An international manufacturer of electronic products is contemplating introducing a new type of compact disk player. After some analysis of the market, the president of the company concludes that, within 2 years, the new product will have a market share of 5%, 10%, or 15%. She assesses the probabilities of these events as .15, .45, and .40, respectively. The vice-president of finance informs her that, if the product captures only a 5% market share, the company will lose $28 million. A 10% market share will produce a $2 million profit, and a 15% market share will produce an $8 million profit. If the company decides not to begin production of the new compact disk player, there will be no profit or loss. Based on the expected value decision, what should the company do?
> Refer to Exercise 13.79, which asked whether there is enough evidence to conclude that heads of households with college degrees (EDCL: 3 = some college, 4 = college degree) have more assets than those who have some college (ASSET). a. The appropriate tec
> Repeat Exercise 17.23 for expenditures on food away from home (FOODAWAY).
> How are middle class households’ expenditures on food eaten at home affected by the age, education, and income of the head of the household? To answer the question conduct a regression analysis using FOODHOME as the dependent variable and AGE, EDUC, and
> How does age and education affect income among middle-class households? To answer the question, conduct a regression analysis of the dependent variable INCOME using the independent variables AGE and years of education (EDUC). a. Estimate the regression c
> A number of retailers regularly survey their customers to determine among other things, whether they were happy with their purchase or service and whether they intended to return. A chain of hardware stores/automobile service centers is one such company.
> In addition to analyzing the relationship between the managers’ characteristic and the performance of the fund, researchers wanted to determine whether the same characteristics are related to the behavior of the fund. In particular, they wanted to know w
> There are thousands of mutual funds available (see page 161 for a brief introduction to mutual funds). There is no shortage of sources of information about them. Newspapers regularly report the value of each unit, mutual fund companies and brokers advert
> Ontario high school students must complete a minimum of six Ontario Academic Credits (OACs) to gain admission to a university in the province. Most students take more than six OACs because universities take the average of the best six in deciding which s
> In city after city, downtown cores have become less and less populated and poorer because shoppers have taken their money to the suburbs and to shopping malls. One reason often given for the decline in downtown shops is the difficulty in parking. To shed
> I C16-01 n July 1990, a rock-and-roll museum opened in Atlanta, Georgia. The museum was located in a large city block containing a variety of stores. In late July 1992, a fire that started in one of these stores burned the entire block, including the mus
> The manager of a large shopping center in Buffalo is in the process of deciding on the type of snowclearing service to hire for his parking lot. Two services are available. The White Christmas Company will clear all snowfalls for a flat fee of $40,000 fo
> Refer to Exercise 22.7. Assume that the probability of each value of demand is the same for all possible demands. a. Determine the EMV decision. b. Determine the EOL decision. Data from Exercise 22.7: A baker must decide how many specialty cakes to bake
> A baker must decide how many specialty cakes to bake each morning. From past experience, she knows that the daily demand for cakes ranges from 0 to 3. Each cake costs $3.00 to produce and sells for $8.00, and any unsold cakes are thrown into the garbage
> If we assign the following probabilities to the states of nature in Exercise 22.5, determine the EOL decision: P(s1) = .2 P(s2) = .6 P(s3) = .2
> Refer to Exercise 22.4. Set up the opportunity loss table. Data from Exercise 22.4: Given the following payoff table, draw the decision tree: a az az 20 5 -1 8 5 4 S3 -10 5 10
> A major movie studio has just completed its latest epic, a musical comedy about the life of Attila the Hun. Because the movie is different (no sex or violence), the studio is uncertain about how to distribute it. The studio executives must decide whether
> The Megabuck Computer Company is thinking of introducing two new products. The first, Model 101, is a small computer designed specifically for children between ages 8 and 16. The second, Model 202, is a medium-size computer suitable for managers. Because
> Max the Bookie is trying to decide how many telephones to install in his new bookmaking operation. Because of heavy police activity, he cannot increase or decrease the number of telephones once he sets up his operation. He has narrowed the possible choic
> Suppose that in Exercise 22.39 a sample of size 5 showed that only one person believes the new ad. In light of this additional information, what should the manager do?
> In an effort to analyze the results of Exercise A15.9, the researcher recorded the total travel length of the course. This variable measures the total distance golfers must walk to play a round of golf. It is the sum of the golf-course playing distance p
> Suppose that in Exercise 22.39 it is possible to perform a survey to determine the percentage of people who believe the ad. What would a sample of size 1 be worth?
> Given the following payoff table, draw the decision tree: a az az 20 5 -1 8 5 4 S3 -10 5 10
> Credibility is often the most effective feature of an advertising campaign. Suppose that, for a particular advertisement, 32% of people surveyed currently believe what the ad claims. A marketing manager believes that for each 1-point increase in that per
> The president of an automobile battery company must decide which one of three new types of batteries to produce. The fixed and variable costs of each battery are shown in the accompanying table. The president believes that demand will be 50,000, 100,000
> Suppose that in Exercise 22.32 a random sample of 25 radio listeners revealed that 2 people would be regular listeners of the station. What is the optimal decision now?
> In Exercise 22.32, suppose that it is possible to survey radio listeners to determine whether they would tune in to the station if the format changed to rock and roll. What would a survey of size 2 be worth?
> Suppose that in Exercise 22.14 a consultant offers to analyze the problem and predict the amount of electricity required by the new community. To induce the electric company to hire her, the consultant provides the set of likelihood probabilities given h
> Repeat Exercise 22.33, given that 12 out of 100 households respond affirmatively.
> There is a garbage crisis in North America—too much garbage and no place to put it. As a consequence, the idea of recycling has become quite popular. A waste-management company in a large city is willing to begin recycling newspapers, aluminum cans, and
> A radio station that currently directs its programming toward middle-age listeners is contemplating switching to rock-and-roll music. After analyzing advertising revenues and operating costs, the owner concludes that, for each percentage point of market
> Refer to Exercise 13.36 where respondents were asked to taste the same wine in two different bottles. The first bottle was capped using a cork, and the second had a metal screw cap. Respondents were also asked to taste the wine and rate it using the foll
> To improve her decision-making capability, the electronics products manufacturer in Exercise 22.16 performs a survey of potential buyers of compact disc players. She describes the product to 25 individuals, 3 of whom say they would buy it. Using this add
> What is the maximum price the electronics productmanufacturer should be willing to pay for perfect information regarding the market share in Exercise 22.16?
> If we assign the following probabilities to the states of nature in Exercise 22.1, determine the EMV decision: P(s1) = .4 P(s2) = .1 P(s3) = .3 P(s4) = .2
> A sporting-goods storeowner has the opportunity to purchase a lot of 50,000 footballs for $100,000. He believes that he can sell some or all by taking out mail-order advertisements in a magazine. Each football will be sold for $6. The advertising cost is
> What conclusions can you draw about the effect of the prior probabilities on EVSI from Exercises 22.25–22.27?
> Repeat Exercise 22.25 with the following prior probabilities. P(s1) = .90 P(s2) = .05 P(s3) = .05
> Repeat Exercise 22.25 with the following prior probabilities. P(s1) = .5 P(s2) = .4 P(s3) = .1
> Given the following payoff table, prior probabilities, and likelihood probabilities, find the expected value of sample information. Payoff Table Prior probabilities Likelihood Probabilities
> With the accompanying payoff table and the prior and posterior probabilities computed in Exercise 22.23 calculate the following. a. The optimal act for each experimental outcome b. The expected value of sample information Payoff Table a, az az 10 18
> Calculate the posterior probabilities from the prior and likelihood probabilities that follow. Prior Probabilities P(s1) = .5 P(s2) = .5 Likelihood Probabilities .98 .02 S2 .05 .95
> Some customers spend a great deal of time doing research before choosing a particular brand of a product, particularly an expensive product. Does this result in a more satisfied customer? To shed light on this question, a random sample of people who purc
> Determine the posterior probabilities, given the following prior and likelihood probabilities. Prior probabilities P(s1) = .25 P(s2) = .40 P(s3) = .35 Likelihood Probabilities .20 .10 .25 .25 S3 .40 .30
> What conclusion can you draw about the effect of the probabilities on EVPI from Exercises 22.19 and 22.20?
> Redo Exercise 22.19, changing the probabilities to the following values. a. P(s1) = .75 P(s2) = .25 b. P(s1) = .95 P(s2) = .05
> Draw the decision tree for Exercise 22.1.
> Given the following payoff table and probabilities, determine EVPI. P(s1) = .5 P(s2) = .5 az a a4 65 20 45 30 S2 70 110 80 95
> For Exercise 22.17, determine the opportunity loss table and compute EOL*. Confirm that EOL* = EVPI.
> Find EPPI, EMV*, and EVPI for the accompanying payoff table and probabilities. P(s1) = .10 P(s2) = .25 P(s3) = .50 P(s4) = .15 a, az 60 110 75 40 110 150 S2 220 120 85 SA 250 120 130
> A retailer buys bushels of mushrooms for $2 each and sells them for $5 each. The quality of the mushrooms begins to decline after the first day they are offered for sale; therefore, to sell the mushrooms for $5/bushel, he must sell them on the first day.
> The electric company is in the process of building a new power plant. There is some uncertainty regarding the size of the plant to be built. If the community that the plant will service attracts a large number of industries, the demand for electricity wi
> Most supermarkets load groceries into plastic bags. However, plastic bags take many years to decompose in garbage dumps. To determine how big the problem might be, a random sample of American households was each asked to determine the number of plastic
> A building contractor must decide how many mountain cabins to build in the ski resort area of Chickoh- pee. He builds each cabin at a cost of $26,000 and sells each for $33,000. All cabins unsold after 10 months will be sold to a local investor for $20,0
> Refer to Exercise 22.11. The owner has assignedthe following probabilities: P(Demand = 100) = .2, P(Demand = 150) = .25, P(Demand = 200) = .40, P(Demand = 250) = .15 Find the EMV decision.
> The owner of a clothing store must decide how many men’s shirts to order for the new season. For a particular type of shirt, she must order in quantities of 100 shirts. If she orders 100 shirts, her cost is $10 per shirt; if she orders 200 shirts, her co
> Refer to Exercise 22.9. Using subjective assessments the manager has assigned the following probabilities to the number of snowfalls. Determine the optimal decision. P(0) = .05 P(1) = .15 P(2) = .30 P(3) = .40 P(4) = .10 Data from Exercise 22.9: The
> Set up the opportunity loss table from the following payoff table: az 55 26 S2 43 38 29 43 S3 SA 15 51
> On average, how many units will be produced until the control chart signals that the process is out of control when it is under control?
> Refer to Exercise 21.7. Determine the ARL until the x chart signals that the process is out of control when it is under control. Data from Exercise 21.7: The control limits of an x chart are set at two standard errors from the centerline. Calculate the
> The control limits of an x chart are set at two standard errors from the centerline. Calculate the probability that on any sample the control chart will indicate that the process is out of control when it is under control.
> Refer to Exercise 21.5. What is the average run length until the x chart signals that the process is out of control when it is under control? Data from Exercise 21.5: If the control limits of an x chart are set at 2.5 standard errors from the centerline
> If the control limits of an x chart are set at 2.5 standard errors from the centerline, what is the probability that on any sample the control chart will indicate that the process is out of control when it is under control?
> In 2003, there were 129,142,000 workers in the United States The general manager for a public transportation company wanted to learn more about how workers commute to work and how long it takes them. A random sample of workers was interviewed. Each repor
> A courier delivery company advertises that it guarantees delivery by noon the following day. The statistical process control plan calls for sampling 2,000 deliveries each day to ensure that the advertisement is reasonable. The number of late deliveries f
> A company that manufactures batteries employs statistical process control to ensure that its product functions properly. The sampling plan for the D-cell batteries calls for samples of 500 batteries to be taken and tested. The numbers of defective batter
> The Woodsworth Publishing Company produces millions of books containing hundreds of millions of pages each year. To ensure the quality of the printed page, Woodsworth uses statistical process control. In each production run, 1,000 pages are randomly insp
> A plant produces 1,000 cordless telephones daily. A random sample of 100 telephones is inspected each day. After 30 days, the following number of defectives were found. Construct a p chart to determine whether the process is out of control. 5 0 4 3 0
> Raytheon of Canada Limited produces printed circuit boards (PCBs), which involve a number of soldering operations. At the end of the process, the PCBs are tested to determine whether they work properly. There are several causes of PCB failure, including
> Random samples of 200 copier machines were taken on an assembly line every hour for the past 25 hours. The number of defective machines is shown here. Are there any points beyond the Control limits? If so, what do they tell you about the production proce
> To ensure that a manufacturing process is under control, 40 samples of size 1,000 were drawn, and the number of defectives in each sample was counted. The mean sample proportion was .035. Compute the centerline and control limits for the p chart.
> Calculate the process capability index for Exercise 21.34. Does the value of this index indicate that the production process is poor? Explain.
> If the specification limits for the plastic pipes in Exercise 21.40 are LSL = 2.9 inches and USL = 3.1 inches, determine the process capability index Cpk.
> Plastic pipe is used for plumbing in almost all new homes. If the pipes are too narrow or too wide, they will not connect properly with other parts of the plumbing system. A manufacturer of 3-inchdiameter pipes uses statistical process control to maintai
> Auto manufacturers are required to test their vehicles for a variety of pollutants in the exhaust. The amount of pollutant varies even among identical vehicles so that several vehicles must be tested. The engineer in charge of testing has collected data
> Your education as a statistics practitioner can be considered a production process overseen by the course instructor. The variable we measure is the grade achieved by each student. a. Discuss chance variation—that is, describe the sources of variation th
> Almost all computer hardware and software producers offer a toll-free telephone number to solve problems associated with their products. The ability to work quickly to resolve difficulties is critical. One software maker’s policy is that all calls must b
> Motor oil is packaged and sold in plastic bottles. The bottles are often handled quite roughly in delivery to the stores (bottles are packed in boxes, which are stacked to conserve truck space), in the stores themselves, and by consumers. The bottles mus
> Refer to Exercise 21.35. Nuts and bolts are used in the assembly of the transmission oil coolers. They are supposed to be tightened by a torque wrench to 7 foot-pounds with specification limits LSL = 6 foot-pounds and USL = 8 foot-pounds. To test the pro
> Find the process capability index for Exercise 21.35.
> Long Manufacturing produces heat exchangers, primarily for the automotive industry. One such product, a transmission oil cooler, is used in the cooling of bus transmissions. It is composed of a series of copper tubes that are soldered into a header. The
> The seats for the F-150 series Ford trucks are manufactured by Lear Seating. The frames must be 1, 496 mm wide with specification limits LSL = 1, 486 mm and USL = 1, 506 mm. Frames that are wider than 1, 506 mm or narrower than 1, 486 mm result in assemb
> Lear Seating of Kitchener, Ontario, produces seats for Cadillacs and other GM cars and trucks. The Cadillac seat includes a part called the EK headrest. The frame of the headrest is made from steel rods. A machine is used to bend the rod into a U-shape d
> Refer to Exercise 21.30. If the lower and upper specification limits are 995 cc and 1005 cc, respectively, what is Cpk? Data from Exercise 21.30: KW Paints is a company that manufactures various kinds of paints and sells them in 1- and 4-liter cans. The
> KW Paints is a company that manufactures various kinds of paints and sells them in 1- and 4-liter cans. The cans are filled on an assembly line with an automatic valve regulating the amount of paint. If the cans are overfilled, paint and money will be wa
> In the presidential elections of 2000 and 2004, the vote in the state of Florida was crucial. It is important for the political parties to track party affiliation. Surveys in Broward and Miami-Dade counties were conducted in 1990, 1996, 2000, and 2004. T
> What is meant by special variation?
> Refer to Exercise 21.28. Find the process capability index Cpk. Data from Exercise 21.28: An arc extinguishing unit (AEU) is used in the high-voltage electrical industry to eliminate the occurrence of electrical flash from one live 25,000-volt switch co
> An arc extinguishing unit (AEU) is used in the high-voltage electrical industry to eliminate the occurrence of electrical flash from one live 25,000-volt switch contact to another. A small but important component of an AEU is a nonconductive sliding bear
> The fence of a saw is set so that it automatically cuts 2-by-4 boards into 96-inch lengths needed to produce prefabricated homes. To ensure that the lumber is cut properly, three pieces of wood are measured after each 100 cuts are made. The measurements
> Thirty samples of size 4 were drawn from a production process. a. Construct an S chart. b. Construct an x chart. c. Do the charts allow you to conclude that the process is under control? d. If the process went out of control, which of the following is th
> The mean of the sample means and the pooled standard deviation of 40 samples of size 9 taken from a production process under control are shown here. Compute the centerline, control limits, and zone boundaries for the x chart. x = 181.1 S = 11.0
> Given the following statistics drawn from 30 samples of size 4, calculate the centerline and control limits for the x chart. x = 453.6 S = 12.5
> Write a brief report comparing the sampling plans described in Exercises 21.16 and 21.19. Discuss the relative costs of the two plans and the frequency of Type I and Type II errors.
> Refer to Exercise 21.19. a. Find the probability that the x chart does not detect a shift of .75 standard deviation on the first sample after the shift occurs. b. Compute the probability that the x chart will not detect the shift for the first four sampl
> The company is considering changing the sampling plan so that 20 components are sampled every hour. What is the average number of units produced until the chart indicates that the process is out of control when it is not?
> The battle between customers and car dealerships is often intense. Customers want the lowest price, and dealers want to extract as much money as possible. One source of conflict is the trade-in car. Most dealers will offer a relatively low trade-in in an
> The United States and Canada (among others) are countries in which a significant proportion of citizens are immigrants. Many arrive in North America with few assets but quickly adapt to a changed economic environment. The question often arises, How quick
> Refer to Exercise 21.16. a. Find the probability that the x chart does not detect a shift of .75 standard deviation on the first sample after the shift occurs. b. Compute the probability that the x chart will not detect the shift for the first four sampl
> On average how many units will be produced until the control chart signals that the process is out of control when it is under control?
> Write a brief report comparing the sampling plans described in Exercises 21.9 and 21.12. Discuss the relative costs of the two plans and the frequency of Type I and Type II errors.
