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Statistics
In a marketing research test, twenty-eight adult males were asked to shave one side of their face with one brand of razor blade and the other side with a second brand. They were to use the blades for
The average energy expenditures for eight elderly women were estimated on the basis of information received from a battery-powered heart rate monitor that each subject wore. Two overall averages were
Use a large-sample Wilcoxon rank sum test to analyze the alpha wave data summarized in Table 9.3.1. Let α = 0.05.
Use the expansion ofto find the pdf of W when n = 5.What α levels are available for testing H0: ˜μ = ˜μ0 versus H1: ˜μ > ˜μ0?
Two manufacturing processes are available for annealing a certain kind of copper tubing, the primary difference being in the temperature required. The critical response variable is the resulting
To measure the effect on coordination associated with mild intoxication, thirteen subjects were each given 15.7mL of ethyl alcohol per square meter of body surface area and asked to write a certain
Test H0: ˜μ = 0.80 versus H1: ˜μ < 0.80 for the FEV1/VC ratio data of Question 5.3.2 using a Wilcoxon signed rank test. Let α = 0.10. Compare this test to the sign test of Question 14.2.7.
Do a Wilcoxon signed rank test on the hemoglobin data summarized in Case Study 13.3.1. Let α be 0.05. Compare your conclusion with the outcome of the sign test done in Question 14.2.11.
Use a signed rank test to analyze the depth perception data given in Question 8.2.6. Let α = 0.05.
Recall Question 9.2.6. Compare the ages at death for authors noted for alcohol abuse with the ages at death for authors not noted for alcohol abuse using a Wilcoxon rank sum test. Let α = 0.05.
Use a Kruskal-Wallis test to analyze the teacher expectation data described in Question 8.2.7. Let α = 0.05. What assumptions are being made?
Recall the fiddler crab data given in Question 9.5.3. Use the Kruskal-Wallis test to compare the times spent waving to females by the two groups of males. Let α = 0.10.
Use the Kruskal-Wallis method to test at the 0.05 level that methylmercury metabolism is different for males and females in Question 9.2.8.
Redo the analysis of the Quintus Curtius Snodgrass/ Mark Twain data in Case Study 9.2.1, this time using a nonparametric procedure.
Use the Kruskal-Wallis technique to test the hypothesis of Case Study 12.2.1 concerning the effect of smoking on heart rate.
A sample of ten 40-W light bulbs was taken from each of three manufacturing plants. The bulbs were burned until failure. The number of hours that each remained lit is listed in the following
The production of a certain organic chemical requires the addition of ammonium chloride. The manufacturer can conveniently obtain the ammonium chloride in any one of three forms€”powdered,
Show that the Kruskal-Wallis statistic, B, as defined in Theorem 14.4.1 can also be writtenWhere
The following data come from a field trial set up to assess the effects of different amounts of potash on the breaking strength of cotton fibers (25). The experiment was done in three blocks. The
Use Friedman€™s test to analyze the Transylvania effect data given in Case Study 13.2.3.
Until its recent indictment as a possible carcinogen, cyclamate was a widely used sweetener in soft drinks. The following data show a comparison of three laboratory methods for determining the
Use Friedman’s test to compare the effects of habitat density on cockroach aggression for the data given in Question 8.2.4. Let α = 0.05. Would the conclusion be any different if the densities
Compare the acrophobia therapies described in Case Study 13.2.1 using the Friedman test. Let α = 0.01. Does your conclusion agree with the inference reached using the analysis of variance?
Suppose that k treatments are to be applied within each of b blocks. Let .. denote the average of the bk ranks and let .j = (1/b)r.j. Show that the Friedman statistic given in Theorem 14.5.1 can also
The data in the table examine the relationship between stock market changes (1) during the first few days in January and (2) over the course of the entire year. Included are the years from 1950
Listed below for two consecutive fiscal years are the monthly numbers of passenger boardings at a Florida airport. Use Theorem 14.6.1 to test whether these twenty-four observations can be considered
Below is a partial statistical summary of the first twenty-four Super Bowls (33). Of particular interest to advertisers is the network share that each game garnered. Can those shares be considered a
In the next column are the lengths (in mm) of furniture dowels recorded as part of an ongoing quality control program. Listed are the measurements made on thirty samples (each of size 4) taken in
Listed below are forty ordered observations generated by Minitab€™s RANDOM command that presumably represent a normal distribution with μ = 5 and σ = 2. Can the sample be considered random
Sunnydale Farms markets an all-purpose fertilizer that is supposed to contain, by weight, 15% potash (K2O). Samples were taken daily in October from three bags chosen at random as they came off the
Socially responsible investing first became fashionable in the 1980s. Such investing involves consideration of the kinds of businesses that a firm engages in and selection of investments that are as
Many decisions are simple, preprogrammed, or already made. For example, retailers do not have to think long to decide how to deal with anew customer. Some operations research models provide
The argument was made that beliefs and preferences can change as we explore and learn. This holds true even for learning about decision analysis. For example, what was your impression of this book
Explain how modeling is used in decision analysis. What is meant by the term requisite decision model?
What role do subjective judgments play in decision analysis?
At a dinner party, an acquaintance asks whether you have read anything interesting lately, and you mention that you have begun to read a text on decision analysis. Your friend asks what decision
Your friend in Question 1.4, upon hearing your answer, is delighted! “This is marvelous,” she exclaims. “I have this very difficult choice to make at work. I’ll tell you the facts, and you
In the Rice University football example, what are some of the issues that you would consider in making this decision? What are the alternative courses of action? What issues involve uncertainty, and
Suppose you are in the market for a new car to be used mainly for commuting to work, shopping, running errands, and visiting friends.a. What are your objectives in this situation? What are some
Find the net present value of a project that has cash flows of − $12,000in Year 1, + $5,000 in Years 2 and 3, − $2,000 in Year 4, and + $6,000in Years 5 and 6. Use an interest rate of 12%. Find
A friend asks you for a loan of $1,000 and offers to pay you back at the rate of $90 per month for 12 months. a. Using an annual interest rate of 10%, find the net present value(to you) of loaning
Terry Martinez is considering taking out a loan to purchase a desk. The furniture store manager rarely finances purchases, but will for Terry “as a special favor.” The rate will be 10% per year,
Lynn Rasmussen is deciding what sports car to purchase. In reflecting about the situation, it becomes obvious that after a few years Lynn may elect to trade in the sports car for a new one, although
Vijay is feeling much better these days. A year ago he took a big risk and opened a cafeteria style restaurant next to a major university. He knew that college students were as interested in quantity
Explain in your own words why it is important in some situations to consider future decisions as well as the immediate decision at hand. Can you give an example from your own experience of an
Sometimes broadening the decision context can change the planning horizon. For example, many companies face specific technical problems. Framed in a narrow decision context, the question is how to
Explain in your own words why it is important to keep track of what information is known and what events are still uncertain for each decision.
What alternatives other than specific protection strategies might Larkin Oil consider (e.g., insurance)?
Imagine the difficulties of an employer whose decision context is choosing a new employee from a set of applicants whom he will interview. What do you think the employer’s objectives should be?
Identify the basic elements of a real-estate investor’s decision situation. What are the investor’s objectives? Is the situation dynamic, that is, are there sequential decisions? What are some of
Calculate the net present value of a business deal that costs $2,500 today and will return $1,500 at the end of this year and $1,700 at the end of the following year. Use an interest rate of 13%.
Describe in your own words the difference between a means objective and a fundamental objective. Why do we focus on coming up with attribute scales that measure accomplishment of fundamental
When patients suffered from hemorrhagic fever, M*A*S*H doctors replaced lost sodium by administering a saline solution intravenously. However, headquarters (HQ) sent a treatment change disallowing
Here is an example that provides a comparison between influence diagrams and decision trees.a. Suppose you are planning a party, and your objective is to have an enjoyable party for all the guests.
The clarity test is an important issue in Exercise 3.11. The weather obviously can be somewhere between full sunshine and rain. Should you include an outcome like cloudy? Would it affect your
Draw the machine-replacement decision (Figure 3.10) as a decision tree.
Modify the influence diagram in Figure 3.11 (the hurricane-forecast example) so that it contains nodes for each of the two objectives (maximize safety and minimize cost). Cost has a natural attribute
Decision analysis can be used on itself! What do you want to accomplish in studying decision analysis? Why is decision analysis important to you? In short, what are your fundamental objectives in
Facebook is a free social-network website that allows you to find groups of people with similar interests and then befriend them virtually. Facebook provides a “ public ” area where you can post
When an amateur astronomer considers purchasing or building a telescope to view deep sky objects (galaxies, clusters, nebulae, etc.), the three primary considerations are minimizing cost, having a
Consider the following situations that involve multiple objectives:a. Suppose you want to go out for dinner. What are your fundamental objectives? Create a fundamental-objectives hierarchy.b. Suppose
Thinking about fundamental objectives and means objectives is relatively easy when the decision context is narrow (buying a telescope, renting an apartment, choosing a restaurant for dinner). But
What are your fundamental objectives in the context of renting an apartment while attending college? What are your means objectives? Create a fundamental-objectives hierarchy and a means-objectives
Occasionally a decision is sensitive to the way it is structured. The following problem shows that leaving out an important part of the problem can affect the way we view the situation. a. Imagine
To be, or not to be, that is the question: Whether ’ this nobler in the mind to suffer The slings and arrows of outrageous fortune Or to take arms against a sea of troubles, And by opposing
On July 3, 1988, the USS Vincennes was engaged in combat in the Persian Gulf. On the radar screen a blip appeared that signified an incoming aircraft. After repeatedly asking the aircraft to identify
Reconsider the research-and-development decision in Figure 3.32. If you decide to continue the project, you will have to come up with the $2 million this year (Year 1). Then there will be a year of
When you purchase a car, you may consider buying a brand-new car or a used one. A fundamental trade-off in this case is whether you pay repair bills (uncertain at the time you buy the car) or make
PrecisionTree will convert any influence diagram into the corresponding decision tree with the click of a button. This provides an excellent opportunity to explore the meaning of arrows in an
Jameson is a 32-year-old father of three who thought he had finally found a career. While working as an assistant manager at a local shoe store, a customer, Vijay, befriended Jameson and invited him
Susan Cooper currently works as an assistant manager at Joe’s Coffee and Tea, a national chain of over 200 coffee shops. Susan has worked at Joe’s for 4 years. Feeling that her career was
In the context of renting an apartment (Exercise 3.2), some of the objectives may have natural attribute scales. Examples are minimizing rent ($) or minimizing the distance to campus (kilometers or
Before making an unsecured loan to an individual a bank orders a report on the applicant’s credit history. To justify making the loan, the bank must find the applicant’s credit record to be
When a movie producer decides whether to produce a major motion picture, the main question is how much revenue the movie will generate. Draw a decision tree of this situation, assuming that there is
You have met an acquaintance for lunch, and he is worried about an upcoming meeting with his boss and some executives from his firm’s headquarters. He has to outline the costs and benefits of some
Reframe your answer to Exercise 3.6 in terms of objectives and alter-natives. That is, what are appropriate fundamental objectives to consider in the context of choosing how to present the investment
Create an influence diagram for the politician’s decision in Figure 3.25 using PrecisionTree. Include the tables showing decision alternatives, chance-event outcomes, and consequences.
A dapper young decision maker has just purchased a new suit for $200. On the way out the door, the decision maker considers taking an umbrella. With the umbrella on hand, the suit will be protected
Is it possible to solve a decision-tree version of a problem and an equivalent influence-diagram version and come up with different answers? If so, explain. If not, why not?
Use PrecisionTree to create and solve the influence diagram that corresponds to the decision tree in Figure 4.44.
Explain why deterministic dominance is a special case of stochastic dominance.
Explain in your own words why it is important to consider the ranges of the consequences in determining a trade-off weight.
Use PrecisionTree to create and solve the influence diagram for the umbrella problem shown in Figure 4.10.
A real-estate investor has the opportunity to purchase a small apartment complex. The apartment complex costs $4 million and is expected to generate net revenue (net after all operating and finance
A stock market investor has $500 to spend and is considering purchasing an option contract on 1,000 shares of Apricot Computer. The shares themselves are currently selling for $28.50 per share.
Johnson Marketing is interested in producing and selling an innovative new food processor. The decision they face is the typical "make or buy" decision often faced by manufacturers. On one hand,
Stacy Ennis eats lunch at a local restaurant two or three times a week. In selecting a restaurant on a typical workday, Stacy uses three criteria. First is to minimize the amount of travel time,
The national coffee store Farbucks needs to decide in August how many holiday-edition insulated coffee mugs to order. Because the mugs are dated, those that are unsold by January 15 are considered a
Explain in your own words what it means when one alternative stochastically dominates another.
Although the expected value is a straightforward and appealing summary of an alternative, it does have its limitations. We interpret the EMV as the average amount that would be obtained by “playing
We mentioned that the probabilities associated with any risk profile must sum to one. To see why, let's consider the decision modeled in Figure 4.45.Because each uncertainty P, Q, R, and T are
What is the relationship between stochastic dominance and expected value? If alternative A dominates alternative B, then is it always true that EV (A) is better than EV (B)? Why?
Consider the decision a contractor faces when bidding on a construction job. The contractor must first decide on the bid amount, then after submitting the bid, waits to see if he won the contract.
The analysis of the Texaco-Pennzoil example shows that the EMV of counter offering with $5 billion far exceeds $2 billion. Why might Liedtke want to accept the $2 billion anyway? If you were Liedtke,
Solve the decision tree in Figure 4.41.
Use PrecisionTree to create and solve the influence diagram that corresponds to the decision tree in Figure 4.41.
Solve the decision tree in Figure 4.42. What principle discussed in Chapter 4 is illustrated by this decision tree?
Which alternative is preferred in Figure 4.43? Do you have to do any calculations? Explain.
Solve the decision tree in Figure 4.44.
Create risk profiles and cumulative risk profiles for all possible strategies in Figure 4.44. Is one strategy stochastically dominant? Explain.
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