Question 1

Which of the following statements is correct?

Accepted Answer

A)  The EMV criterion selects the act with the largest 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 smallest expected opportunity loss. 
D)  All of these choices are true. 
A)  The EMV criterion selects the act with the largest 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 smallest expected opportunity loss. 
D)  All of these choices are true.

Question 2

Lingerie Store
The following table displays the payoffs (in thousands of dollars)for five different decision alternatives under three possible states of nature for a new Lingerie store:
  $\quad $ $\quad $ $\quad $ $\quad $ $\quad $ $\quad $ $\quad $ $\quad $ $\quad $ $\quad $ $\quad $Alternativa
 $\quad $ $\quad $ $\quad $ $\quad $ $\quad $ $\quad $ $\quad $ $\quad $ $\quad $ $\quad $ $\quad $(Decising)
$\begin{array}{c|ccccc}
\text { State of Nature } & a_{1} & a_{2} & a_{3} & a_{4} & a_{5} \
\hline s_{1} & \$ 100 & \$ 80 & \$ 35 & \$ 20 & \$ 0 \
s_{2} & \$ 70 & \$ 75 & \$ 55 & \$ 50 & \$ 15 \
s_{3} & -\$ 30 & \$ 0 & \$ 35 & \$ 55 & \$ 60
\end{array}$  The prior probabilities of the states of nature are: P(sS1U1B11S1U1B0)= 0.2,P(sS1U1B12S1U1B0)= 0.3,and P(sS1U1B13S1U1B0)= 0.5.
-{Lingerie Store Narrative} Calculate the expected payoff with perfect information.

Accepted Answer

EPPI = (0.2)(100)+ (

Question 3

Gross Profits
The following payoff table shows gross profits (in $1000)associated with a set of 3 acts under 2 possible states of nature.
 $$\begin{array} { | c | r c c | } 
\hline \text { States of Nature } & \boldsymbol { a } _ { 1 } & \boldsymbol { a } _ { \mathbf { 7 } } & \boldsymbol { a } _ { \mathbf { 3 } } \
\hline \boldsymbol { s } _ { 1 } & 12 & - 2 & \mathbf { g } \
\boldsymbol { s } _ { \mathbf { 7 } } & 4 & 10 & 5 \
\hline
\end{array}$$
-{Gross Profits Narrative} If the probability of s1 is 0.5,then the expected opportunity loss (EOL)for a1 is ____________________.

Accepted Answer

Question 4

Which of the following statements is false regarding the expected monetary value (EMV)?

Accepted Answer

A)  To calculate the EMV,the probabilities of the states of nature must be already decided upon. 
B)  We choose the decision with the largest EMV. 
C)  In general,the expected monetary values represent possible payoffs. 
D)  None of these choices. 
A)  To calculate the EMV,the probabilities of the states of nature must be already decided upon. 
B)  We choose the decision with the largest EMV. 
C)  In general,the expected monetary values represent possible payoffs. 
D)  None of these choices.

Question 5

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

Question 6

What is meant by a payoff table?

Accepted Answer

The payoff table is a table in which the

Question 7

If EOL(a1)= $13,000,EOL(a2)= $25,000,and EOL(a3)= $20,000,then EOL* = $13,000.

Accepted Answer

A) True 
 B)False

Question 8

Gross Profits
The following payoff table shows gross profits (in $1000)associated with a set of 3 acts under 2 possible states of nature.
 $$\begin{array} { | c | r c c | } 
\hline \text { States of Nature } & \boldsymbol { a } _ { 1 } & \boldsymbol { a } _ { \mathbf { 7 } } & \boldsymbol { a } _ { \mathbf { 3 } } \
\hline \boldsymbol { s } _ { 1 } & 12 & - 2 & \mathbf { g } \
\boldsymbol { s } _ { \mathbf { 7 } } & 4 & 10 & 5 \
\hline
\end{array}$$
-{Gross Profits Narrative} If the probability of s1 is 0.5,then the expected monetary value (EMV)for a2 is ____________________.

Accepted Answer

Question 9

A company must decide whether or not to change its packaging to a more environmentally safe material.The impact of the decision on profits depends on which of the following three possible scenarios develops in the future.
Scenario 1:
The media does not focus heavily on concerns about packaging and no new laws requiring changes in packaging are passed.Under this scenario,the company will make $35 million if they change their packaging now,but will make $75 million if they do not change their packaging now.
Scenario 2:
The media does focus heavily on concerns about packaging and no new laws requiring changes in packaging are passed.Under this scenario,the company will make $50 million if they change their packaging now,but will make $55 million if they do not change their packaging now.
Scenario 3:
The media does focus heavily on concerns about packaging and new laws requiring changes in packaging are passed.Under this scenario,the company will make $60 million if they change their packaging now,but will make only $15 million if they do not change their packaging now.
The prior probabilities of the three scenarios are 0.3,0.5,and 0.2,respectively.What is the most the company should be willing to pay for a research study designed to reduce its uncertainty about media and legal developments concerning packaging?

Accepted Answer

The value we need to determine is the ex

Question 10

Demolition Company
The payoff table and the prior probabilities for three states of nature for a demolition company are shown below:
 $$\begin{array}{l}
\text { Alsrmativa }\
\begin{array} { | c | c c c | } 
\hline \text { State of Nature } & \boldsymbol { a } _ { 1 } & \boldsymbol { a } _ { \mathbf { 2 } } & \boldsymbol { a } _ { \mathbf { 3 } } \
\hline \mathbf { s } _ { 1 } & \mathbf { 8 0 } & 120 & 90 \
\mathbf { s } _ { \mathbf { 2 } } & 60 & 130 & 170 \
\mathbf { s } _ { \mathbf { 3 } } & 200 & 140 & 100 \
\hline
\end{array}
\end{array}$$ Prior Probabilities:
P(sS1U1B11S1U1B0)= 0.4,P(sS1U1B12S1U1B0)= 0.5,and P(sS1U1B13S1U1B0)= 0.1.
-{Demolition Company Narrative} Determine the EMV decision.

Accepted Answer

EMV (a₁)= (0.4)(80)+ (0.5)(60)+

Question 11

Gross Profits
The following payoff table shows gross profits (in $1000)associated with a set of 3 acts under 2 possible states of nature.
 $$\begin{array} { | c | r c c | } 
\hline \text { States of Nature } & \boldsymbol { a } _ { 1 } & \boldsymbol { a } _ { \mathbf { 7 } } & \boldsymbol { a } _ { \mathbf { 3 } } \
\hline \boldsymbol { s } _ { 1 } & 12 & - 2 & \mathbf { g } \
\boldsymbol { s } _ { \mathbf { 7 } } & 4 & 10 & 5 \
\hline
\end{array}$$
-{Gross Profits Narrative} If the probability of s1 is 0.2 and s2 is 0.8,then the expected monetary value (EMV)of a1 is ____________________.

Accepted Answer

Question 12

Maintenance Company
For a maintenance company,a payoff table,the prior probabilities for three states of nature,and the likelihood probabilities are shown below:
Payoff Table:
 $$\begin{array}{l}
\quad\quad\quad\quad\quad\quad\quad\quad\quad\text { Alternative }\
\begin{array} { | c | c c c | } 
\hline \text { syate of Nature } & \boldsymbol { a } _ { 1 } & \boldsymbol { a } _ { 2 } & \boldsymbol { a } _ { \mathbf { 3 } } \
\hline \mathbf { s } _ { 1 } & 80 & 120 & 90 \
\mathbf { s  } _ { \mathbf { 2 } } & 60 & 130 & 170 \
\mathbf { s  } _3& 200 & 140 & 100 \
\hline
\end{array}
\end{array}$$ Prior Probabilities:
P(sS1U1B11S1U1B0)= 0.4,P(sS1U1B12S1U1B0)= 0.5,and P(sS1U1B13S1U1B0)= 0.1.
Likelihood Probabilities:
 $$\begin{array} { | l | c c c | } 
\hline & I _ { 1 } & \boldsymbol { I } _ { \mathbf { 2 } } & \boldsymbol { I } _ { \mathbf { 3 } } \
\hline \mathbf { s } _ { 1 } &0 .5 & 0 .3 & 0 .2 \
\mathbf { s } _ { \mathbf { 2 } } &0 .2 & 0.6 & 0 .2 \
\mathbf { s } _ { \mathbf { 3 } } & 0 .1 & 0 .2 &0 .7 \
\hline
\end{array}$$
-{Maintenance Company Narrative} Use the posterior probabilities for I1 in the previous question to recalculate the expected monetary value of each act,then determine the optimal act and the EMV*.

Accepted Answer

EMV (a₁)= (0.645)(80)+ (0.323)(60)+ (0.03

Question 13

Candy Store
A payoff table for a Candy store is shown below.
  $\quad $ $\quad $ $\quad $ $\quad $ $\quad $ $\quad $ $\quad $ $\quad $Alarnativa 
$ \begin{array}{rrr}\text {State of Nature}&a_{1} & a_{2} & a_{3} \ 
s_{1} &25 & 8 & -3 \
s_{2}  &12 & 8 & 6 \ 
s_{3} &-13 & 8 & 13\end{array} $ The following prior probabilities are assigned to the states of nature: P(sS1U1B11S1U1B0)= 0.2,P(sS1U1B12S1U1B0)= 0.6,and P(sS1U1B13S1U1B0)= 0.2.
-{Candy Store Narrative} What is the expected payoff with perfect information?

Accepted Answer

EPPI = (0.

Question 14

Sporting Goods Store
A payoff table for a clothing store is shown below.
 $$\begin{array}{l}
\quad \quad \quad \quad \quad \quad \quad \quad \text { Altrnative }\
\begin{array} { | c | c c c | } 
\hline \text { state of Nature } & \boldsymbol { a } _ { 1 } & \boldsymbol { a } _ { \mathbf { 2 } } & \boldsymbol { a } _ { \mathbf { 3 } } \
\hline \mathbf { s } _ { 1 } & 25 & \mathbf { 8 } & - 3 \
\mathbf { s  } _ { \mathbf { 2 } } & 12 & \mathbf { 8 } & 6 \
\mathbf { s  } _ { 3 } & - 13 & \mathbf { 8 } & 13 \
\hline
\end{array}
\end{array}$$ The following prior probabilities are assigned to the states of nature: P(sS1U1B11S1U1B0)= 0.2,P(sS1U1B12S1U1B0)= 0.6,and P(sS1U1B13S1U1B0)= 0.2.
-{Sporting Goods Store Narrative} Determine the EMV decision.

Accepted Answer

EMV (a₁)= (0.2)(25)+ (0.6)(12

Question 15

To calculate expected profit under certainty,we need to have perfect information about which event will occur.

Accepted Answer

A) True 
 B)False

Question 16

____________________ statistics specifies that parameters are variables that can assume various probability distributions.

Accepted Answer

The answer of ____________________ statistics specifies that parameters are variables...

Question 17

Maintenance Company
For a maintenance company,a payoff table,the prior probabilities for three states of nature,and the likelihood probabilities are shown below:
Payoff Table:
 $$\begin{array}{l}
\quad\quad\quad\quad\quad\quad\quad\quad\quad\text { Alternative }\
\begin{array} { | c | c c c | } 
\hline \text { syate of Nature } & \boldsymbol { a } _ { 1 } & \boldsymbol { a } _ { 2 } & \boldsymbol { a } _ { \mathbf { 3 } } \
\hline \mathbf { s } _ { 1 } & 80 & 120 & 90 \
\mathbf { s  } _ { \mathbf { 2 } } & 60 & 130 & 170 \
\mathbf { s  } _3& 200 & 140 & 100 \
\hline
\end{array}
\end{array}$$ Prior Probabilities:
P(sS1U1B11S1U1B0)= 0.4,P(sS1U1B12S1U1B0)= 0.5,and P(sS1U1B13S1U1B0)= 0.1.
Likelihood Probabilities:
 $$\begin{array} { | l | c c c | } 
\hline & I _ { 1 } & \boldsymbol { I } _ { \mathbf { 2 } } & \boldsymbol { I } _ { \mathbf { 3 } } \
\hline \mathbf { s } _ { 1 } &0 .5 & 0 .3 & 0 .2 \
\mathbf { s } _ { \mathbf { 2 } } &0 .2 & 0.6 & 0 .2 \
\mathbf { s } _ { \mathbf { 3 } } & 0 .1 & 0 .2 &0 .7 \
\hline
\end{array}$$
-{Maintenance Company Narrative} Calculate the expected value of sample information.

Accepted Answer

EVSI = EMV' -(EMV<su

Question 18

The EVPI represents the ____________________ amount that a decision maker should be willing to pay for perfect information.

Accepted Answer

maximum
hi

Question 19

Maintenance Company
For a maintenance company,a payoff table,the prior probabilities for three states of nature,and the likelihood probabilities are shown below:
Payoff Table:
 $$\begin{array}{l}
\quad\quad\quad\quad\quad\quad\quad\quad\quad\text { Alternative }\
\begin{array} { | c | c c c | } 
\hline \text { syate of Nature } & \boldsymbol { a } _ { 1 } & \boldsymbol { a } _ { 2 } & \boldsymbol { a } _ { \mathbf { 3 } } \
\hline \mathbf { s } _ { 1 } & 80 & 120 & 90 \
\mathbf { s  } _ { \mathbf { 2 } } & 60 & 130 & 170 \
\mathbf { s  } _3& 200 & 140 & 100 \
\hline
\end{array}
\end{array}$$ Prior Probabilities:
P(sS1U1B11S1U1B0)= 0.4,P(sS1U1B12S1U1B0)= 0.5,and P(sS1U1B13S1U1B0)= 0.1.
Likelihood Probabilities:
 $$\begin{array} { | l | c c c | } 
\hline & I _ { 1 } & \boldsymbol { I } _ { \mathbf { 2 } } & \boldsymbol { I } _ { \mathbf { 3 } } \
\hline \mathbf { s } _ { 1 } &0 .5 & 0 .3 & 0 .2 \
\mathbf { s } _ { \mathbf { 2 } } &0 .2 & 0.6 & 0 .2 \
\mathbf { s } _ { \mathbf { 3 } } & 0 .1 & 0 .2 &0 .7 \
\hline
\end{array}$$
-{Maintenance Company Narrative} Use the posterior probabilities for I2 in the previous question to recalculate the expected monetary value of each act,then determine the optimal act and the EMV*.

Accepted Answer

EMV (a₁)= (0.273)(80)+ (0.682)(60)+ (0.04

Question 20

Maintenance Company
For a maintenance company,a payoff table,the prior probabilities for three states of nature,and the likelihood probabilities are shown below:
Payoff Table:
 $$\begin{array}{l}
\quad\quad\quad\quad\quad\quad\quad\quad\quad\text { Alternative }\
\begin{array} { | c | c c c | } 
\hline \text { syate of Nature } & \boldsymbol { a } _ { 1 } & \boldsymbol { a } _ { 2 } & \boldsymbol { a } _ { \mathbf { 3 } } \
\hline \mathbf { s } _ { 1 } & 80 & 120 & 90 \
\mathbf { s  } _ { \mathbf { 2 } } & 60 & 130 & 170 \
\mathbf { s  } _3& 200 & 140 & 100 \
\hline
\end{array}
\end{array}$$ Prior Probabilities:
P(sS1U1B11S1U1B0)= 0.4,P(sS1U1B12S1U1B0)= 0.5,and P(sS1U1B13S1U1B0)= 0.1.
Likelihood Probabilities:
 $$\begin{array} { | l | c c c | } 
\hline & I _ { 1 } & \boldsymbol { I } _ { \mathbf { 2 } } & \boldsymbol { I } _ { \mathbf { 3 } } \
\hline \mathbf { s } _ { 1 } &0 .5 & 0 .3 & 0 .2 \
\mathbf { s } _ { \mathbf { 2 } } &0 .2 & 0.6 & 0 .2 \
\mathbf { s } _ { \mathbf { 3 } } & 0 .1 & 0 .2 &0 .7 \
\hline
\end{array}$$
-{Maintenance Company Narrative} What is the expected value of perfect information?

Accepted Answer

EVPI = EPPI = EMV<su

Which of the following statements is correct?

Which of the following statements is false regarding the expected monetary value (EMV)?

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.

What is meant by a payoff table?

If EOL(a₁)= $13,000,EOL(a₂)= $25,000,and EOL(a₃)= $20,000,then EOL^* = $13,000.

Gross Profits The following payoff table shows gross profits (in $1000)associated with a set of 3 acts under 2 possible states of nature. States of Nature 12 -2 4 10 5 -{Gross Profits Narrative} If the probability of s₁ is 0.5,then the expected monetary value (EMV)for a₂ is ____________________.

Sporting Goods Store A payoff table for a clothing store is shown below. Altrnative state of Nature 25 -3 12 6 -13 13 The following prior probabilities are assigned to the states of nature: P(s₁)= 0.2,P(s₂)= 0.6,and P(s₃)= 0.2. -{Sporting Goods Store Narrative} Determine the EMV decision.

To calculate expected profit under certainty,we need to have perfect information about which event will occur.

____________________ statistics specifies that parameters are variables that can assume various probability distributions.

The EVPI represents the ____________________ amount that a decision maker should be willing to pay for perfect information.

What Is Statistics

Graphical Descriptive Techniques I

Graphical Descriptive Techniques II

A: Numerical Descriptive Techniques

B: Numerical Descriptive Techniques

C: Numerical Descriptive Techniques

Data Collection and Sampling

Probability

A: Random Variables and Discrete Probability Distributions

B: Random Variables and Discrete Probability Distributions

Continuous Probability Distributions

Sampling Distributions

Introduction to Estimation

Introduction to Hypothesis Testing

Inference About a Population

Inference About Comparing Two Populations

Analysis of Variance

Chi-Squared Tests

A: Simple Linear Regression and Correlation

B: Simple Linear Regression and Correlation

Multiple Regression

Model Building

Nonparametric Statistics

Time-Series Analysis and Forecasting

Statistical Process Control

Conclusion

Filters

Exam 22: Decision Analysis

Which of the following statements is correct?

Gross Profits The following payoff table shows gross profits (in $1000)associated with a set of 3 acts under 2 possible states of nature. States of Nature 12 -2 4 10 5 -{Gross Profits Narrative} If the probability of s1 is 0.5,then the expected opportunity loss (EOL)for a1 is ____________________.

Which of the following statements is false regarding the expected monetary value (EMV)?

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.

What is meant by a payoff table?

If EOL(a1)= $13,000,EOL(a2)= $25,000,and EOL(a3)= $20,000,then EOL* = $13,000.

Gross Profits The following payoff table shows gross profits (in $1000)associated with a set of 3 acts under 2 possible states of nature. States of Nature 12 -2 4 10 5 -{Gross Profits Narrative} If the probability of s1 is 0.5,then the expected monetary value (EMV)for a2 is ____________________.

Sporting Goods Store A payoff table for a clothing store is shown below. Altrnative state of Nature 25 -3 12 6 -13 13 The following prior probabilities are assigned to the states of nature: P(s1)= 0.2,P(s2)= 0.6,and P(s3)= 0.2. -{Sporting Goods Store Narrative} Determine the EMV decision.

To calculate expected profit under certainty,we need to have perfect information about which event will occur.

____________________ statistics specifies that parameters are variables that can assume various probability distributions.

The EVPI represents the ____________________ amount that a decision maker should be willing to pay for perfect information.

What Is Statistics

Graphical Descriptive Techniques I

Graphical Descriptive Techniques II

A: Numerical Descriptive Techniques

B: Numerical Descriptive Techniques

C: Numerical Descriptive Techniques

Data Collection and Sampling

Probability

A: Random Variables and Discrete Probability Distributions

B: Random Variables and Discrete Probability Distributions

Continuous Probability Distributions

Sampling Distributions

Introduction to Estimation

Introduction to Hypothesis Testing

Inference About a Population

Inference About Comparing Two Populations

Analysis of Variance

Chi-Squared Tests

A: Simple Linear Regression and Correlation

B: Simple Linear Regression and Correlation

Multiple Regression

Model Building

Nonparametric Statistics

Time-Series Analysis and Forecasting

Statistical Process Control

Conclusion

Filters

If EOL(a₁)= $13,000,EOL(a₂)= $25,000,and EOL(a₃)= $20,000,then EOL^* = $13,000.

Sporting Goods Store A payoff table for a clothing store is shown below. Altrnative state of Nature 25 -3 12 6 -13 13 The following prior probabilities are assigned to the states of nature: P(s₁)= 0.2,P(s₂)= 0.6,and P(s₃)= 0.2. -{Sporting Goods Store Narrative} Determine the EMV decision.