Statistics Chapter 5

a graphic representation of a problem, the possible consequences and the attributes of each consequence.

Decision Diagram (or decision tree)

Squares that show show where a decision must be made among two or more alternatives

Decision Nodes

This process begins with defining the problem, then analyzing the alternatives and considering the possible results of each alternative.

Decomposition Process

T/F The construction of a decision tree with subsequent evaluation eliminates the uncertainty in a decision making process

FALSE. A decision tree is used to graphically represent the alternative decisions in a problem, recognizing the uncertainty in the possible consequences, but not eliminating it.

T/F Decomposition is the process of making a decision after having analyzed the parts of that decision

FALSE. Decomposition is the process of breaking a decision into parts and analyzing alternatives and their consequences. This is separate from decision making, which takes place after the process of decomposition is complete.

T/F The alternatives on the branches of a decision tree must be mutually exclusive and equally likely

FALSE. The alternatives on the branch of a decision tree must be mutually exclusive and collectively exhaustive. They do not necessarily have to be equally likely when a probability is assigned to them.

T/F The event node is the point at which the decision maker must take action.

FALSE. The event node is the point at which something happens. The decision node is the point at which the decision maker must take action

T/F There is exactly one decision tree for each decision problem

FALSE. The reason that the answer is false is that some nodes can be combined if desired, which would mean that more than one structure is possible.

T/F When the alternative with the lowest expected returns are eliminated, you should erase them from a decision diagram.

FALSE. You should prune the branches of a decision tree, not erase them, so others can see what you have done.

Samantha will open one of five doors. A prize will be behind two of those doors. If there is a prize behind the door Samantha opens, she will grab it. How many branches of this decision diagram have an event node after the decision node.

FIVE. 2 doors have prizes behind them which Samantha intends to grab, but since she has 5 doors to choose from and all of them have a chance of having a price behind them, her decision node will have 5 branches indicating her choices. At the end of each branch would be an event node, indicating a prize or not. All five have a decision since all five have a chance of holding a prize.

each alternative is different from the others

mutually exclusive

A decision node is represented by a(n) _________ and a chance node by a(n) _________.

square, circle

There is a 75% probability of chris earning $4,000 and a 25% probability that he will earn nothing. What is the EMV?

$3000. (.75 x 4000) + (.25 X 0) =3000

Mary has 2 parcels of oil producing property. If Mary can drill on only one property, her decision tree has how many branches?

3

A market research survey is available for $10,000. Using a decision tree analysis, it is found that the expected monetary value with the survey is $65,000. The expected monetary value with no survey is $62,000. What is the expected value of the information from this sample? Select one: a. $3,000 b. $10,000 c. $13,000 d. -$7,000 e. none of the above

3000

The alternatives depicted on the branches of a decision tree must be: a. mutually exclusive b. collectively exhaustive c. all of the above d. none of the above

C. All of the above

A point of uncertainty is represented by a circle.

TRUE.

T/F A decision node is shown as a square.

TRUE.

T/F Do nothing is an alternative

TRUE.

T/F A decision tree is construvted from left to right with the event and decision nodes in chronological order.

TRUE. Events and decision nodes from chronologically from left to right to represent the order in which the decision maker will encounter them.

T/F When using the Pearson-Tukey Method, you assess the .05, .5, and .95 fractiles only.

TRUE. The Pearson-Tukey Method requires assessing the .05, .5, and .95 fractiles and multiplying each of the values assigned to those fractiles by the probabilities of .185, .63, and .185 respecitively.

Expected Monetary Value (EMV) utilizes Select one: a. binomial distribution b. median values c. averages d. none of the above

c. averages

The Miramar Company is going to introduce one of three new products: a wrench, a hammer, or a nut remover. The market conditions (favorable, stable, or unfavorable) will determine the profit or loss the company realizes. A market research firm will do a survey to predict future market conditions. The results will indicate either positive or negative market conditions. There is a 0.60 probability of a positive report given favorable market conditions, a 0.30 probability of a positive report given stable market conditions, and a 0.10 probability of a positive report given unfavorable conditions. The survey will cost $2,000. The first node of this decision tree will be a Select one: a. chance node with Favorable, Stable, and Unfavorable as branches b. decision node with Wrench, Hammer, and Nut remover as branches c. decision node with buy survey and do not buy survey as branches d. chance node with favorable and unfavorable market conditions as branches

c. decision node with buy survey and do not buy survey as branches

all alternatives have been cosidered and presented on the tree

collectively exhaustive

the process of breaking a decision down into manageable parts in order to come to a conclusion.

decomposition

Branches connected by circles that represent points of uncertainty where one of two or more things will happen out of the control of the decision maker

event nodes

What does EMV stand for?

expected monetary value

The value of an event node is Select one: a. the sum of the values on the branches emanating from it. b. the value of the next node on the branch the decision maker decides to take. c. the value of the branch the decision maker decides to take. d. the expected value of the branches emanating from it.

the expected value of the branches emanating from it.