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 accept state?

A) 24 B) 52 C) 18 D) 39 E) 48 A) 24 B) 52 C) 18 D) 39 E) 48 E

Exam 15: Decision Theory

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. States of Nature Decision Accept 20 30 90 Further analyze 60 70 15 Reject 80 50 30 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 accept state?

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Question 1

Correct Answer:

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E

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. -What is the probability that an insured driver of any age will be involved in an accident?

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Question 2

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$P ( \text { Accident } ) = .205$
$\begin{array} { l l l l l } \text { State of Nature } & \mathrm { P } \left( \mathrm { S } _ { \mathrm { j } } \right) & P \left( \text { Accident } \mid S _ { j } \right) & P \left( \text { Acc. } \cap S _ { j } \right) & P \left( S _ { j } \mid \text { Acc. } \right) \\\left. \mathrm { S } _ { 1 } \text { (under } 25 \right) & 0.35 & 0.40 & 0.14 & 0.683 \\\mathrm {~S} _ { 2 } ( 25 \text { or older } ) & \underline { 0.65 } & 0.10 & \underline { 0.065 } & \underline { 0.317 }\\&1.0&&0.205&1.0\end{array}$

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 (S_i,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. $\text { States of nature }$ Alternatives Strategy 1 110 80 70 Strategy 2 60 120 50 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. -Construct the revised probability table for poor weather conditions and find the probability of high demand given that the weather conditions are poor.

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Question 3

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.1364 $\begin{array} { l } \text { P } ( \text { Poor } \mid \text { High } ) = 1 - \frac { 12 } { 15 } = .2 \\P ( \text { Poor } \mid \text { Medium } ) = 1 - \frac { 14 } { 28 } = .5 \\P ( \text { Poor } \mid \text { Low } ) = 1 - \frac { 1 } { 5 } = .8\end{array}$
$\begin{array} { l l l l l } \text { State of Nature } & \mathrm { P } \left( \mathrm { S } _ { \mathrm { j } } \right) & P \left( F \mid S _ { j } \right) & P \left( F \cap S _ { j } \right) & P \left( S _ { j } \mid F \right) \\\mathrm { S } _ { 1 } & .3 & .2 & .06 & .1364 \\\mathrm {~S} _ { 2 } & .6 & .5 & .3 & .6818 \\\mathrm {~S} _ { 3 } & \underline { 1 } & .8 & \underline { .08 } & \underline { .1818 } \\& \underline { 1.0 } & & \underline { .4 4} & \underline { 1.0 }\end{array}$

The maximax criterion finds the worst possible payoff for each alternative and then chooses the alternative that yields the maximum payoff.

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Question 4

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

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Question 5

When making a decision in an environment of ________________,the decision maker knows which of the states of nature will actually occur.

(Short Answer)

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Question 6

When we assess the worth of sample information in a decision-making problem,we are performing a(n)_____________ analysis.

(Short Answer)

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Question 7

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 (S_i,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. $\text { States of nature }$ Alternatives Strategy 1 110 80 70 Strategy 2 60 120 50 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. -What is the probability that weather conditions are poor,given that the demand is high? What is the probability that weather conditions are poor,given that the demand is medium? What is the probability that weather conditions are poor,given that the demand is low?

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Question 8

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. States of Nature Decision Accept 20 30 90 Further analyze 60 70 15 Reject 80 50 30 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,determine the revised (posterior)probabilities for each of the three states of nature.

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Question 9

A tire manufacturer needs to make a decision about the amount of production for the coming month (high vs.low).The level of production largely depends on the level of demand.For this situation,the levels of demand (high,medium,low)represent alternatives.

(True/False)

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Question 10

Maximin is a criterion used when making decisions under _____________.

(Multiple Choice)

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Question 11

In a decision tree,the branches emanating from a circular node represent the possible ___________________.

(Short Answer)

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Question 12

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. $\text { States of nature }$ Alternatives Strategy 1 110 80 70 Strategy 2 60 120 50 -Determine the best alternative (course of action)for the EKA manufacturing company using the maximax criterion.

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Question 13

The expected net gain of sampling equals the expected ______________ minus the cost of sampling.

(Multiple Choice)

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Question 14

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. States of Nature Decision Accept 20 30 90 Further analyze 60 70 15 Reject 80 50 30 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. -A company wants to add a new product to its existing line of products.There are two similar candidate products A and B.The demand for the new product could be high,medium,or low with probabilities of .25,.5,and .25 respectively.The demand and the corresponding profit for each product is: High Medium Low Product A 40,000 30,000 20,000 Product B 70,000 20,000 0 Which product should the company select based on the expected monetary value criterion? Product A has a higher expected monetary value A Expected monetary value = .25(40000)+ .5(30000)+ .25(20000)= 30,000 B Expected monetary value = .25(70000)+ .5(20000)+ .25(0)= 27,500

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Question 15

The _____________ criterion finds the best possible payoff for each alternative and then chooses the alternative that yields the maximum payoff.

(Short Answer)

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Question 16

The maximin criterion is preferred by optimistic decision-makers.

(True/False)

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Question 17

_____ represent a set of potential future conditions that affect the results of the decision.

(Short Answer)

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Question 18

The _____________________ criterion is attractive to those decision-makers who exhibit a neutral approach towards decision choices involving risk.

(Multiple Choice)

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Question 19

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. States of nature Alternative (strategy) 1 10 80 70 Alternative (strategy) 2 60 120 50 -Find the expected monetary value for each of the alternatives and determine the best alternative (course of action)for the EKA manufacturing company using the expected monetary value criterion.

(Multiple Choice)

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Question 20

The maximax criterion finds the worst possible payoff for each alternative and then chooses the alternative that yields the maximum payoff.

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

When making a decision in an environment of ________________,the decision maker knows which of the states of nature will actually occur.

When we assess the worth of sample information in a decision-making problem,we are performing a(n)_____________ analysis.

A tire manufacturer needs to make a decision about the amount of production for the coming month (high vs.low).The level of production largely depends on the level of demand.For this situation,the levels of demand (high,medium,low)represent alternatives.

Maximin is a criterion used when making decisions under _____________.

In a decision tree,the branches emanating from a circular node represent the possible ___________________.

The expected net gain of sampling equals the expected ______________ minus the cost of sampling.

The _____________ criterion finds the best possible payoff for each alternative and then chooses the alternative that yields the maximum payoff.

The maximin criterion is preferred by optimistic decision-makers.

_____ represent a set of potential future conditions that affect the results of the decision.

The _____________________ criterion is attractive to those decision-makers who exhibit a neutral approach towards decision choices involving risk.

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

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