5. Determine the course of action that has the highest expected payoff for this decision tree.
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Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
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- You wish to assess whether Los Angeles has an equitable distribution of police services among its precincts compared to nearby cities. You theorize that if police resources are distributed equitably, average response times for emergency calls should be fairly similar from one precinct to another within the city. On the other hand, if response times are much higher in some precincts than others, police resources are probably not distributed as equitably as possible. You decide to compare the City of LA to the other cities in the rest of LA County. You are hypothesizing about differences in the mean between the City of LA and other cities. State in plain English the null and research hypotheses for this study.Let's say that a local TV station plans to drop three Friday evening programs at the endof the season. Bill Shapiro, the station's manager, developed a list of three potentialreplacement programs. Estimates of the advertising revenue (in dollars) that canbe expected for each of the new programs in the three vacated time slots are as in the table above. Steve has asked you to find the assignment of programs to time slots that will maximize total advertising revenue. PLEASE USE PENCIL AND PAPER (NEATLY) SHOWING STEPS OR USE EXCEL, SHOWING STEPS AND FORMULAS, IF POSSIBLECBS poll of March 2005 referred to in Exercise 65, 49% agreed that Social Security taxes should be raised if necessary to keep the system afloat, and 43% agreed that it would be a good idea to invest part of their Social Security taxes on their own. What is the largest percentage of people who could have agreed with at least one of these statements? What is the smallest percentage of people who could have agreed with at least one of these statements?
- he National Football League (NFL) holds its annual draft of the nation's best college football players in April each year. Prior to the draft, various sporting news services project the players who will be drafted along with the order in which each will be selected in what are called mock drafts. Players who are considered to have superior potential as professional football players are selected earlier in the draft. Suppose the following table shows projections by one mock draft service of what position in the first round players from the Atlantic Coast Conference, the Big Ten Conference, the PAC-12 Conference, and the Southeastern Conference will be selected. ACC Big Ten PAC-12 SEC CollegeAttended ProjectedDraftPosition CollegeAttended ProjectedDraftPosition CollegeAttended ProjectedDraftPosition CollegeAttended ProjectedDraftPosition Florida State 4 Iowa 9 USC 1 Florida 2 Clemson 5 Michigan St 10 Oregon 6 Alabama 3 Miami 7 Nebraska 14 Oregon 15 Kentucky 8 Georgia Tech 13…The National Football League (NFL) holds its annual draft of the nation's best college football players in April each year. Prior to the draft, various sporting news services project the players who will be drafted along with the order in which each will be selected in what are called mock drafts. Players who are considered to have superior potential as professional football players are selected earlier in the draft. Suppose the following table shows projections by one mock draft service of what position in the first round players from the Atlantic Coast Conference, the Big Ten Conference, the PAC-12 Conference, and the Southeastern Conference will be selected. ACC Big Ten PAC-12 SEC CollegeAttended ProjectedDraftPosition CollegeAttended ProjectedDraftPosition CollegeAttended ProjectedDraftPosition CollegeAttended ProjectedDraftPosition Florida State 4 Iowa 7 USC 2 Florida 1 Clemson 5 Michigan St 10 Oregon 9 Alabama 3 Miami 6 Nebraska 12 Oregon 15 Kentucky 8 Georgia Tech…2. A decision tree is provided. Develop Product Sell Idea Lease for Royalty Show Transcribed Text Produce & Market Sell Idea Company A Company B A. Calculate Expected value (EV) at every node. Show work. B. What is the optimum decision and EV? C. If your risk tolerance is $0, what is the best decision and EV? (.5) Large Market (.5) Low Mkt. (.5) Large Market (.5) Low Mkt. (.5) Large Market (.5) Low Mkt. (.5) Large Market (.5) Low Mkt. Payoff (S millions) 5.0 -3.0 3.0 0 1.8 1.0 6.0 -1.0 1.0
- Westminster Financial has released a summary of investor and investment package information from the past fiscal year. During this time, Westminster provided a choice among 12 pre-designed investment packages. The investment packages were classified according to two variables: riskiness of investment package chosen ("Risky", "Moderate/mixed", and "Conservative") and age of investor ("Under 35", "35-49", or "50+"). Suppose that we're interested in the possible relationship between the age of the investor and the riskiness of the investment package the investor chose. The following contingency table gives a summary of the information released by Westminster regarding age and riskiness of investment package for 150 investors. In the cells of the table are the respective observed frequencies, and three of the cells also have blanks. Fill in these blanks with the frequencies expected if the two variables, riskiness of investment package chosen and age of investor, are independent. Round…Mrs Moore is a agriculturalist and would like to drill for water on her farm. She needs water for irrigation and estimates the benefits of having a successful borehole as $2.0m. However, there is only a 10% chance that she will strike water if she drills and the cost of drilling is $100 000. The alternative is not to drill at all, in which case the benefit will be zero. Draw a decision tree to represent the problem. Should Mrs Moore go ahead and drill? There is another agriculturalist in a nearby state who claims to have supernatural powers to indicate underground water sources. However, he charges a fee and also travel cost. What is the most Mrs Moore should pay for the services? Before Mrs Moore drills, she could also consult a geologist who can assess the promise of the piece of land. He can tell her whether the prospects are “good” or “poor.” But he is not a perfect predictor. If there is water, the conditional probability is 0,95 that he will say that prospects are good. If…Question The craft vendors in Grand Anse, St. George's, Grenada are to be relocated into one large mega-craft market that can hold the majority of vendors. The idea is that the several locations are too dispersed and cause friction when cruise ship visitors and all-inclusive guests are to be entertained. There is a great deal of controversy about the optimal location. The Minister of Tourism commissioned a study and four competing locations were examined. The data in the payoff table shows the possible value of revenue ($000) to the different locations per week under three scenarios. Future Growth Conditions Mall Site Stable Moderate High 1 2,500 2,500 2,510 2 2,430 2,510 2,710 3 1,140 2,100 3,200 4 1,460 2,180 3,050 Which site would be selected if the decision makers used the: (a) LaPlace criterion? (b) Maximin criterion? (c) Maximax criterion?
- Suppose a realtor wants to determine the current percentage of customers who have a family of five or more. How many customers should the realtor survey in order to be 98% confident that the estimated (sample) proportion is within 2 percentage points of the true population proportion of customers who have a family of five or more? z0.10 z0.05 z0.025 z0.01 z0.005 1.282 1.645 1.960 2.326 2.576 Use the table of values above.17. A manager of an inventory system believes that inventory models are important decision-making aids. The manager has experience with the EOQ policy, but has never considered a backorder model because of the assumption that backorders were "bad" and should be avoided. However, with upper management's continued pressure for cost reduction, you have been asked to analyze the economics of a backorder policy for some products that can possibly be backordered. For a specific product with D = 800 units per year, C. = $150, C₁ = $3, and C₁ = $20, what is the difference in total annual cost between the EOQ model and the planned shortage or backorder model? If the manager adds constraints that no more than 25% of the units can be backordered and that no customer will have to wait more than 15 days for an order, should the backorder inventory policy be adopted? Assume 250 working days per year.You are a hotel manager and you are considering four projects that yield different payoffs, depending upon whether there is an economic boom or a recession. The potential payoffs and corresponding payoffs are summarized in the accompanying table. \table[[Project, Boom (50% ), Recession (50%)], [A, $20, -$10 You are a hotel manager and you are considering four projects that yield different payoffs, depending upon whether there is an economic boom or a recession. The potential payoffs and corresponding payoffs are summarized in the accompanying table. Project A Boom (50%) $ 20 -$10 Recession (50%) -$ 10 $ 20 B C $30 -$30 D $ 50 -$ 50 If a manager adopted both projects A and B simultaneously, the expected value of this joint project would be Multiple Choice 10.