Question 1

The utility curve given below represents the preferences of a _________________ decision maker.

Accepted Answer

A) risk averse 
B) risk neutral 
C) risk seeking 
A) risk averse 
B) risk neutral 
C) risk seeking

Question 2

The alternatives 1 and 2 in the following payoff table represent the two possible manufacturing strategies that the EKA manufacturing company can adopt.The level of demand affects the success of both strategies.The states of nature (Si,i = 1,2,3)represent the levels of demand for the company products.S1,S2 and S3 characterize high,medium,and low demand respectively.The payoff values are in thousands of dollars. $$\begin{array} { l c c c } 
& { \text { States of nature } } \
& \mathrm { s } _ { 1 } & \mathrm {~s} _ { 2 } & \mathrm {~s} _ { 3 } \
\text { Alternative (strategy) 1 } & 10 & 80 & 70 \
\text { Alternative (strategy) 2 } & 60 & 120 & 50
\end{array}$$ 
The best alternative (course of action)for the EKA manufacturing company using the maximax criterion is alternative 1.

Accepted Answer

A) True 
 B)False

Question 3

The quality control manager for the NKA Inc.must decide whether to accept (alternative 1),further analyze (alternative 2),or reject (alternative 3)the shipment (lot)of incoming material.The historical data indicates that there is 30% chance that the lot is poor quality (SS1U1B11S1U1B0),50% chance that the lot is fair quality (SS1U1B12S1U1B0),and 20% chance that the lot is good quality (SS1U1B13S1U1B0).Assume the following payoff table is available.The values in the payoff table are in thousands of dollars. $$\begin{array} { l c c c } 
& { \text { States of Nature } } \
\text { Decision } & \mathrm { S } _ { 1 } & \mathrm {~S} _ { 2 } & \mathrm {~S} _ { 3 } \
\text { Accept } & 20 & 30 & 90 \
\text { Further analyze } & 60 & 70 & 15 \
\text { Reject } & 80 & 50 & 30
\end{array}$$
-What is the maximum amount that the quality control manager would be willing to pay for perfect information?

Accepted Answer

EVPI = 21
Expected payoff under certaint

Question 4

The alternatives 1 and 2 in the following payoff table represent the two possible manufacturing strategies that the EKA manufacturing company can adopt.The level of demand affects the success of both strategies.The states of nature (SS1U1B1iS1U1B0,i = 1,2 3)represent the levels of demand for the company products.SS1U1B11S1U1B0,SS1U1B12S1U1B0,and SS1U1B13S1U1B0 characterize high,medium,and low demand respectively.The payoff values are in thousands of dollars. $\text { States of nature }$
$\begin{array} { | l | r | r | r |  } 
\hline \text { Alternatives } & \mathbf { s } _ { \mathbf { 1 } }  & \mathbf { s } _ { \mathbf { 2 } } &  { \mathbf { s } _ { \mathbf { 3 } } } \
\hline \text { Strategy 1 }  & 110 & 80 & 70 \
\hline \text { Strategy 2 } & 60 & 120 & 50 \
\hline
\end{array}$ The management believes that the weather conditions significantly affect the level of demand.48 monthly sales reports are randomly selected.These monthly sales reports showed 15 months with high demand,28 months with medium demand,and 5 months with low demand.12 of the 15 months with high demand had favourable weather conditions.14 of the 28 months with medium demand had favourable weather conditions.Only 1 of the 5 months with low demand had favourable weather conditions.Based on this information,the prior probabilities have been revised.If the weather conditions are favourable,P(SS1U1B11S1U1B0)= .4286,P(SS1U1B12S1U1B0)= .5357,and P(SS1U1B13S1U1B0)= .0357,and if the weather conditions are poor,P(SS1U1B11S1U1B0)= .1364,P(SS1U1B12S1U1B0)= .6818,and P(SS1U1B13S1U1B0)= .1818.It is also determined that the probability of favourable weather is 0.56 and the probability of poor weather is 0.44.
-Carry out a preposterior analysis and using the revised probabilities,determine the expected monetary value when the weather conditions are favourable and determine the expected monetary value when the weather conditions are poor.

Accepted Answer

EPS = 95.5
If the weather conditions are

Question 5

The alternatives 1 and 2 in the following payoff table represent the two possible manufacturing strategies that the EKA manufacturing company can adopt.The level of demand affects the success of both strategies.The states of nature (SS1U1B1iS1U1B0,i = 1,2,3)represent the levels of demand for the company products.SS1U1B11S1U1B0,SS1U1B12S1U1B0 and SS1U1B13S1U1B0 characterize high,medium,and low demand,respectively.The payoff values are in thousands of dollars. $\text { States of nature }$
$\begin{array} { | l | r | r | r |  } 
\hline \text { Alternatives } & \mathbf { s } _ { \mathbf { 1 } }  & \mathbf { s } _ { \mathbf { 2 } } & \mathbf { s } _ { \mathbf { 3 } } \
\hline \text { Strategy 1 } & 110 & 80 & 70 \
\hline \text { Strategy 2 } & 60 & 120 & 50 \
\hline
\end{array}$ The management believes that the weather conditions significantly affect the level of demand.48 monthly sales reports are randomly selected.These monthly sales reports showed 15 months with high demand,28 months with medium demand,and 5 months with low demand.12 of the 15 months with high demand had favourable weather conditions.14 of the 28 months with medium demand had favourable weather conditions.Only 1 of the 5 months with low demand had favourable weather conditions.
-If the weather conditions are favourable,determine which manufacturing strategy the company should implement?

Accepted Answer

Strategy 1 @#IMG-DLM& (EMV)₁ = (.4286)(1

Question 6

The quality control manager for the NKA Inc.must decide whether to accept (alternative 1),further analyze (alternative 2),or reject (alternative 3)the shipment (lot)of incoming material.The historical data indicates that there is 30% chance that the lot is poor quality (SS1U1B11S1U1B0),50% chance that the lot is fair quality (SS1U1B12S1U1B0),and 20% chance that the lot is good quality (SS1U1B13S1U1B0).Assume the following payoff table is available.The values in the payoff table are in thousands of dollars. $$\begin{array} { l c c c } 
& { \text { States of Nature } } \
\text { Decision } & \mathrm { S } _ { 1 } & \mathrm {~S} _ { 2 } & \mathrm {~S} _ { 3 } \
\text { Accept } & 20 & 30 & 90 \
\text { Further analyze } & 60 & 70 & 15 \
\text { Reject } & 80 & 50 & 30
\end{array}$$ Based on historical data,if the lot is of poor quality,40% of the items are defective.If the lot is fair quality,22% of the items are defective.If the lot is good quality,10 % of the items are defective.The quality control manager inspects one unit from a recent shipment.
-After inspecting one unit,the manager determines that the unit is defective.If the inspected item is defective,determine which alternative action the quality control manager should choose.

Accepted Answer

Choose alternative 2 and further analyze

Question 7

When we assess the worth of sample information in a decision making problem,we are performing a:

Accepted Answer

A) Prior analysis 
B) Preposterior analysis 
C) Posterior analysis 
D) Payoff analysis 
E) Utility analysis 
A) Prior analysis 
B) Preposterior analysis 
C) Posterior analysis 
D) Payoff analysis 
E) Utility analysis

Question 8

The alternatives 1 and 2 in the following payoff table represent the two possible manufacturing strategies that the EKA manufacturing company can adopt. The level of demand affects the success of both strategies. The states of nature (Si, i = 1, 2, 3) represent the levels of demand for the company products. S1, S2 and S3 characterize high, medium and low demand with probabilities of .3, .6 and .1 respectively. The payoff values are in thousands of dollars.
$$\begin{array} { l c c c } 
& { \text { States of nature } } \
& \mathrm { s } _ { 1 } & \mathrm {~s} _ { 2 } & \mathrm {~s} _ { 3 } \
\text { Alternative (strategy) } 1 & 10 & 80 & 70 \
\text { Alternative (strategy) } 2 & 60 & 120 & 50
\end{array}$$
-What is the maximum amount that the company would be willing to pay for perfect information?

Accepted Answer

A) $95,000 
B) $112,000 
C) $17,000 
D) $24,000 
E) $2,000 
A) $95,000 
B) $112,000 
C) $17,000 
D) $24,000 
E) $2,000

Question 9

The alternatives 1 and 2 in the following payoff table represent the two possible manufacturing strategies that the EKA manufacturing company can adopt.The level of demand affects the success of both strategies.The states of nature (SS1U1B1iS1U1B0,i = 1,2,3)represent the levels of demand for the company products.SS1U1B11S1U1B0,SS1U1B12S1U1B0 and SS1U1B13S1U1B0 characterize high,medium,and low demand,respectively.The payoff values are in thousands of dollars. $\text { States of nature }$
$\begin{array} { | l | r | r | r |  } 
\hline \text { Alternatives } & \mathbf { s } _ { \mathbf { 1 } }  & \mathbf { s } _ { \mathbf { 2 } } & \mathbf { s } _ { \mathbf { 3 } } \
\hline \text { Strategy 1 } & 110 & 80 & 70 \
\hline \text { Strategy 2 } & 60 & 120 & 50 \
\hline
\end{array}$ The management believes that the weather conditions significantly affect the level of demand.48 monthly sales reports are randomly selected.These monthly sales reports showed 15 months with high demand,28 months with medium demand,and 5 months with low demand.12 of the 15 months with high demand had favourable weather conditions.14 of the 28 months with medium demand had favourable weather conditions.Only 1 of the 5 months with low demand had favourable weather conditions.
-If the weather conditions are poor,determine which manufacturing strategy the company should implement.

Accepted Answer

Strategy 2 @#IMG-DLM& @#IMG-DLM& (EMV)₁ = (.1364

Question 10

An investor is looking at three possible investments: growth stock,blue chip stock,or municipal bonds.The investment performance will vary depending on the investment market condition of Bull (market rising),flat,or Bear (market falling).The investment return for each investment for the corresponding market conditions is given below: $$\begin{array} { | l | l | l | l | } 
\hline & \text { Bull } & \text { Flat } & \text { Bear } \
\hline \text { Growth Stock } & 20 & 1 & - 6 \
\hline \text { Blue Chip } & 9 & 8 & 0 \
\hline \text { Bonds } & 4 & 4 & 4 \
\hline
\end{array}$$
-Which investment would the investor select if the maximax criterion is used?

Accepted Answer

Growth stock
Best investment p

Question 11

The expected monetary value criterion is best used when a large number of similar decisions will be made.

Accepted Answer

A) True 
 B)False

Question 12

A pharmaceutical company manufacturing a virus detection kit wants to determine the probability of a person without the virus receiving a positive text result.It is estimated that the probability of infected potential users of the kit is 10%.According to the company laboratory test results,1 out of 100 viral-free people tested positive (false positive).On the other hand,1 out of 200 infected people tested negative (false negative).A person has just used the detection kit manufactured by the company and the results showed they had the virus.What is the probability that the person is infected?

Accepted Answer

A) 1% 
B) 0.9% 
C) 0.05% 
D) 8.3% 
E) 0.056% 
A) 1% 
B) 0.9% 
C) 0.05% 
D) 8.3% 
E) 0.056%

Question 13

The _______________________ is the difference between the expected payoff that would have been realized had the best alternative action been selected if we know which state of nature has occurred and the expected payoff under risk.

Accepted Answer

A) maximax criterion 
B) maximin criterion 
C) expected utility 
D) expected value of perfect information 
E) expected value of sample information 
A) maximax criterion 
B) maximin criterion 
C) expected utility 
D) expected value of perfect information 
E) expected value of sample information

Question 14

The ____________________ criterion for choosing among alternative actions assumes that the state of nature with the worst payoff will be experienced.

Accepted Answer

The answer of The ____________________ criterion for choosing among alternative...

Question 15

A pharmaceutical company manufacturing a virus detection kit wants to determine the probability of a person without the virus receiving a positive text result.It is estimated that the probability of infected potential users of the kit is 10%.According to the company laboratory test results,1 out of 100 viral-free people tested positive (false positive).On the other hand,1 out of 200 infected people tested negative (false negative).A person has just used the detection kit manufactured by the company and the results showed they had the virus.What is the probability that the person is viral-free?

Accepted Answer

A) 90% 
B) 0.9% 
C) 8.3% 
D) 91.7% 
E) 10.85% 
A) 90% 
B) 0.9% 
C) 8.3% 
D) 91.7% 
E) 10.85%

Question 16

An investor has the following utilities corresponding to various possible returns on an investment:
$\begin{array}{|c|l|}
\hline \text { Profit } &{\text { Utility }} \
\hline \$ 100,000 & 1 \
\hline \$ 75,000 & 0.9 \
\hline \$ 40,000 & 0.6 \
\hline \$  0 & 0.25 \
\hline-\$  5,000 & 0.10 \
\hline-\$  10,000 & 0 \
\hline
\end{array}$
-The investor is considering two potential investments with the following potential returns and the probability of these returns. $\begin{array}{|l|l|r|l|}
\hline \text { Investment } 1&&\text { Investment } 2\
\hline \text { Profit } & \text { Probability } &{\text { Profit }} & \text { Probability } \
\hline \$ 75,000 & 0.1 & \$ 100,000 & 0.2 \
\hline \$ 40,000 & 0.4 & \$ 75,000 & 0.3 \
\hline \$ \quad 0 & 0.5 & -\$ \quad 5000 & 0.5 \
\hline
\end{array}$
Which investment should the investor choose and why?

Accepted Answer

A) Investment 2 because it has the highest expected monetary value of $40,000. 
B) Investment 1 because it has the lowest expected monetary value of $23,500. 
C) Investment 2 because it has the highest expected utility of 0.52. 
D) Investment 1 because it has the lowest expected utility of 0.455. 
E) Cannot be determined without more information. 
A) Investment 2 because it has the highest expected monetary value of $40,000. 
B) Investment 1 because it has the lowest expected monetary value of $23,500. 
C) Investment 2 because it has the highest expected utility of 0.52. 
D) Investment 1 because it has the lowest expected utility of 0.455. 
E) Cannot be determined without more information.

Question 17

The quality control manager for the NKA Inc.must decide whether to accept (alternative 1),further analyze (alternative 2),or reject (alternative 3)the shipment (lot)of incoming material.The historical data indicates that there is 30% chance that the lot is poor quality (S1),50% chance that the lot is fair quality (S2),and 20% chance that the lot is good quality (S3).Assume the following payoff table is available.The values in the payoff table are in thousands of dollars. $$\begin{array} { l c c c } 
& { \text { States of Nature } } \
\text { Decision } & \mathrm { S } _ { 1 } & \mathrm {~S} _ { 2 } & \mathrm {~S} _ { 3 } \
\text { Accept } & 20 & 30 & 90 \
\text { Further analyze } & 60 & 70 & 15 \
\text { Reject } & 80 & 50 & 30
\end{array}$$
Based on historical data,if the lot is of poor quality,40% of the items are defective.If the lot is fair quality,22% of the items are defective.If the lot is good quality,10 % of the items are defective.The quality control manager inspects one unit from a recent shipment.After inspecting one unit,the manager determines that the unit is defective.Based on this additional information,what is the revised (posterior)probability for the further analyze state?

Accepted Answer

A) 44 
B) 52 
C) 18 
D) 39 
E) 48 
A) 44 
B) 52 
C) 18 
D) 39 
E) 48

Question 18

The quality control manager for the NKA Inc.must decide whether to accept (alternative 1),further analyze (alternative 2),or reject (alternative 3)the shipment (lot)of incoming material.The historical data indicates that there is 30% chance that the lot is poor quality (SS1U1B11S1U1B0),50% chance that the lot is fair quality (SS1U1B12S1U1B0),and 20% chance that the lot is good quality (SS1U1B13S1U1B0).Assume the following payoff table is available.The values in the payoff table are in thousands of dollars. $$\begin{array} { l c c c } 
& { \text { States of Nature } } \
\text { Decision } & \mathrm { S } _ { 1 } & \mathrm {~S} _ { 2 } & \mathrm {~S} _ { 3 } \
\text { Accept } & 20 & 30 & 90 \
\text { Further analyze } & 60 & 70 & 15 \
\text { Reject } & 80 & 50 & 30
\end{array}$$
-What alternative action should be selected according to maximax criterion?

Accepted Answer

Choose alternative 1

Question 19

An automobile insurance company is in the process of reviewing its policies.Currently drivers under the age of 25 have to pay a premium.The company is considering increasing the value of the premium charged to drivers under 25.According to company records,35% of the insured drivers are under the age of 25.The company records also show that 280 of the 700 insured drivers under the age of 25 had been involved in at least one automobile accident.On the other hand,only 130 of the 1300 insured drivers 25 years or older had been involved in at least one automobile accident.
-An accident has just been reported.What is the probability that the insured driver is under the age of 25?

Accepted Answer

The answer of An automobile insurance company is in the...

Question 20

A person's utility is determined by the preferences they exhibit for decision choices involving __________.

Accepted Answer

A) certainty 
B) uncertainty 
C) risk 
D) Bayes' Theorem 
E) optimism 
A) certainty 
B) uncertainty 
C) risk 
D) Bayes' Theorem 
E) optimism

The utility curve given below represents the preferences of a _________________ decision maker.

When we assess the worth of sample information in a decision making problem,we are performing a:

The expected monetary value criterion is best used when a large number of similar decisions will be made.

The _______________________ is the difference between the expected payoff that would have been realized had the best alternative action been selected if we know which state of nature has occurred and the expected payoff under risk.

The ____________________ criterion for choosing among alternative actions assumes that the state of nature with the worst payoff will be experienced.

A person's utility is determined by the preferences they exhibit for decision choices involving __________.

An Introduction to Business Statistics

Descriptive Statistics

Probability

Discrete Random Variables

Continuous Random Variables

Sampling Distributions

Confidence Intervals

Hypothesis Testing

Statistical Inferences Based on Two Samples

Experimental Design and Analysis of Variance

Correlation Coefficient and Simple Linear Regression Analysis

Multiple Regression and Model Building

Nonparametric Methods

Chi-Square Tests

Time Series Forecasting

Filters

Exam 15: Decision Theory

The utility curve given below represents the preferences of a _________________ decision maker.

When we assess the worth of sample information in a decision making problem,we are performing a:

The expected monetary value criterion is best used when a large number of similar decisions will be made.

The _______________________ is the difference between the expected payoff that would have been realized had the best alternative action been selected if we know which state of nature has occurred and the expected payoff under risk.

The ____________________ criterion for choosing among alternative actions assumes that the state of nature with the worst payoff will be experienced.

A person's utility is determined by the preferences they exhibit for decision choices involving __________.

An Introduction to Business Statistics

Descriptive Statistics

Probability

Discrete Random Variables

Continuous Random Variables

Sampling Distributions

Confidence Intervals

Hypothesis Testing

Statistical Inferences Based on Two Samples

Experimental Design and Analysis of Variance

Correlation Coefficient and Simple Linear Regression Analysis

Multiple Regression and Model Building

Nonparametric Methods

Chi-Square Tests

Time Series Forecasting

Filters