What is meant by special variation?
> 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
> 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
> 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
> 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.
> Refer to Exercise 21.12. a. Find the probability that the x chart does not detect a shift of 1.5 standard deviations on the first sample after the shift occurs. b. Compute the probability that the x chart will not detect the shift for the first eight sam
> The operations manager is unsatisfied with the current sampling plan. He changes it to samples of size 2 every half hour. What is the average number of units produced until the chart indicates that the process is out of control when it is not?
> Refer to Exercise 21.9. a. Find the probability that the x chart does not detect a shift of 1.5 standard deviations on the first sample after the shift occurs. b. Compute the probability that the x chart will not detect the shift for the first eight samp
> What is meant by chance variation?
> The general manager of an engineering firm wants to know whether a draftsman’s experience influences the quality of his work. She selects 24 draftsmen at random and records their years of work experience and their quality rating (as ass
> The weekly returns of two stocks for a 13-week period were recorded and are listed here. Assuming that the returns are not normally distributed, can we infer at the 5% significance level that the stock returns are correlated? Stock 1 -7 -4 -7 -3 2 -1
> Does the number of commercials shown during a half-hour television program affect how viewers rate the show? In a preliminary study eight people were asked to watch a pilot for a situation comedy and rate the show (1 = Terrible, 2 = Bad, 3 = OK, 4 = Good
> Millions of people suffer from migraine headaches. The costs in work days lost, medication, and treatment are measured in the billions of dollars. A study reported in the Journal of the American Medical Association (2005, 203: 2118–2125) described an exp
> A statistics student asked seven first-year economics students to report their grades in the required mathematics and economics courses. The results (where 1 = F, 2 = D, 3 = C, 4 = B, 5 = A) are as follows: Calculate the Spearman rank correlation coeffi
> Is there sufficient evidence at the 5% significance level to infer that there is a positive relationship between two ordinal variables given that rs = .15 and n = 12?
> Test the following hypotheses: H: P,=0 H;: P,#0 n= 50 r,= .23 a= .05
> In recent years, insurance companies offeringmedical coverage have given discounts to companies that are committed to improving the health of their employees. To help determine whether this policy is reasonable, the general manager of onelarge insurance
> In anticipation of buying a new scanner, a student turned to a website that reported the results of surveys of users of the different scanners. A sample of 133 responses was listed showing the ease of use of five different brands. The survey responses we
> Do university students become more supportive of their varsity teams as they progress through their 4-year stint? To help answer this question, a sample of students was drawn. Each was asked their class standing (freshman, sophomore, junior, or senior) a
> It is common practice in the advertising business to create several different advertisements and then ask a random sample of potential customers to rate the ads on several different dimensions. Suppose that an advertising firm developed four different ad
> During the last presidential campaign, the Gallup organization surveyed a random sample of 30 registered Democrats in January, another 30 in February, and yet another 30 in March. All 90 Democrats were asked to “rate the chances of the Democrats winning
> A consumer testing service compared the effectiveness of four different brands of drain cleaner. The experiment consisted of using each product on 50 different clogged sinks and measuring the amount of time that elapsed until each drain became unclogged.
> A survey of statistics professors asked them to rate the importance of teaching nonparametric techniques. The possible responses are Very important Quite important Somewhat important Not too important Not important at all The professors were classified a
> An economist working for a state university wanted to acquire information about salaries in publicly funded and private colleges and universities. She conducted a survey of 623 public-university faculty members and 592 private-university faculty members
> The management of fast-food restaurants is extremely interested in knowing how their customers rate the quality of food and service and the cleanliness of the restaurants. Customers are given the opportunity to fill out customer comment cards. Suppose th
> A well-known soft-drink manufacturer has used the same secret recipe for its product since its introduction over 100 years ago. In response to a decreasing market share, however, the president of the company is contemplating changing the recipe. He has d
> Many North Americans suffer from high levels of cholesterol, which can lead to heart attacks. For those with very high levels (over 280), doctors prescribe drugs to reduce cholesterol levels. A pharmaceutical company has recently developed three such dru
> Because there are no national or regional standards, it is difficult for university admission committees to compare graduates of different high schools. University administrators have noted that an 80% average at a high school with low standards may be e
> The manager of a personnel company is in the process of examining her company’s advertising programs. Currently, the company advertises in each of the three local newspapers for a wide variety of positions, including computer programmer
> In recent years, lack of confidence in the U.S. Postal Service has led many companies to send all of their correspondence by private courier. A large company is in the process of selecting one of three possible couriers to act as its sole delivery method
> The manager of a chain of electronicproducts retailers is trying to decide on a location for its newest store. After a thorough analysis, the choice has been narrowed to three possibilities. An important factor in the decision is the number of people pas
> Ten judges were asked to test the quality of fourdifferent brands of orange juice. The judges assigned scores using a 5-point scale where 1 = Bad, 2 = Poor, 3 = Average, 4 = Good, and 5 = Excellent. The results are shown here. Can we conclude at the 5% s
> Applicants to MBA programs must take the Graduate Management Admission Test (GMAT). There are several companies that offer assistance in preparing for the test. To determine whether they work, and if so, which one is best, an experiment was conducted. Se
> In an effort to determine whether differences exist between three methods of teaching statistics, a professor of business taught his course differently in each of three large sections. In the first section, he taught by lecturing; in the second, he taugh
> Physicians have been recommending more exercise for their patients, particularly those who are overweight. One benefit of regular exercise appears to be a reduction in cholesterol, a substance associated with heart disease. To study the relationship more
> Conduct tests of hypotheses at the 5% significance level. a. Refer to Example 19.2. Suppose that the responses were coded as follows: 100 = The drug was extremely effective. 60 = The drug was quite effective. 40 = The drug was somewhat effective. 35 = Th
> a. Refer to Example 19.6. Suppose that the responses were recoded so that the numbers equaled the midpoint of the range of percentiles. That is: 97.5 = The candidate is in the top 5% of applicants 92.5 = The candidate is in the top 10% of applicants, but
> a. A random sample of 30 people was asked to rate each of four different premium brands of coffee. The ratings are: Excellent Good Fair Poor The responses were assigned numbers 1 through 4, respectively. Can we infer that differences exist between the ra
> The following data were generated from a blocked experiment. Conduct a Friedman test to determine whether at least two population locations differ. (Use  = .05.) Treatment Block 1 3 1 73 6.9 8.4 2 8.2 7.0 7.3 3 5.7 6.0 8.1 4 6.1 6.
> Apply the Friedman test to the accompanying table of data to determine whether we can conclude that at least two population locations differ. (Use  = .10.) Treatment Block 1 2 3 4 1 10 12 15 9 8 10 11 6 3 13 14 16 11 4 9 9. 12 13 5
> a. Four random samples of 50 people each were asked to rate four different computer printers in terms of their ease of use. The responses are: Very easy to use Easy to use Difficult to use Very difficult to use The responses were coded using a 4-3-2-1 sy
> Using the Kruskal–Wallis test, determine whether there is enough evidence provided by the accompanying data to enable us to infer that at least two population locations differ. (Use  = .05.) Sample 1: 25 15 20 22
