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Statistics Ch4 & 5 Problems

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Subject: Statistics
Due on: 04/25/2014
Posted On: 04/25/2014 04:36 AM

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1. A risk avoider is a person for whom the utility of an outcome
A) decreases as the monetary value increases.
B) stays the same as monetary value increases.
C) increases at an increasing rate as the monetary value increases.
D) increases at a decreasing rate as monetary value increases.
E) none of these.
2. The following is a payoff table giving profits for various situations.
States of Nature
Alternatives A B C
Alternative 1 100 120 180
Alternative 2 120 140 120
Alternative 3 200 100 50
Do Nothing 0 0 0
The probabilities for states of nature A, B, and C are 0.3, 0.5, and 0.2, respectively.
what are the expected values for each alternative?
What decision should be made under expected value?
What is the EVPI?
3. Which of the following statements is NOT true?
A) A feasible solution satisfies all constraints.
B) An optimal solution satisfies all constraints.
C) An infeasible solution violates all constraints.
D) A feasible solution point does not have to lie on the boundary of the feasible region.

4. Payoffs are
A) called chance events.
B) under the control of the decision maker.
C) states of nature.
D) All of the alternatives are true
E) associated with each decision alternative and each chance event outcome.
5. Decision variables
A) tell how much or how many of something to produce, invest, purchase, hire, etc.
B) represent the values of the constraints.
C) measure the objective function.
D) must exist for each constraint.
6. When consequences are measured on a scale that reflects a decision maker's attitude toward profit, loss, and risk, payoffs are replaced by
A) utility.
B) multicriteria measures.
C) sample information.
D) opportunity loss.
9. Values of utility
A) must be between 0 and 1.
B) must be between 0 and 10.
C) must be nonnegative.
D) must increase as the payoff improves.
10. When a careful decision analysis has been conducted
A) A change in estimated payoffs will not affect the final decision.
B) A change in estimated payoffs may affect the final decision.
C) Assessed risks will not change.
D) Estimated payoffs will not change.
11. To find the optimal solution to a linear programming problem using the graphical method
A) find the feasible point that is the farthest away from the origin.
B) find the feasible point that is at the highest location.
C) find the feasible point that is closest to the origin.
D) None of the alternatives is correct.
12. The maximization or minimization of a quantity is the
A) goal of management science.
B) decision for decision analysis.
C) constraint of operations research.
D) objective of linear programming.
13. A decision maker has chosen .4 as the probability for which he cannot choose between a certain loss of 10,000 and the lottery p(-25000) + (1-p)(5000). If the utility of -25,000 is 0 and of 5000 is 1, then the utility of -10,000 is
A) .5
B) .6
C) .4
D) 4
14. Optimistic decision makers tend to
A) magnify favorable outcomes
B) ignore bad outcomes
C) discount favorable outcomes
D) magnify favorable outcomes and ignore bad outcomes
E) ignore bad outcomes and discount favorable outcomes
15. Solve the following system of simultaneous equations.
17. Which of the following is not a property of linear programs?
A) one objective function
B) at least two separate feasible regions
C) alternative courses of action
D) one or more constraints
E) objective function and constraints are linear
18. A decision alternative with the highest Expected Value
A) Is always preferred
B) Reflects factors such as risk, image or other nonmonetary criteria
C) Is preferred when the Expected Value is within a range the decision maker considers reasonable
D) Will never have the highest Expected Utility
19. The following is a payoff table giving profits for various situations.
States of Nature
Alternatives A B C
Alternative 1 100 120 180
Alternative 2 120 140 120
The probabilities for states of nature A, B, and C are 0.3, 0.5, and 0.2, respectively.
Calculate the expected values for both alternatives. What alternative would be chosen according to expected value?

20. The purchase of insurance and lottery tickets shows that people make decisions based on
A) expected value.
B) sample information.
C) utility.
D) maximum likelihood.
22. For a game with an optimal pure strategy, which of the following statements is false?
A) The maximin equals the minimax.
B) The value of the game cannot be improved by either player changing strategies.
C) A saddle point exists.
D) Dominated strategies cannot exist.
23. A decision tree
A) presents all decision alternatives first and follows them with all states of nature.
B) presents all states of nature first and follows them with all decision alternatives.
C) alternates the decision alternatives and states of nature.
D) arranges decision alternatives and states of nature in their natural chronological order.
24. Maxwell Manufacturing makes two models of felt tip marking pens. Requirements for each lot of pens are given below.
Fliptop Model Tiptop Model Available
Plastic 3 4 36
Ink Assembly 5 4 40
Molding Time 5 2 30
The profit for either model is $1000 per lot.
What is the linear programming model for this problem?
What are the boundary points of the feasible region?
What is the profitability at each boundary point of the feasible region?
Find the optimal solution.
Will there be excess capacity in any resource? If so, how much excess capacity?
5. A decision maker has chosen .6 as the probability for which she cannot choose between a certain loss of 10,000 and the lottery of p(5000) + (1 - p)(-25,000). If the utility of -25,000 is 0 and 5000 is 1, then the utility of -10,000 is
A) .5
B) .6
C) .4
D) 4
26. Infeasibility means that the number of solutions to the linear programming models that satisfies all constraints is
A) at least 1.
B) 0.
C) an infinite number.
D) at least 2.
27. The expected utility approach
A) does not require probabilities.
B) leads to the same decision as the expected value approach.
C) is most useful when excessively large or small payoffs are possible.
D) requires a decision tree.
28. The options from which a decision maker chooses a course of action are
A) called the decision alternatives.
B) under the control of the decision maker.
C) not the same as the states of nature.
D) All of the alternatives are true.
29. Which of the following is a valid objective function for a linear programming problem?
A) Max 5xy
B) Min 4x + 3y + (2/3)z
C) Max 5x2 + 6y2
D) Min (x1 + x2)/x3
30. Slack
A) is the difference between the left and right sides of a constraint.
B) is the amount by which the left side of a ? constraint is smaller than the right side.
C) is the amount by which the left side of a ? constraint is larger than the right side.
D) exists for each variable in a linear programming problem.

Tags problems statistics decision expected feasible states value linear following alternatives payoffs point utility programming solution objective favorable values 0 alternative model maker outcomes nature monetary optimal constraint satisfies natured boundary estimated highest

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Statistics Ch4 & 5 Problems Solution

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Tutorial Preview …(s2) xxxxxxx $250,000 xxxxxxxxx Do Not xxxxxxx -$50,000 -$20,000 xxxxxxx management xxx xxxxxxxxxx the xxxxxxxxx utility values: xxxxxx $250,000 -$20,000 xxxxxxxx -$300,000 xxxxxxx xxx 60 xx 0 What xx the Expected xxxxxxx of xxxx xx Super xxxxxxxx decision alternatives? xxxxxxxxxx = 0 xxxxxxx 4*0 x xx E(Do xxx produce) = xxxxxx 4*55 = xx 9 xxxxxx xx utility xx must be xxxxxxx 0 and x B) xxxx xx between x and 10 xx must be xxxxxxxxxxx D) xxxx xxxxxxxx as xxx payoff improves xx When a xxxxxxx decision xxxxxxxx xxx been xxxxxxxxx A) A xxxxxx in estimated xxxxxxx will xxx xxxxxx the xxxxx decision B) x change in xxxxxxxxx payoffs xxx xxxxxx the xxxxx decision C) xxxxxxxx risks will xxx change xx xxxxxxxxx payoffs xxxx not change xx To find xxx optimal xxxxxxxx xx a xxxxxx programming problem xxxxx the graphical xxxxxx A) xxxx xxx feasible xxxxx that is xxx farthest away xxxx the xxxxxx xx find xxx feasible point xxxx is at xxx highest xxxxxxxx xx find xxx feasible point xxxx is closest xx the xxxxxx xx None xx the alternatives xx correct 12 xxx maximization xx xxxxxxxxxxxx of x quantity is xxx A) goal xx management xxxxxxx xx decision xxx decision analysis xx constraint of xxxxxxxxxx research xx xxxxxxxxx of xxxxxx programming 13 x decision maker xxx chosen x xx the xxxxxxxxxxx for which xx cannot choose xxxxxxx a xxxxxxx xxxx of xxxxxx and the xxxxxxx p(-25000) + xxxxxxxxxxx If xxx xxxxxxx of xxxxxxx is 0 xxx of 5000 xx 1, xxxx xxx utility xx -10,000 is xx 5 B) x C) x xx 4 xx Optimistic decision xxxxxx tend to xx magnify xxxxxxxxx xxxxxxxx B) xxxxxx bad outcomes xx discount favorable xxxxxxxx D) xxxxxxx xxxxxxxxx outcomes xxx ignore bad xxxxxxxx E) ignore…
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Stats_-_Chapter_4_5_Solution.docx (22.8 KB)
Preview: point xxxxxx D) xxxxxxxxx strategies cannot xxxxx 23 A xxxxxxxx treeA) xxxxxxxx xxx decision xxxxxxxxxxxx first and xxxxxxx them with xxx states xx xxxxxx B) xxxxxxxx all states xx nature first xxx follows xxxx xxxx all xxxxxxxx alternatives C) xxxxxxxxxx the decision xxxxxxxxxxxx and xxxxxx xx nature xx arranges decision xxxxxxxxxxxx and states xx nature xx xxxxx natural xxxxxxxxxxxxx order 24 xxxxxxx Manufacturing makes xxx models xx xxxx tip xxxxxxx pens Requirements xxx each lot xx pens xxx xxxxx below xxxxxxx ModelTiptop Model xxxxxxxxxxxxxxxx 3 4 xx Ink xxxxxxxx x 4 xx Molding Time x 2 30The xxxxxx for xxxxxx xxxxx is xxxxx per lot xxxx is the xxxxxx programming xxxxx xxx this xxxxxxxxxxxxxxxxx Z = xxxxxxxxxxxxxxxxxx to,3x+ 4y x 365x+ xxx xxxxx 2y? xxxxx ? 0What xxx the boundary xxxxxx of xxx xxxxxxxx region?The xxxxxxxx points are xxxxxx (2,7 5),(4,5) xxx (6,0)What xx xxx profitability xx each boundary xxxxx of the xxxxxxxx region?Profit xxx xxxxx (0,9) x $9000Profit for xxxxx (2,7 5) x $9500Profit xxx xxxxx (4,5) x $9000Profit for xxxxx (6,0) = xxxxxxxxx the xxxxxxx xxxxxxxx Profit xxx point (2,7 xx is maximum xxxx optimal xxxxxxxx xx 2 xx Fliptop Model xxx 7 5 xxxxxx Model xxxx xxxxx be xxxxxx capacity in xxx resource? If xxx how xxxx xxxxxx capacity?There xxxx be an xxxxxx molding time xx 5 xxxx xx A xxxxxxxx maker has xxxxxx 6 as xxx probability xxx xxxxx she xxxxxx choose between x certain loss xx 10,000 xxx xxx lottery xx p(5000) + xx - p)(-25,000) xx the xxxxxxx xx -25,000 xx 0 and xxxx is 1, xxxx the xxxxxxx xx.....
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