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business statistics a first course
Introduction To Business Statistics 7th Edition Ronald M. Weiers - Solutions
14.45 Using the data of Exercise 14.13 and the 0.10 level, apply the sign test to compare the two samples.How do the results compare to those of that exercise?If they differ, what does this imply about the respective tests?
14.44 For n 5 6 nonzero differences in a one-sample test, there are 5 (1) differences for d 5 x 2 20. Use the 0.10 level of significance in testing H0: md # 20 versus H1: md . 20.
14.43 For n 5 8 nonzero differences between paired observations, there are 5 (1) differences for d 5 x1 2 x2.Use the 0.05 level of significance in testing H0: md 5 0 versus H1: md 0.
14.42 Whether testing a single sample or comparing paired samples, how should one go about deciding whether to use the sign test versus the Wilcoxon signed rank test?
14.41 What role does the binomial distribution play in the sign test, and when is it permissible to use the normal approximation in carrying out the test?
14.40 To evaluate whether three of its slopes should be classified as equally difficult, a ski resort sets up an experiment in which three skiers from each skill category(A beginner to F expert) are randomly selected to make one run on the slope to which they have been assigned. Given the times
14.39 Three movie critics have each rated a number of current movies on a scale of 1 poor to 10 excellent.Given the ratings in file XR14039, use the 0.025 level of significance in comparing the critics. Does it appear that they may be relying on different value systems in assigning their
14.38 An extermination firm is testing several brands of pesticide spray, all of which claim to be effective against ants. Under controlled conditions, each spray is used on 10 ants of the species listed here. The measurement in each cell is the number of seconds until all 10 ants are dead. Given
14.37 A researcher has obtained the following salary figures for the mayor, police chief, and fire chief for a sample of U.S. cities. Assuming these to be a random sample of major cities in the United States, and using the 0.10 level of significance, can we conclude that the median national
14.36 The randomized block design has been used in comparing the effectiveness of three treatments, with the data as shown in the table. Using the 0.05 level of significance, can we conclude that the treatments are equally effective? Block 12345 Treatment 1 2 3 80 60 75 70 72 60 53 45 50 72 65 49
14.35 Compare the Friedman test with the randomized block ANOVA in terms of (a) their respective null and alternative hypotheses, and (b) the assumptions required in order to use each test.
14.34 The Environmental Protection Agency measures city fuel economy by placing the vehicle on a laboratory dynamometer and determining the amount of fuel consumed during a standard speed-distance schedule that simulates an urban trip. File XR14034 lists the miles per gallon data for three
14.33 For three random samples of employees, each sample consisting of employees from a given age group, the data in file XR14033 show the number of absences over the past 6 months. At the 0.10 level, can we conclude that the populations of such employee groups have the same median number of days
14.32 In an agricultural test, each of four organic compounds is applied to a sample of plants. At the end of 4 weeks, the heights of the plants are as shown here. At the 0.025 level, are the compounds equally effective in promoting plant growth?Formula 1: 19 18 20 20 18 inches Formula 2: 9 13 20
14.31 In testing three different rubber compounds, a tire manufacturer finds the tread life of tires made from each to be as shown below. At the 0.05 level, could the three compounds deliver the same median tread life?Design 1: 34 38 33 30 30 thousand miles Design 2: 46 43 39 46 36 Design 3: 48 39
14.30 A sample of five law firms has been selected from each of three major cities for the purpose of obtaining a quote for legal services on a relatively routine business contract. The quotes provided by the fifteen firms are as shown in the accompanying table. At the 0.05 level of significance,
14.29 For the following independent and random samples, use the 0.10 level of significance in testing whether the population medians could be equal. Sample 1 Sample 2 Sample 3 Sample 4 313 361 197 382 240 316 203 302 262 149 244 260 218 325 108 370 236 171 102 190 253 382
14.28 For the following independent and random samples, use the 0.05 level of significance in testing whether the population medians could be equal. Sample 1 Sample 2 Sample 3 31.3 29.4 36.0 30.7 20.8 37.7 35.4 22.2 31.0 36.1 24.9 28.4 30.3 21.4 31.7 25.5 24.1 32.6
14.27 Differentiate between the Kruskal-Wallis test and the one-way analysis of variance in terms of their assumptions and the circumstances under which each should be applied.
14.19 A company has randomly selected a number of employees to test the effectiveness of a speed-reading course. If the course is found to significantly increase reading speed, it will be offered to all of the firm’s clerical employees. For each of the employees selected for the test, reading
14.18 Early in the 1995–1996 NHL hockey season, players and coaches observed with great interest an apparent drop in the number of goals scored so far during that season, compared to scoring over the same number of games during the previous season. For each team, the number of goals in the
14.17 A new procedure is being tested for the assembly of electronic circuit boards. For each of five employees, the time required to assemble a board is measured for both the current procedure and the method that has been proposed.Given the times listed in the table, use the 0.025 level of
14.16 A researcher studying the purchase habits of eight married couples has found they spent the amounts shown below for clothing. At the 0.05 level, can we conclude that the population of husbands and wives do not spend equally in this purchase category? 1 2 3 4 5 6 7 8 Husband $300 240 230 250
14.15 Tom Frederick is the computer support manager for a large company whose employees have been complaining about “spam,” which many of us know as unwanted e-mail to solicit our money or our attention. Tom asked a sample of 9 employees to keep track of the number of spam messages they
14.14 For ten paired samples, the data are as listed here.For d the difference between paired observations(x1 x2), use the 0.10 level of significance in testing H0: md 0 versus H1: md 0. Sample: 1 2 3 4 5 6 7 8 9 10 X2 12.5 11.2 14.4 8.9 10.5 12.3 11.8 12.4 13.9 8.8 12.7 11.2 15.6 8.7 11.8 12.2
14.13 For nine paired samples, the data are as listed in the table. For d the difference between paired observations(x1 x2), use the 0.10 level of significance in testing H0: md 0 versus H1: md 0. Sample: 1 2 3 4 5 6789 X2 7.8 4.0 4.2 9.8 8.7 4.3 8.7 8.1 8.9 9.7 2.1 3.7 8.2 6.6 5.7 5.6 7.7 8.6
14.12 What is the parametric counterpart to the Wilcoxon signed rank test for paired samples? Compare the assumptions involved in using the respective tests.
14.11 The median age for a male at the time of his first marriage has been reported as 27.5 years. In a given region, a random sample of males’ first marriages showed the ages listed in data file XR14011. Using the 0.05 level of significance, test whether the median age at which males in this
14.10 The placement director for a university claims that last year’s graduates had a median starting salary of $35,000. For a random sample of graduates, the starting salaries, in thousands of dollars, are listed in data file XR14010. At the 0.05 level, could the director’s claim be true?
14.9 As a guideline, a local Internal Revenue Service office recommends that auditors try to spend 15 minutes or less with taxpayers who are called in for audit interviews. In a recent random sample of 22 interviews, the interview times were as shown below. Using the 0.025 level, do these data
14.8 According to the director of a county tourist bureau, there is a median of 10 hours of sunshine per day during the summer months. For a random sample of 20 days during the past three summers, the number of hours of sunshine has been recorded as shown below. Use the 0.05 level in evaluating the
14.7 Given the following randomly selected observations, use the Wilcoxon signed rank test and the 0.01 level of significance in examining whether the population median could be greater than 37.0. Using the appropriate statistical table, what is the most accurate statement that can be made about
14.6 Given the following randomly selected observations, use the Wilcoxon signed rank test and the 0.05 level of significance in examining whether the population median could be equal to 4.9. Using the appropriate statistical table, what is the most accurate statement that can be made about the
14.5 What is the parametric counterpart to the Wilcoxon signed rank test for one sample? Compare the assumptions involved in using the respective tests.
13.88 Given the information in Exercise 13.87 and data file XR13087, determine the 95% confidence interval for the population variance of the speeds of vehicles passing this location on the urban interstate.
13.87 Safety researchers in a government agency believe that too much variability in the speeds of vehicles on urban sections of interstate highways can contribute to accidents by causing a greater level of interaction between vehicles traveling in the same direction. They believe that a standard
13.86 Researchers have coded a random sample of house holds according to household income (1 5 under$30,000, 2 5 $30,000–$49,999, 3 5 $50,000–$69,999, and 4 5 $70,000 or more) and number of vehicles owned (1 5 0, 2 5 1 or 2, and 3 5 3 or more). The data are in file XR13086. Using the 0.05 level
13.85 For a random sample of households in a county, file XR13085 lists the number of TV sets owned by each of the households in the study. Using the 0.025 level of significance, test whether x 5 the number of television sets per household could be Poisson distributed in the county’s households.
13.84 The data in file XR13084 represent the Scholastic Aptitude Test (SAT) scores for a random sample of 200 high school seniors who have taken the exam.Using the 0.025 level of significance, test whether the sample scores could have come from a population that is normally distributed.
13.83 At the beginning of last year, a power company asked each of its industrial customers to estimate how much electricity it would require during the year. At the end of the year, the power company recorded the extent to which a customer’s estimate was over or under the amount of electricity
13.82 A casting machine is supposed to produce units for which the standard deviation of weights is 0.4 ounces.According to the maker of the machine, it should be shut down and thoroughly examined for wear if the standard deviation becomes greater than the 0.4 ounces that has been specified. In a
13.81 A campus newspaper is examining the extent to which various segments of the university community favor the Student Government Association’s recommendation that the school make the transition from Division II to Division I NCAA football. A random sample of 100 students is chosen from each of
13.80 An aspirin manufacturer has designed the childproof cap on its bottles so that it must be pressed down before it can be turned and removed. A consumer magazine has randomly purchased 15 bottles of the company’s aspirin for analysis in a feature article on pain relievers and their packaging.
13.79 Union members in a large firm work in three departments: assembly, maintenance, and shipping/receiving. Twenty of a random sample of 30 assembly workers say they intend to ratify the new contract negotiated by union leaders and management. This compares to 30 of 40 maintenance workers and 25
13.78 Over the past year, an audio store has sold stereo systems produced by three different manufacturers. Of the 400 units from company A, 12% were returned for service during the warranty period. This compares to 15% of 300 units from company B, and 16% of 500 from company C. Assuming that the
13.77 According to the Bureau of the Census, 36%of U.S. adults in the $20,001–$35,000 income group participated in adult education during the most recent reporting year. Data for this and other groups are shown here.Assuming independent samples of 1000 for each of these income groups, use the
13.76 A local bank has recently installed an automatic teller machine (ATM). At a regional meeting, an ATM specialist tells the bank manager that usage times will be normally distributed and the variability in the amount of time customers require to use the machine will start out relatively high,
13.75 Taking air samples at random times during a 2-month period, an environmental group finds the standard deviation of ozone concentration measurements in the vicinity of a chemical plant to be 0.03 parts per million(ppm). The group believes the population of ozone measurements is normally
13.74 Three different instructional techniques are being considered for training mechanics to perform a difficult emissions-reduction adjustment on fuel-injection engines.Each of 60 mechanics is randomly assigned to receive one of the training techniques. For the 20 trained by technique A, 70% are
13.73 Of the students at a large university, 30% are freshmen, 25% are sophomores, 25% are juniors, and 20%are seniors. The representation of the four classes in the 100-member marching band is found to be 24%, 28%, 19%, and 29%. At the 0.05 level of significance, does the composition of the
13.72 The following contingency table describes types of collisions versus driving environments for a random sample of two-vehicle accidents that occurred in a given region last year. At the 0.01 level of significance, can we conclude that the type of collision is independent of whether the
13.71 Twenty-five percent of the employees of a large firm have been with the firm less than 10 years, 40% have been with the firm for 10 to 20 years, and 35% have been with the firm for more than 20 years.Management claims to have randomly selected 20 employees to participate in a drawing for a
13.70 A national public television network has found that 35% of its contributions are for less than $20, with 45% for $20–$50, and 20% for more than $50. In a random sample of 200 of the contributions to a local station, 42% were for less than $20, 43% were for$20–$50, and 15% were over $50.
13.69 According to the Bureau of the Census, the U.S.population includes 37.7 million persons who were born in Europe, Asia, the Caribbean, Central America, South America, or in another area outside the United States. A percentage breakdown of the regions of birth is shown here. If a random sample
13.68 A newspaper reporter, collecting data for a feature article on her state lottery system, has found the 200 digits most recently selected to be distributed as shown below. Based on this information, and using the 0.10 level of significance, can she conclude that the digits have not been drawn
13.67 The following data are the number of persons who were waiting in line at a checkout counter at 100 randomly selected times during the week. At the 0.05 level, test whether the population of these values could be Poisson distributed.x Number Number of of Persons Observations 0 24 1 24 2 18 3
13.66 For the most recent year reported, the Federal Bureau of Investigation has listed the following data for robberies in the United States. Source: Statistical Abstract of the United States 2006, p. 201.Street or highway 179,000 robberies Bank or commercial establishment 70,000 Gas station or
13.65 Frank Gerbel, a local insurance representative, has hired a part-time assistant to make “cold” calls on potential customers. The assistant has been given a quota of 20 such calls to make each day, and a call is deemed a success if the potential customer agrees to set up an appointment to
13.64 The personnel director of a large firm has summarized a random sample of last year’s absentee reports in the accompanying contingency table. At the 0.01 level of significance, test the independence of age versus length of absence. Number of Days Absent 1 2-4 5-7 >7 40 years 18 22 11 10 61
13.63 Given the information in Exercise 13.62 and data file XR13062, determine the 98% confidence interval for the population variance of the cooked weights for hamburgers prepared using the consultant’s recommended cooking procedure.
13.62 In past studies, a fast-food franchise has found the standard deviation of weights for quarter-pound hamburgers to be approximately 0.28 ounces after cooking. A consultant has suggested a new procedure for hamburger preparation and cooking that she believes will reduce the variability in the
13.61 According to industry specifications, the standard deviation of gasket thicknesses for a given application must be no more than 3 thousandths of an inch. In a random sample of 25 gaskets produced by one of the firms, the sample standard deviation is found to be 3.7 thousandths of an inch.
13.60 A random sample of n 5 12 is drawn from a population that is normally distributed, and the sample variance is s2 5 19.3. Use 5 0.025 in testing H0:2 # 9.4 versus H1: 2 . 9.4.
13.59 A random sample of n 5 30 is drawn from a population that is normally distributed, and the sample variance is s2 5 41.5. Use 5 0.05 in testing H0:2 5 29.0 versus H1: 2 29.0.
13.58 An instrument maker has randomly selected and submitted 20 of its electronic blood- pressure measurement units to a medical laboratory for testing. At the lab, each unit measures the “blood pressure” of a testing device that simulates a human arm; within the device the pressure is a known
13.57 During the early stages of production for a single-cylinder engine designed for use in portable generators, the manufacturer randomly selects 12 engines from the end of the assembly line and subjects them to a battery of tests. In the horsepower tests, the engines are found to have an output
13.56 A pharmaceutical company has specified that the variation in the quantity of active ingredient in its leading prescription medication must be such that the population standard deviation must be no more than 1.20 micrograms. The ingredient content of the pills is normally distributed. In a
13.55 A random sample of 20 observations has been drawn from a normal population, and the sample variance is found to be s2 5 4.53. Determine the 95%confidence interval for 2.
13.54 A random sample of 10 observations has been drawn from a normal population, and the sample variance is found to be s2 5 19.5. Determine the 98%confidence interval for 2.
13.53 A random sample of 30 observations has been drawn from a normal population, and the sample variance is found to be s2 5 23.8. Determine the 95%confidence interval for 2.
13.52 In previous chapters, confidence intervals have been expressed in terms of a sample statistic plus or minus a given expression—e.g., }x 6 t(syÏwn ). However, the confidence interval for 2 cannot be expressed as s2 plus or minus a comparable term. Why is this not possible?
13.51 In applying the chi-square statistic to estimation and tests for a population variance, why must the population be normally distributed?
13.50 An experiment has been conducted to compare the ease of use of several pocket calculators, with subjects randomly provided with one of four calculator designs. The subjects have been coded according to which one of the four calculators they tried (codes 5 1–4) and whether they thought the
13.49 The movie complex at a shopping mall shows three movies simultaneously on the same evening. On a recent Friday evening, each movie drew a capacity crowd. A sample of the evening’s movie patrons have been coded according to whether they purchased snacks(1 5 pur chased snacks, 2 5 did not
13.48 In analyzing the consumption of cottage cheese by members of various occupational groups, the United Dairy Industry Association found that 326 of 837 professionals seldom or never ate cottage cheese, versus 220 of 489 white- collar workers and 522 of 1243 blue-collar workers. Assuming
13.47 It has been reported that 18.3% of all U.S. households were heated by electricity in 1980, compared to 27.4% in 1995 and 31.5% in 2005. At the 0.05 level, and assuming a sample size of 1000 U.S. households for each year, test whether the population percentages could be equal for these years.
13.46 According to a study by the Pew Research Center, 75% of adults 18–30 said they went online daily, compared with 40% of those 65–74, and just 16% for those 75 or older. Using the 0.01 level of significance, and assuming that a random sample of 200 persons was surveyed from each age group,
13.45 An investment firm survey included the finding that 52% of 150 clients describing themselves as “very aggressive” investors said they were optimistic about the near-term future of the stock market, compared to 46%of 100 describing themselves as “moderate” and 38% of 100 describing
13.44 For three independent samples, each with n 5 100, the respective sample proportions are 0.30, 0.35, and 0.25. Use the 0.05 level in testing whether the three population proportions could be the same.
13.43 For the following data obtained from four independent samples, use the 0.025 level in testing H0: 1 5 2 5 3 5 4 versus H1: At least one population proportion differs from the others.n1 5 150, p1 5 0.30 n2 5 80, p2 5 0.20 n3 5 140, p3 5 0.25 n4 5 50, p4 5 0.26
13.42 For the following data obtained from three independent samples, use the 0.05 level in testing H0: 1 5 2 5 3 versus H1: “At least one population proportion differs from the others.”n1 5 100, p1 5 0.20 n2 5 120, p2 5 0.25 n3 5 200, p3 5 0.18
13.41 For a random sample of returns audited by the IRS, the data in file XR13041 describe the results according to the income category of the audited party(coded as 1 5 low, 2 5 medium, 3 5 moderate, and 4 5 high) and the type of IRS personnel who examined the return (coded as 1 5 revenue agent, 2
13.40 The manager of a television station employs three different weather reporters (coded as 1–3) and has surveyed viewers to find out whether education level (coded as 1–4) might be related to the weather reporter the viewer prefers. For the results listed in data file XR13040, use the 0.05
13.39 Collecting data for eight games, a basketball coach has compiled the following contingency table for the quarter of the game versus the result of “one-andone”free-throw attempts in which a second shot can be attempted if the first one is made. At the 0.025 level, can he conclude that the
13.38 Upon leaving an assembly area, production items are examined and some of them are found to be in need of either further work or total scrapping. Tags on a sample of 150 items that failed final inspection show both the recommended action and the identity of the inspector who examined the item.
13.37 Customers of the Sky Mountain Grocery chain are routinely asked at the checkout whether they prefer paper or plastic bags for their purchases. In a recent study, researchers observed the type of bag specified and surveyed the customer for other information, including his or her level of
13.36 A pharmaceutical firm, studying the selection of “name brand” versus “generic equivalent” on prescription forms, has been given a sample of 150 recent prescriptions submitted to a local pharmacy. Of the 44 under-40 patients in the sample, 16 submitted a prescription form with the
13.35 Researchers in a California community have asked a sample of 175 automobile owners to select their favorite from three popular automotive magazines. Of the 111 import owners in the sample, 54 selected Car and Driver, 25 selected Motor Trend, and 32 selected Road & Track.Of the 64
13.34 A research organization has collected the following data on household size and telephone ownership for 200 U.S. households. At the 0.05 level, are the two variables independent? Based on the chi-square table, what is the most accurate statement that can be made about the p-value for the test?
13.33 A researcher has observed 100 shoppers from three different age groups entering a large discount store and noted the nature of the greeting received by the shopper.Given the results shown here, and using the 0.025 level of significance, can we conclude that the age category of the shopper is
13.32 In a test of the independence of two variables, one of the variables has two possible categories and the other has three possible categories. What will be the critical value of chi-square if the test is to be carried out at the 0.025 level? At the 0.05 level?
13.31 In testing the independence of two variables described in a contingency table, determine the critical value of chi-square if the test is to be conducted at thea. 5 0.025 level and df 5 5b. 5 0.05 level and df 5 8c. 5 0.01 level and df 5 6d. 5 0.10 level and df 5 4
13.30 In testing the independence of two variables described in a contingency table, determine the critical value of chi-square if the test is to be conducted at thea. 5 0.05 level and df 5 3b. 5 0.01 level and df 5 5c. 5 0.10 level and df 5 2d. 5 0.025 level and df 5 4
13.29 For a contingency table with r rows and k columns, determine the df for the test ifa. r 5 3, k 5 4b. r 5 2, k 5 3c. r 5 4, k 5 5d. r 5 5, k 5 3e. r 5 3, k 5 7f. r 5 3, k 5 3
13.28 In carrying out a chi-square test for the independence of variables, what is the procedure for determining the number of degrees of freedom to be used in the test?
13.27 In conducting a chi-square test, why is it advisable that each expected frequency be at least 5.0? If the expected frequency in a cell happens to be less than 5.0, what should be done in order to carry out the analysis?
13.26 The outstanding balances for 500 credit-card customers are listed in file XR13026. Using the 0.10 level of significance, examine whether the data could have come from a normal distribution.
13.25 For Exercise 13.24, use the 0.05 level of significance in examining whether the data could have come from a normal distribution.
13.24 For the previous 300 plywood panels from a lumber company’s production line, the data in file XR13024 list the number of surface defects per panel.Based on this information, use the 0.05 level of significance in examining whether the data could have come from a Poisson distribution.
13.23 For a random sample of 200 U.S. motorists, the mileages driven last year are in data file XR13023. Use the 0.01 level of significance in determining whether the mileages driven by the population of U.S. motorists could be normally distributed.
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