \
s_{2} & 32 & 29 & 25
\end{array}$
 Prior Probabilities:
P( $S _ { 1 }$ ) = 0.4, P( $S _ { 2 }$ ) = 0.6.
Likelihood Probabilities: $\begin{array}{ccc} 
& I_{1} & I_{2} \
s_{1} & 0.95 & 0.05 \

s_{2} & 0.08 & 0.92
\end{array}$ a. Determine the EMV decision.
b. Set up the opportunity loss table.
c. Determine the EOL decision.
d. What is the expected payoff with perfect information?
e. What is the expected value of perfect information?

Accepted Answer

a. EMV ( @#LAT-DLM&

) = (0.4)(20) + (0.6)(32) =

Question 9

In general, the expected monetary values (EMV) do not represent possible payoffs.

Accepted Answer

A) True 
 B)False

Question 10

A payoff table, the prior probabilities for two states of nature, and the likelihood probabilities are shown below.
Payoff Table: $\begin{array} { ccc  }
&\text { Alternative }\
\text { State of Nature }& a_{1} & a_{2} & a_{3}\
s_{1} & 20 & 28 & 33 \
s_{2} & 32 & 29 & 25
\end{array}$
 Prior Probabilities:
P( $S _ { 1 }$ ) = 0.4, P( $S _ { 2 }$ ) = 0.6.
Likelihood Probabilities: $\begin{array}{ccc} 
& I_{1} & I_{2} \
s_{1} & 0.95 & 0.05 \
s_{2} & 0.08 & 0.92
\end{array}$ a. Use the prior and likelihood probabilities to calculate the posterior probabilities for the experimental outcome $I _ { 1 }$ .
b. Use the posterior probabilities from a. to recalculate the expected monetary value of each act, then determine the optimal act and the EMV*.
c. Use the prior and likelihood probabilities to calculate the posterior probabilities for the experimental outcome $I _ { 2 }$ .
d. Use the posterior probabilities from c. to recalculate the expected monetary value of each act, then determine the optimal act and the $\mathrm { EMV } ^ { * }$ .
e. Use your answers to parts a. to d. to calculate the expected monetary value with additional information.
f. Calculate the expected value of sample information.

Accepted Answer

a.   ). Thus
EMV´= (0.428)(32.

Question 11

If EMV( $a _ { 1 }$ ) = $50 000, EMV( $a _ { 2 }$ ) = $65 000, and EMV( $a _ { 3 }$ ) = $45 000, then EMV* = $160 000.

Accepted Answer

A) True 
 B)False

Question 12

The expected monetary value (EMV) decision is always the same as the expected opportunity loss (EOL) decision, simply because the opportunity loss table is produced directly from the payoff table.

Accepted Answer

A) True 
 B)False

Question 13

Which of the following would be considered a state of nature for a business firm?

Accepted Answer

A)  Inventory levels. 
B)  Salaries for employees. 
C)  Site for new plant. 
D)  Worker safety laws. 
A)  Inventory levels. 
B)  Salaries for employees. 
C)  Site for new plant. 
D)  Worker safety laws.

Question 14

Which of the following statements is correct?

Accepted Answer

A)  The EMV criterion selects the act with the smallest expected monetary value. 
B)  The EOL criterion selects the act with the smallest expected opportunity loss. 
C)  The expected value of perfect information (EVPI) equals the largest expected opportunity loss. 
D)  All these choices are correct. 
A)  The EMV criterion selects the act with the smallest expected monetary value. 
B)  The EOL criterion selects the act with the smallest expected opportunity loss. 
C)  The expected value of perfect information (EVPI) equals the largest expected opportunity loss. 
D)  All these choices are correct.

Question 15

The expected value of sample information (EVSI) is the difference between the expected monetary value with additional information (EMV´)and the expected monetary value without additional information (EMV*). That is, EVSI = EMV´ - EMV*.

Accepted Answer

A) True 
 B)False

Question 16

The number of administration staff to employ would be considered a state of nature for a business firm.

Accepted Answer

A) True 
 B)False

Question 17

Define the expected monetary value (EMV) of a decision alternative.

Accepted Answer

The EMV of a decision alternat

Question 18

A high-school student who started doing photography as a hobby is considering going into the photography business. The anticipated payoff table is: $\begin{array} { ccc  }
&\text { Alternative }\
\text { State of Nature }& \text { Start new business}& \text { Do not start new business}\
\text { Poor } & -\$ 12000 & 0 \
\text { Fair } & \$ 10000 & 0 \
\text { Super } & \$ 15000 & 0 \
\end{array}$
 The following prior probabilities are assigned to the states of nature:
P(poor) = 0.4, P(fair) = 0.4 , P(super) = 0.2.
a. Calculate the expected monetary value for each act with present information. What decision should be made using the EMV criterion?
b. Convert the payoff table to an opportunity loss table.
c. Calculate the expected opportunity loss for each act with present information. What decision should be made using the EOL criterion?
d. Review the decisions made in a. and c. Is this a coincidence? Explain.
e. What is the expected payoff with perfect information?
f. What is the expected value of perfect information? What does it mean?

Accepted Answer

a. EMV (Start) = (0.4)(-12 000) + (0.4)(

Question 19

A payoff table is shown below: $\begin{array} { ccc  }
&\text { Alternative }\
\text { State of Nature }& a_{1} & a_{2} & a_{3}& a_{4}\
s_{1} & 7 & 0 & 4 & 6 \
s_{2} & 2 & 4 & 3 & 5
\end{array}$
 The following prior probabilities are assigned to the states of nature:
P( $S _ { 1 }$ ) = 0.3, P( $S _ { 2 }$ ) = 0.7.
a. Calculate the expected monetary value for each act with present information. What decision should be made using the EMV criterion?
b. Convert the payoff table to an opportunity loss table.
c. Calculate the expected opportunity loss for each act with present information. What decision should be made using the EOL criterion?
d. What is the expected payoff with perfect information?
e. What is the expected value of perfect information?

Accepted Answer

a. EMV ( @#LAT-DLM& ) = (0.3)(7) + (0.7)(2) = 3.5.

Question 20

A payoff table, the prior probabilities for three states of nature and the likelihood probabilities are shown below.
Payoff Table: $\begin{array} { ccc  }
&\text { Alternative }\
\text { State of Nature }& a_{1} & a_{2} & a_{3}\
s_{1} & 80 & 120 & 90 \
s_{2} & 60 & 130 & 170 \
s_{3} & 200 & 140 & 100
\end{array}$
 Prior Probabilities:
P( $S _ { 1 }$ ) = 0.4, P( $S _ { 2 }$ ) = 0.5, P( $S _ { 3 }$ ) = 0.1.
Likelihood Probabilities: $\begin{array}{ccc} 
& I_{1} & I_{2}& I_{3} \
s_{1} & 0.5 & 0.3 & 0.2 \
s_{2} & 0.2 & 0.6 & 0.2 \
s_{3} & 0.1 & 0.2 & 0.7
\end{array}$ a. Use the prior and likelihood probabilities to calculate the posterior probabilities for the experimental outcome $I _ { 1 }$ .
b. Use the posterior probabilities from a. to recalculate the expected monetary value of each act, then determine the optimal act and the EMV*.
c. Use the prior and likelihood probabilities to calculate the posterior probabilities for the experimental outcome $I _ { 2 }$ .
d. Use the posterior probabilities from c. to recalculate the expected monetary value of each act, then determine the optimal act and the EMV*.
e. Use the prior and likelihood probabilities to calculate the posterior probabilities for the experimental outcome $I _ { 3 }$ .
f. Use the posterior probabilities from e. to recalculate the expected monetary value of each act, then determine the optimal act and the EMV*.
g. Use your answers to parts a. to f. to calculate the expected monetary value with additional information.
h. Calculate the expected value of sample information.

Accepted Answer

a. \[\begin{array} { | c | c | c | c | c

In most business situations, the choice of the best alternative will be made under conditions of risk and ignorance.

The payoff table is a table in which the rows are states of nature, the columns are decision alternatives, and the entry at each intersection of a row and column is a numerical payoff such as a profit or loss.

Which of the following best describes a decision tree?

The expected monetary value (EMV) of a decision alternative is the sum of the products of the payoffs and the state-of-nature probabilities.

Incentive programs for sales staff would be considered a state of nature for a business firm.

In general, the expected monetary values (EMV) do not represent possible payoffs.

If EMV( $a _ { 1 }$ ) = $50 000, EMV( $a _ { 2 }$ ) = $65 000, and EMV( $a _ { 3 }$ ) = $45 000, then EMV* = $160 000.

The expected monetary value (EMV) decision is always the same as the expected opportunity loss (EOL) decision, simply because the opportunity loss table is produced directly from the payoff table.

Which of the following would be considered a state of nature for a business firm?

Which of the following statements is correct?

The expected value of sample information (EVSI) is the difference between the expected monetary value with additional information (EMV´)and the expected monetary value without additional information (EMV). That is, EVSI = EMV´ - EMV.

The number of administration staff to employ would be considered a state of nature for a business firm.

Define the expected monetary value (EMV) of a decision alternative.

What Is Statistics

Types of Data, Data Collection and Sampling

Graphical Descriptive Methods Nominal Data

Graphical Descriptive Techniques Numerical Data

Numerical Descriptive Measures

Probability

Random Variables and Discrete Probability Distributions

Continuous Probability Distributions

Statistical Inference: Introduction

Sampling Distributions

Estimation: Describing a Single Population

Estimation: Comparing Two Populations

Hypothesis Testing: Describing a Single Population

Hypothesis Testing: Comparing Two Populations

Inference About Population Variances

Analysis of Variance

Additional Tests for Nominal Data: Chi-Squared Tests

Simple Linear Regression and Correlation

Multiple Regression

Model Building

Nonparametric Techniques

Statistical Inference: Conclusion

Time-Series Analysis and Forecasting

Index Numbers

Filters

Exam 25: Decision Analysis

In most business situations, the choice of the best alternative will be made under conditions of risk and ignorance.

The payoff table is a table in which the rows are states of nature, the columns are decision alternatives, and the entry at each intersection of a row and column is a numerical payoff such as a profit or loss.

Which of the following best describes a decision tree?

The expected monetary value (EMV) of a decision alternative is the sum of the products of the payoffs and the state-of-nature probabilities.

Incentive programs for sales staff would be considered a state of nature for a business firm.

In general, the expected monetary values (EMV) do not represent possible payoffs.

If EMV( a1a _ { 1 }a1​ ) = $50 000, EMV( a2a _ { 2 }a2​ ) = $65 000, and EMV( a3a _ { 3 }a3​ ) = $45 000, then EMV* = $160 000.

The expected monetary value (EMV) decision is always the same as the expected opportunity loss (EOL) decision, simply because the opportunity loss table is produced directly from the payoff table.

Which of the following would be considered a state of nature for a business firm?

Which of the following statements is correct?

The expected value of sample information (EVSI) is the difference between the expected monetary value with additional information (EMV´)and the expected monetary value without additional information (EMV*). That is, EVSI = EMV´ - EMV*.

The number of administration staff to employ would be considered a state of nature for a business firm.

Define the expected monetary value (EMV) of a decision alternative.

What Is Statistics

Types of Data, Data Collection and Sampling

Graphical Descriptive Methods Nominal Data

Graphical Descriptive Techniques Numerical Data

Numerical Descriptive Measures

Probability

Random Variables and Discrete Probability Distributions

Continuous Probability Distributions

Statistical Inference: Introduction

Sampling Distributions

Estimation: Describing a Single Population

Estimation: Comparing Two Populations

Hypothesis Testing: Describing a Single Population

Hypothesis Testing: Comparing Two Populations

Inference About Population Variances

Analysis of Variance

Additional Tests for Nominal Data: Chi-Squared Tests

Simple Linear Regression and Correlation

Multiple Regression

Model Building

Nonparametric Techniques

Statistical Inference: Conclusion

Time-Series Analysis and Forecasting

Index Numbers

Filters

If EMV( $a _ { 1 }$ ) = $50 000, EMV( $a _ { 2 }$ ) = $65 000, and EMV( $a _ { 3 }$ ) = $45 000, then EMV* = $160 000.

The expected value of sample information (EVSI) is the difference between the expected monetary value with additional information (EMV´)and the expected monetary value without additional information (EMV). That is, EVSI = EMV´ - EMV.