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) and to what extent they supported the university’s football team, the Hawks. The responses to the latter question are: Wildly fanatic Support the Hawks wholeheartedly Support the Hawks, but not that enthusiastically Who are the Hawks? The responses were coded using a 4-3-2-1 numbering system. Can we conclude that the four levels of students differ in their support for the Hawks?
> 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.
> 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
> 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
> Use the Kruskal–Wallis test on the following data to determine whether the population locations differ. (Use  = .05.) Sample 1: Sample 2: 27 33 18 29 41 52 75 37 12 17 22 30 Sample 3: 19 12 33 41 28 18
> Apply the Kruskal–Wallis test and the following statistics to determine whether there is enough statistical evidence at the 10% significance level to infer that the population locations differ. T1 = 3,741 n1 = 47 T2 = 1,610 n2 = 29 T3 = 4,945 n3 = 67
> From the following statistics, use the Kruskal–Wallis test (with = .01) to determine whether the population locations differ. T1 = 1,207 n1 = 25 T2 = 1,088 n2 = 25 T3 = 1,310 n3 = 25 T4 = 1,445 n4 = 25
> How does mental outlook affect a person’s health? The answer to this question may allow physicians to care more effectively for their patients. In an experiment to examine the relationship between attitude and physical health, Dr. Daniel Mark, a heart sp
> Conduct the Kruskal–Wallis test on the following statistics. Use a 5% significance level. T, = 984 n, = 23 T2 = 1,502 n2 = 36 T3 = 1,430 n3 = 29
> Conduct tests of hypotheses at the 5% significance level. a. To determine whether the satisfaction rating of an airline differs between business class and economy class, a survey was performed. Random samples of both groups were asked to rate their satis
> Some movie studios believe that by adding sexually explicit scenes to the home video version of a movie, they can increase the movie’s appeal and profitability. A studio executive decided to test this belief. She organized a study that involved 40 movies
> Admissions officers at universities and colleges face the problem of comparing grades achieved at different high schools. As a step toward developing a more informed interpretation of such grades, an admissions officer at a large state university conduct
> In a study to determine whether gender affects salary offers for graduating MBA students, 45 pairs of students were selected. Each pair consisted of a male and a female student who had almost identical grade-point averages, courses taken, ages, and previ
> Do children feel less pain than adults? That question was addressed by nursing professors at the University of Alberta and the University of Saskatchewan. Suppose that in a preliminary study, 50 8-year-old children and their mothers were subjected to mod
> Does the brand name of an ice cream affect consumers’ perceptions of it? The marketing manager of a major dairy pondered this question. She decided to ask 60 randomly selected people to taste the same flavor of ice cream in two different dishes. The dish
> A large sporting-goods store located in Florida is planning a renovation that will result in an increase in the floor space for one department. The manager of the store has narrowed her choice about which department’s floor space to increase to two possi
> A locksmith is in the process of selecting a new key-cutting machine. If there is a difference in key-cutting speed between the two machines under consideration, he will purchase the faster one. If there is no difference, he will purchase the cheaper mac
> At the height of the energy shortage during the 1970s, governments were actively seeking ways to persuade consumers to reduce their energy consumption. Among other efforts undertaken, several advertising campaigns were launched. To provide input on how t
> As all baseball fans know, first base is the only base that the base runner may overrun. At both second and third base, the runner may be tagged out if he runs past the base. Consequently, on close plays at second and third base, the runner will slide, e
> Conduct tests of hypotheses at the 5% significance level. a. In a taste test of a new beer, 25 people rated the new beer and another 25 rated the leading brand on the market. The possible ratings were Poor, Fair, Good, Very Good, and Excellent. The respo
> Suppose that the housework study referred to in Exercise 19.10 was repeated with some changes. In the revised experiment, 60 women were asked last year and again this year how many hours of housework they perform weekly. Can we conclude at the 1% signifi
> Research scientists at a pharmaceutical company have recently developed a new nonprescription sleeping pill. They decide to test its effectiveness by measuring the time it takes for people to fall asleep after taking the pill. Preliminary analysis indica
> a. Data from a matched pairs experiment were recorded. Use the sign test to determine whether the population locations differ. b. Repeat Part (a) using the Wilcoxon signed rank sum test. c. Why do the results of Parts (a) and (b) differ?
> a. Data from a matched pairs experiment were recorded. Use the sign test to determine whether the population locations differ. b. Repeat Part (a) using the Wilcoxon signed rank sum test. c. Why do the answers to Parts (a) and (b) differ?
> a. A random sample of 50 people was asked to rate two brands of ice cream using the following responses: Delicious OK Not bad Terrible The responses were converted to codes 4, 3, 2, and 1, respectively. Can we infer that Brand A is preferred? b. The resp
> a. In a taste test of a new beer 100 people rated the new beer and the leading brand on the market. The possible ratings were Poor, Fair, Good, Very good, and Excellent. The responses for the new beer and the leading beer were recorded using a 1-2-3-4-5
> Perform the Wilcoxon signed rank sum test to determine whether the location of population 1 differs from the location of population 2 given the data shown here. (Use  = .05.) 1 2 3 4 5 6 7 8 9 10 11 12 Sample 1 18.2 14.1 245 11.9 9
> Perform the Wilcoxon signed rank sum test for the following matched pairs to determine whether the two population locations differ. (Use  = .10.) Pair 1 3 4 5 6. Sample 1 Sample 2 9 12 13 8 7 10 10 11 9 3 9
> A matched pairs experiment produced the following statistics. Conduct a Wilcoxon signed rank sum test to determine whether the location of population 1 is to the right of the location of population 2. (Use = .01.) T+ = 3,457 T− = 2,429 n = 108
> Betting on the results of National Football League games is a popular North American activity. In some states and provinces, it is legal to do so provided that wagers are made through a government-authorized betting organization. In the province of Ontar
> Use the Wilcoxon Rank Sum Test on the following data to determine whether the two population locations differ. (Use a 10% significance level.) Sample 1: 15 7 22 20 32 18 26 17 23 30 Sample 2: 8 27 17 25 20 16 21 17 10 18
> Given the following statistics from a matched pairs experiment, perform the Wilcoxon signed rank sum test to determine whether we can infer at the 5% significance level that the two population locations differ. T+ = 660 T− = 880 n = 55
