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business
business statistics in practice
Business Statistics Plus Pearson Mylab Statistics With Pearson Etext 3rd Edition Norean R Sharpe ,Richard D De Veaux ,Paul Velleman - Solutions
=+company for both the Miles and Enroll factor effect. What effect does the cardholder segment have on your recommendations?
=+5. Write a report giving recommendations on whether the double-miles program is successful. Be sure to include confidence intervals for the effects and the profit to the
=+4. Keep in mind that the credit card company gains about $0.02 profit on every dollar of increased spending. Assume that adding double miles costs $0.005 for each mile awarded, but Internet enrollment is essentially free.
=+3. If the three-way interaction is important, consider running separate models for the three levels of Cardholder Segment. Use interaction plots for each segment to understand whether the two-way interaction between Miles and Enroll changes for the three segments.
=+2. Are any of the interactions of the variables significant?
=+1. Examine displays to see if the conditions of your model are satisfied.
=+What can we learn about the PVA data from this decision tree?
=+Looking just at the variable AGE, what corrections or adjustments would be appropriate so that it can be a more effective predictor in a regression-based model?
=+add about $15,000 in contracts. If he purchases the mowers, he could expand his business by $10,000 in a good year or by just $5000 in a bad one. And if he spends nothing, he won’t expand his business. In a bad year, his income would contract by about $1000.Construct a payoff table and tree
=+b) What is the best choice using the expected-value approach?Section 23.7
=+b) What action would have the highest expected value if they think the probability of rising consumer confidence is only 0.40?
=+22. Energy investment decisions.
=+a) For the payoff table in Exercise 14, find the investment strategy under the assumption that the probability that the price of oil goes substantially higher is 0.4 and that the probability that it goes substantially lower is 0.2.
=+b) What if those two probabilities are reversed?
=+23. Advertising strategies EVPI.
=+a) For the advertising strategies of Exercise 21 and using the probability of 0.70 for rising consumer confidence, what is the Expected Value of Perfect Information (EVPI)?b) What is the EVPI if the probability of rising consumer confidence is only 0.40?24. Energy investment EVPI. For the energy
=+a) Draw the decision tree including the decision to hire the consultants.
=+b) Would the consultants’ information be useful? Explain.
=+c) The company thinks there’s an equal chance of either of the consulting alternatives being what the consultants report. What’s the value to the company (per customer) of the extra information?
=+26. Energy investment with information. The company in Exercises 14, 22, and 24 could send a team to Saudi Arabia to obtain additional information about the probabilities that oil will increase or decrease in price. They hope that the fact-finding trip would choose between the two alternatives
=+a) Make a decision tree for these decisions.
=+b) Should the company send the fact-finding trip? Explain.
=+c) The company’s experts estimate that if they send the fact-finding mission, there’s a 70% chance that they’ll conclude there’s a 0.4 probability of higher oil prices. What would the value of the additional information be to the company?
=+27. Investing in equipment. KickGrass Lawncare is a service that cares for lawns in a large, affluent community. Shawn Overgrowth, the owner, is considering the purchase of new zero-turn riding lawn tractors, which would allow him to expand his business. The tractors cost $6300 each, and he
=+a) If forecasters think the probability of rising consumer confidence is 0.70, what is its expected value?
=+21. Advertising strategies decisions. For the payoff table in Exercise 13, find the action with the highest expected value.
=+20. Product introduction, part 4. For the product launch decision of Exercise 12, the economy isn’t looking that good.Your very cautious boss says that he thinks there’s a 60%chance of low sales, and a 30% chance of moderate sales.Which course should the company follow?
=+9. For the probabilities of Exercise 7 and the cost matrix of Exercise 3, using the expected values you found in Exercise
=+7, compute the standard deviation of values associated with each action and the corresponding coefficient of variation.
=+10. For the probabilities of Exercise 8 and the decision tree of Exercise 4, using the expected values found in Exercise 8, compute the standard deviations of the values associated with each action and the corresponding coefficient of variation.Chapter Exercises
=+11. Flight decision. You are planning a trip home at the end of the semester and need to make plane reservations soon.However, you’ve just had a preliminary interview with
=+a consulting firm that seemed to go very well. There’s a chance that they will want you to stay for a few days at the end of the semester for a round of interviews at their offices, which will mean you’ll have to change the date of the flight if you make the reservation now. Suppose that you
=+12. Product introduction. A small company has the technology to develop a new personal data assistant (PDA), but it worries about sales in the crowded market. They estimate that it will cost $600,000 to develop, launch, and market the product. Analysts have produced revenue estimates for three
=+13. Advertising strategies. After a series of extensive meetings, several of the key decisionmakers for a small marketing firm have produced the following payoff table (expected profit per customer) for various advertising strategies and two possible states of the economy.Consumer Confidence
=+14. Energy investment. An investment bank is thinking of investing in a start-up alternative energy company. They can become a major investor for $6M, a moderate investor for $3M, or a small investor for $1.5M. The worth of their investment in 12 months will depend on how the price of oil behaves
=+15. Flight decision tree. Construct a decision tree for the payoff table in Exercise 11.
=+16. Product introduction tree. Construct a decision tree for the payoff table in Exercise 12.
=+17. Flight decision expected value. If you think the probability of being called for an interview is 0.30, calculate the expected value of each action in Exercise 15. Which is the better action in this case?
=+18. Product introduction expected value. An analyst for the company in Exercise 12 thinks the probabilities of high, moderate, and low sales are 0.2, 0.5, and 0.3, respectively.
=+In this case calculate the expected value of each action.Which is the best action in this case?
=+19. Flight decision, part 4. For the decision of Exercise 11, you’ve just learned that you are on the short list and now estimate the chance that you’ll be called for an interview is 0.70. Does that change your choice of actions?
=+would purchase two of them. Another alternative is to purchase three additional mowers of the current type to add to his current equipment. Those would cost $475 apiece.Or he could face the coming gardening season with his existing equipment. Shawn estimates that in a good growing
=+28. Market segmentation. Demand and price are related;raising prices typically lowers demand. Many companies understand that if they can segment their market and offer different prices to different segments, they can often capture more revenue. Aaron’sAir is a small commuter airline.They
=+b) Aaron thinks the market survey is likely to be optimistic.He’d estimate a 65% probability that it would predict the higher (.5) probability of high demand. What would be the EVwSI?
=+c) If the consultant’s report costs $2000, should Aaron pay for it?
=+35. Investment decision. An investor wants to invest $1 million for one year in a portfolio of stocks. She has narrowed her choice to two portfolios. The value of the portfolio depends on the interest rates. There are two states of nature:an increase in the interest rates and a decrease in the
=+Portfolio A $180,000 –$50,000 Portfolio B $120,000 –$20,000 M23_SHAR8696_03_SE_C23.indd 855 14/07/14 8:05 AM 856 CHAPTER 23 Decision Making and Riska) Compute the EV for each alternative decision.b) Compute the SD for each decision.c) Compute the CV and RRR for each decision.d) Which
=+36. Mutual fund investing. An investor is considering how to invest her money. She has a choice between two mutual funds: a fund that invests in biotechnological firms and a fund that invests in infrastructure. The payoff (profit) after one year for these investments depends on the state of the
=+a) Compute the EV for each alternative decision.
=+b) Compute the SD for each decision.
=+c) Compute the CV and RRR for each decision.
=+d) Which mutual fund would you invest in and why?
=+37. Automobile Production. An automobile company is deciding which cars to produce. The company has a choice between two models: a high-end model selling at $45,000, and a moderately priced model selling at $25,000. The payoff table shows monthly sales for each model. Based on past experience,
=+a) Compute the EV for each alternative product (decision).
=+b) Compute the SD for each decision.
=+c) Compute the CV and RRR for each decision.
=+d) Which car would you produce and why?
=+a) Draw the decision tree.
=+34. Segments and surveys. Aaron’sAir (see Exercises 28, 30, and 32) could purchase a market survey from a firm that has advised the island tourist and conference bureau. He thinks their projections would help him determine whether the probability of high demand might be as high as .5 or as low
=+c) Should Shawn purchase the long-range predictions?
=+of low demand he’d sell 30 high-fare and 80 low-fare tickets—revenue of 30 * +210 + 80 * +90 = +13,500. In times of medium demand, he estimates 110 high-fare and 250 low-fare tickets, for an estimated revenue of $45,600.And in times of high demand, he expects 500 low-fare customers and 250
=+29. Investing in equipment, maxes and mins. Shawn Overgrowth, whom we met in Exercise 27, is an entrepreneur who is optimistic about the growing season. What choice should he make to maximize his return? His assistant, Lance Broadleaf, is very conservative, and argues that KickGrass should
=+30. Market segmentation minimax. Aaron, who we met in Exercise 28, tends to be optimistic about business conditions. What is his maximax strategy that would maximize his results?
=+31. “Weather” or not to invest in equipment. Shawn Overgrowth, from Exercise 27, estimates that the probability of a good growing season is 0.70. Based on that:
=+a) Find the EV for his actions.
=+b) Find the standard deviations.
=+c) Compute the RRRs. Which action is preferred based on the RRRs?
=+32. Market segmentation and chance. Aaron’sAir (see Exercises 28 and 30) estimates that high-demand periods(which depend on the weather and on bookings for conferences) occur with probability .3 and medium demand periods occur with probability .5. The rest are low-demand periods.
=+a) What’s the expected value of each of Aaron’s alternative actions?
=+b) What are the standard deviations for each action?
=+c) What are the RRRs? Based on the RRRs, what action is best?
=+33. Equipment and data. Shawn, of Exercises 27, 29, and 31, could obtain long-range predictions of the growing conditions for next summer. He thinks that those might show a probability of good growing conditions as low as 50%or as high as 80%. If he doesn’t obtain those predictions, he’ll
=+a) Draw the decision tree.
=+b) If Shawn thinks there’s a 60% chance the long-range predictions will predict a 50% chance of good conditions, find the corresponding EVwSI.
=+38. Automobile Production, part 2. The automobile company has now done a bit more research and believes that the demand for high-end cars has changed, so that now the low demand is 60% likely and the high demand is only 10% likely. How does this change your responses to Exercise 37? Find the
=+a) Suppose P1Warm2 = 0.5, P1Moderate2 = 0.3, and P1Cold2= 0.2. What is the expected value of each action?
=+What are the actions in this decision process?
=+What are the states of nature?
=+b) Whether your chief competitor decides to launch a new advertising campaign.
=+c) Whether the decision you made to out-source manufacturing last year turned out to be the cost-saver you thought it would be.Section 23.2
=+3. You are called on to decide how your company should produce its new cell phone screen defroster (for use by skiers and others spending time out of doors in the cold.) You
=+develop the following cost matrix ($000’s):State of Nature(State of the Economy)Production Recession Stable Expansion Out-source 220 350 300 In-house 150 240 390 Draw the corresponding decision tree.Exercises M23_SHAR8696_03_SE_C23.indd 852 14/07/14 8:05 AM Exercises 853
=+4. Here is a decision tree for the profits (in $000’s)projected for sales of a new car wiper system, depending on the weather during this winter and the choice of advertising channel:Action State Outcome Warm 550 600 710 410 590 800 750 710 590 Moderate Cold Point of Sale Magazine Internet
=+5. For the cost matrix of Exercise 3,
=+a) What is the minimax choice?
=+b) What is the minimin choice?
=+6. For the decision tree of Exercise 4,
=+a) What is the maximin choice?
=+b) What is the maximax choice?Section 23.4
=+7. For the cost matrix of Exercise 3,
=+a) Suppose P1Recession2 = 0.2, P1Stable2 = 0.2, and P1Expansion2 = 0.6. What is the expected value of each action?
=+b) What is the best choice using the expected-value approach?
=+a) Whether to invest in solar energy companies.
=+2. Which of the following are Actions and which are States of Nature?
=+31. Income and housing. The Office of Federal Housing Enterprise Oversight (www.ofheo.gov) collects data on various aspects of housing costs around the United States.Here is a scatterplot of the Housing Cost Index versus the Median Family Income for each of the 50 states. The correlation is
=+b) Find rho for the full data and for the relationship with the Prius removed. Comment.
=+c) Whether to inform students that all classes have been cancelled due to a sand storm.
=+a) Would Spearman’s rho be an appropriate summary of the strength of the association shown here?
=+30. Carbon footprint. Here are data relating the carbon footprint (tons of CO2 per year) to the new Environmental Protection Agency (EPA) highway mileage for 82 family sedans as reported by the U.S. government (www.fueleconomy.gov/feg/byclass.htm). The car with the highest highway mpg and lowest
=+b) What could we learn from Kendall’s tau that we wouldn’t learn from the Pearson correlation?M22_SHAR8696_03_SE_C22.indd 833 14/07/14 7:36 AM 834 CHAPTER 22 Nonparametric Methods
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