Question 1

The preposterior analysis determines whether or not sample information should be purchased to revise the prior probabilities associated with the states of nature.

Accepted Answer

A) True 
 B)False

Question 2

Car Audio Store
For a car audio store,a payoff table,the prior probabilities for two states of nature,and the likelihood probabilities are shown below:
Payoff Table:
 $$\begin{array}{l}
\quad \quad \quad \quad \quad \quad \quad \quad \text { Alternative  }\
\begin{array} { | c | l l l | } 
\hline \text { state of Natura } & \boldsymbol { a } _ { 1 } & \boldsymbol { a } _ { 7 } & \boldsymbol { a } _ { \mathbf { 3 } } \
\hline \mathrm { s } _ { 1 } & 20 & 28 & 33 \
s _ { \mathrm { 2 } } & 32 & 29 & 25 \
\hline
\end{array}
\end{array}$$  
-{Car Audio Store Narrative} What is the expected value of perfect information?

Accepted Answer

EVPI = EPPI - EMV<su

Question 3

The expected value of perfect information (EVPI)equals the smallest ____________________.This is not a coincidence.

Accepted Answer

EOL^* expect

Question 4

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 EOL decision.

Accepted Answer

EOL (a₁)= (0.2)(0)+ (0.6)(0)+ (

Question 5

Graphic Design Business
A high school student,who started doing graphic designs as a hobby,is considering going into the graphic design business.The anticipated payoff table is:
 $$\begin{array}{l}
\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\text { Alternative }\
\begin{array} { | c | c c | } 
\hline \text { State of Nature } & \begin{array} { c } 
\text { Start } \
\text { new business }
\end{array} & \begin{array} { c } 
\text { Da Nat Start } \
\text { new business }
\end{array} \
\hline \text { Puar } & - \$ 12,000 & 0 \
\text { Fair } & \$ 10,000 & 0 \
\text { Super } & \$ 15,000 & 0 \
\hline
\end{array}
\end{array}$$ The following prior probabilities are assigned to the states of nature: P(poor)= 0.4,P(fair)= 0.4,and P(super)= 0.2.
-{Graphic Design Business Narrative} What is the expected value of perfect information? What does it mean?

Accepted Answer

EVPI = EPPI - EMV^* = $7,000 -

Question 6

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 value of perfect information?

Accepted Answer

EVPI = EPPI - EMV<su

Question 7

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 0.4,then the probability of s2 is______________.

Accepted Answer

Question 8

Container Company
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.
-{Container Company Narrative} Develop a payoff table for this decision situation.

Accepted Answer

The amounts in the p

Question 9

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 I3 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)= (0.32)(80)+ (0.40)(60

Question 10

Car Audio Store
For a car audio store,a payoff table,the prior probabilities for two states of nature,and the likelihood probabilities are shown below:
Payoff Table:
 $$\begin{array}{l}
\quad \quad \quad \quad \quad \quad \quad \quad \text { Alternative  }\
\begin{array} { | c | l l l | } 
\hline \text { state of Natura } & \boldsymbol { a } _ { 1 } & \boldsymbol { a } _ { 7 } & \boldsymbol { a } _ { \mathbf { 3 } } \
\hline \mathrm { s } _ { 1 } & 20 & 28 & 33 \
s _ { \mathrm { 2 } } & 32 & 29 & 25 \
\hline
\end{array}
\end{array}$$  
-{Car Audio Store 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)= (0.888)(20)+ (0.112)(

Question 11

Removal of uncertainty from a decision-making problem leads to a case referred to as perfect information.

Accepted Answer

A) True 
 B)False

Question 12

The expected payoff with perfect information (EPPI)represents the maximum amount a decision maker would be willing to pay for perfect information.

Accepted Answer

A) True 
 B)False

Question 13

All entries of any opportunity loss table are negative values since they represent losses.

Accepted Answer

A) True 
 B)False

Question 14

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 prior and likelihood probabilities to calculate the posterior probabilities for the experimental outcome I2.

Accepted Answer

Question 15

The difference between the expected monetary value with additional information (EMV')and the expected monetary value without additional information (EMV*)is called the expected value of ____________________ information and is denoted EVSI.

Accepted Answer

Question 16

The objective of a(n)____________________ analysis is to determine whether the value of the prediction is greater or less than the cost of the information.

Accepted Answer

The answer of The objective of a(n)____________________ analysis is to...

Question 17

Graphic Design Business
A high school student,who started doing graphic designs as a hobby,is considering going into the graphic design business.The anticipated payoff table is:
 $$\begin{array}{l}
\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\text { Alternative }\
\begin{array} { | c | c c | } 
\hline \text { State of Nature } & \begin{array} { c } 
\text { Start } \
\text { new business }
\end{array} & \begin{array} { c } 
\text { Da Nat Start } \
\text { new business }
\end{array} \
\hline \text { Puar } & - \$ 12,000 & 0 \
\text { Fair } & \$ 10,000 & 0 \
\text { Super } & \$ 15,000 & 0 \
\hline
\end{array}
\end{array}$$ The following prior probabilities are assigned to the states of nature: P(poor)= 0.4,P(fair)= 0.4,and P(super)= 0.2.
-{Graphic Design Business Narrative} What is the expected payoff with perfect information?

Accepted Answer

EPPI = (0.4)(0)+ (0.

Question 18

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 optimal alternative using EMV is ____________________.

Accepted Answer

Question 19

What is meant by the expected payoff with perfect information (EPPI)?

Accepted Answer

The EPPI is the maximum price that a dec

Question 20

Hobby Shop
A payoff table and the prior probabilities for two states of nature for a Hobby Shop are shown below:
Payoff Table:
 $$\begin{array}{l}
\quad \quad \quad \quad \quad \quad \quad \quad \text { Alternative }\
\begin{array} { | c | l l l | } 
\hline \text { state of Natura } & \boldsymbol { a } _ { 1 } & \boldsymbol { a } _ { 2 } & \boldsymbol { a } _ { \mathbf { 3 } } \
\hline \mathrm { s } _ { 1 } & 20 & 28 & 33 \
s _ { \mathrm { 2 } } & 32 & 29 & 25 \
\hline
\end{array}
\end{array}$$ Prior Probabilities:
P(sS1U1B11S1U1B0)= 0.4,and P(sS1U1B12S1U1B0)= 0.6.
-{Hobby Shop Narrative} Determine the EOL decision.

Accepted Answer

EOL (a₁)= (0.4)(13)+ (0.6)(0)=

The preposterior analysis determines whether or not sample information should be purchased to revise the prior probabilities associated with the states of nature.

The expected value of perfect information (EVPI)equals the smallest ____________________.This is not a coincidence.

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 EOL decision.

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 0.4,then the probability of s₂ is______________.

Removal of uncertainty from a decision-making problem leads to a case referred to as perfect information.

The expected payoff with perfect information (EPPI)represents the maximum amount a decision maker would be willing to pay for perfect information.

All entries of any opportunity loss table are negative values since they represent losses.

The difference between the expected monetary value with additional information (EMV')and the expected monetary value without additional information (EMV^*)is called the expected value of ____________________ information and is denoted EVSI.

The objective of a(n)____________________ analysis is to determine whether the value of the prediction is greater or less than the cost of the information.

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 optimal alternative using EMV is ____________________.

What is meant by the expected payoff with perfect information (EPPI)?

Hobby Shop A payoff table and the prior probabilities for two states of nature for a Hobby Shop are shown below: Payoff Table: Alternative state of Natura 20 28 33 32 29 25 Prior Probabilities: P(s₁)= 0.4,and P(s₂)= 0.6. -{Hobby Shop Narrative} Determine the EOL decision.

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

The preposterior analysis determines whether or not sample information should be purchased to revise the prior probabilities associated with the states of nature.

Car Audio Store For a car audio store,a payoff table,the prior probabilities for two states of nature,and the likelihood probabilities are shown below: Payoff Table: Alternative state of Natura 20 28 33 32 29 25 -{Car Audio Store Narrative} What is the expected value of perfect information?

The expected value of perfect information (EVPI)equals the smallest ____________________.This is not a coincidence.

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 EOL decision.

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 0.4,then the probability of s2 is______________.

Removal of uncertainty from a decision-making problem leads to a case referred to as perfect information.

The expected payoff with perfect information (EPPI)represents the maximum amount a decision maker would be willing to pay for perfect information.

All entries of any opportunity loss table are negative values since they represent losses.

The difference between the expected monetary value with additional information (EMV')and the expected monetary value without additional information (EMV*)is called the expected value of ____________________ information and is denoted EVSI.

The objective of a(n)____________________ analysis is to determine whether the value of the prediction is greater or less than the cost of the information.

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 optimal alternative using EMV is ____________________.

What is meant by the expected payoff with perfect information (EPPI)?

Hobby Shop A payoff table and the prior probabilities for two states of nature for a Hobby Shop are shown below: Payoff Table: Alternative state of Natura 20 28 33 32 29 25 Prior Probabilities: P(s1)= 0.4,and P(s2)= 0.6. -{Hobby Shop Narrative} Determine the EOL decision.

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

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 EOL decision.

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 0.4,then the probability of s₂ is______________.

The difference between the expected monetary value with additional information (EMV')and the expected monetary value without additional information (EMV^*)is called the expected value of ____________________ information and is denoted EVSI.

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 optimal alternative using EMV is ____________________.

Hobby Shop A payoff table and the prior probabilities for two states of nature for a Hobby Shop are shown below: Payoff Table: Alternative state of Natura 20 28 33 32 29 25 Prior Probabilities: P(s₁)= 0.4,and P(s₂)= 0.6. -{Hobby Shop Narrative} Determine the EOL decision.