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applied statistics and probability for engineers
Applied Statistics For Engineers And Scientists 3rd Edition Jay L. Devore, Nicholas R. Farnum, Jimmy A. Doi - Solutions
74. The mode of a numerical data set is the value that occurs most frequently in the set.a. Determine the mode for the cadence data given in Exercise 73.b. For a categorical sample, how would you define the modal category?
73. The article “Can We Really Walk Straight?” (Amer. J. of Physical Anthropology, 1992: 19–27) reported on an experiment in which each of 20 healthy men was asked to walk as straight as possible to a target 60 m away at normal speed.Consider the following observations on cadence (number of
72. Anxiety disorders and symptoms can often be effectively treated with benzodiazepine medications. It is known that animals exposed to stress exhibit a decrease in benzodiazepine receptor binding in the frontal cortex. The paper “Decreased Benzodiazepine Receptor Binding in Prefrontal Cortex in
71. Here is a description from MINITAB of the strength data given in Exercise 13.Variable N Mean Median TrMean StDev SE Mean strength 153 135.39 135.40 135.41 4.59 0.37 Variable Minimum Maximum Q1 Q3 strength 122.20 147.70 132.95 138.25a. Comment on any interesting features (the quartiles and
70. Elevated energy consumption during exercise continues after the workout ends. Because calories burned after exercise contribute to weight loss and have other consequences, it is important to understand this process. The paper “Effect of Weight Training Exercise and Treadmill Exercise on
69.a. Let a and b be constants and let yi axi b for i 1, 2, . . . , n. What are the relationships between x and y and between and ?b. A sample of temperatures for initiating a certain chemical reaction yielded a sample average (°C) of 87.3 and a sample standard deviation of 1.04. What are the
68.a. For what value of c is the quantity (xi c)2 minimized? [Hint: Take the derivative with respect toc, set equal to 0, and solve.]b. Using the result of part (a), which of the two quantities(xi x)2 and (xi )2 will be smaller than the other(assuming that x)?
67. Aortic stenosis refers to a narrowing of the aortic valve in the heart. The paper “Correlation Analysis of Stenotic Aortic Valve Flow Patterns Using Phase Contrast MRI” (Annals of Biomed. Engr., 2005: 878–887) gave the following data on aortic root diameter (cm) and gender for a sample of
66. A deficiency of the trace element selenium in the diet can negatively impact growth, immunity, muscle and neuromuscular function, and fertility. The introduction of selenium supplements to dairy cows is justified when pastures have low selenium levels. Authors of the paper “Effects of
65. The accompanying frequency distribution of fracture strength(MPa) observations for ceramic bars fired in a particular kiln appeared in the article “Evaluating Tunnel Kiln Performance”(Amer. Ceramic Soc. Bull., Aug. 1997: 59–63).Class 81–83 83–85 85–87 87–89 89–91 Frequency
64. The following data on HC and CO emissions for one particular vehicle was given in the chapter introduction.HC (gm/mi) 13.8 18.3 32.2 32.5 CO (gm/mi) 118 149 232 236a. Compute the sample standard deviations for the HC and CO observations. Does the widespread belief appear to be justified?b. The
63. The amount of radiation received at a greenhouse plays an important role in determining the rate of photosynthesis.The accompanying observations on incoming solar radiation were read from a graph in the article “Radiation Components over Bare and Planted Soils in a Greenhouse”(Solar Energy,
62. Consider the following information on ultimate tensile strength (lb/in) for a sample of n 4 hard zirconium copper wire specimens (from “Characterization Methods for Fine Copper Wire,” Wire J. Intl., Aug., 1997: 74–80): 76,831 s 180 smallest xi 76,683 largest xi 77,048 Determine
61. The accompanying comparative boxplot of gasoline vapor coefficients for vehicles in Detroit appeared in the article“Receptor Modeling Approach to VOC Emission Inventory Validation,” (J. of Envir. Engr., 1995: 483–490). Discuss any interesting features.
60. Observations on burst strength (lb/in2) were obtained both for test nozzle closure welds and for production cannister nozzle welds (“Proper Procedures Are the Key to Welding Radioactive Waste Cannisters,” Welding J., Aug. 1997:61–67).Test 7200 6100 7300 7300 8000 7400 7300 7300 8000 6700
59. Blood cocaine concentration (mg/L) was determined both for a sample of individuals who had died from cocaineinduced excited delirium (ED) and for a sample of those who had died from a cocaine overdose without excited delirium;survival time for people in both groups was at most 6 hours.
58. A company utilizes two different machines to manufacture parts of a certain type. During a single shift, a sample of n 20 parts produced by each machine is obtained, and the value of a particular critical dimension for each part is determined.The comparative boxplot at the top of page 41 is
56. The amount of aluminum contamination (ppm) in plastic of a certain type was determined for a sample of 26 plastic specimens, resulting in the following data (“The Lognormal Distribution for Modeling Quality Data when the Mean Is Near Zero,” J. of Quality Technology, 1990: 105–110):30 30
55. Here is a stem-and-leaf display of the escape time data introduced in Exercise 36 of this chapter.32 55 33 49 34 35 6699 36 34469 37 03345 38 9 39 2347 40 23 41 42 4a. Determine the value of the fourth spread.b. Are there any outliers in the sample? Any extreme outliers?c. Construct a boxplot
54. Consider the following observations on shear strength (MPa)of a joint bonded in a particular manner (from a graph in the article “Diffusion of Silicon Nitride to Austenitic Stainless Steel without Interlayers,” Metallurgical Trans., 1993:1835–1843).22.2 40.4 16.4 73.7 36.6 109.9 30.0 4.4
53. Reconsider the data on area of scleral lamina given in Exercise 49.a. Determine the lower and upper fourths.b. Calculate the value of the fourth spread.c. If the two largest sample values, 4.33 and 4.52, had instead been 5.33 and 5.52, how would this affect fs? Explain.d. By how much could the
52. The first four deviations from the mean in a sample of n 5 reaction times were .3, .9, 1.0, and 1.3. What is the fifth deviation from the mean? Give a sample for which these are the five deviations from the mean.
51. The article “A Thin-Film Oxygen Uptake Test for the Evaluation of Automotive Crankcase Lubricants” (Lubric.Engr., 1984: 75–83) reported the following data on oxidationinduction time (min) for various commercial oils:87 103 130 160 180 195 132 145 211 105 145 153 152 138 87 99 93 119 129a.
50. In 1997 a woman sued a computer keyboard manufacturer, charging that her repetitive stress injuries were caused by the keyboard (Genessy v. Digital Equipment Corp.). The injury awarded about $3.5 million for pain and suffering, but the court then set aside that award as being unreasonable
49. A study of the relationship between age and various visual functions (such as acuity and depth perception) reported the following observations on area of scleral lamina (mm2) from human optic nerve heads (“Morphometry of Nerve Fiber Bundle Pores in the Optic Nerve Head of the
48. Exercise 34 presented the following data on endotoxin concentration in settled dust both for a sample of urban homes and for a sample of farm homes:U: 6.0 5.0 11.0 33.0 4.0 5.0 80.0 18.0 35.0 17.0 23.0 F: 4.0 14.0 11.0 9.0 9.0 8.0 4.0 20.0 5.0 8.9 21.0 9.2 3.0 2.0 0.3a. Determine the value of
47. Calculate and interpret the values of the sample median, sample mean, and sample standard deviation for the following observations on fracture strength (MPa, read from a graph in“Heat-Resistant Active Brazing of Silicon Nitride: Mechanical Evaluation of Braze Joints,” Welding J., August,
46. The accompanying observations on stabilized viscosity (cP)for specimens of a certain grade of asphalt with 18% rubber added are from the article “Viscosity Characteristics of Rubber-Modified Asphalts” (J. of Materials in Civil Engr., 1996: 153–156):2781 2900 3013 2856 2888a. What are the
45. The value of Young’s modulus (GPa) was determined for cast plates consisting of certain intermetallic substrates, resulting in the following sample observations (“Strength and Modulus of a Molybdenum-Coated Ti-25Al-10Nb-3U1Mo Intermetallic,” J. of Materials Engr. and Performance, 1997:
44. The article “Oxygen Consumption During Fire Suppression:Error of Heart Rate Estimation” (Ergonomics, 1991:1469–1474) reported the following data on oxygen consumption (mL/kg/min) for a sample of ten firefighters performing a fire-suppression simulation:29.5 49.3 30.6 28.2 28.0 26.3 33.9
43. An experiment to study the lifetime (in hours) for a certain type of component involved putting ten components into operation and observing them for 100 hours. Eight of the components failed during that period, and those lifetimes were recorded. Denote the lifetimes of the two components still
42.a. If a constant c is added to each xi in a sample, yielding yi xic, how do the sample mean and median of the yis relate to the mean and median of the xis? Verify your conjectures.b. If each xi is multiplied by a constantc, yielding yi cxi, answer the question of part (a). Again, verify your
41. A sample of n 10 automobiles was selected, and each was subjected to a 5-mph crash test. Denoting a car with no visible damage by S (for success) and a car with such damage by F, results were as follows:S S F SSS F F S Sa. What is the value of the sample proportion of successes x/n?b. Replace
40. Compute the sample median, 25% trimmed mean, 10%trimmed mean, and sample mean for the lifetime data given in Exercise 27, and compare these measures.
39. The propagation of fatigue cracks in various aircraft parts has been the subject of extensive study in recent years. The accompanying data consists of propagation lives (flight hours/104) to reach a given crack size in fastener holes intended for use in military aircraft (“Statistical Crack
38. Blood pressure values are often reported to the nearest 5 mmHg (100, 105, 110, etc.). Suppose the actual blood pressure values for nine randomly selected individuals are 118.6 127.4 138.4 130.0 113.7 122.0 108.3 131.5 133.2a. What is the median of the reported blood pressure values?b. Suppose
37. The article “Snow Cover and Temperature Relationships in North America and Eurasia” (J. Climate and Applied Meteorology, 1983: 460–469) used statistical techniques to relate the amount of snow cover on each continent to average continental temperature. Data presented there included the
36. A sample of 26 offshore oil workers took part in a simulated escape exercise, resulting in the accompanying data on time(sec) to complete the escape (“Oxygen Consumption and Ventilation During Escape from an Offshore Platform,”Ergonomics, 1997: 281–292):389 356 359 363 375 424 325 394 402
35. The minimum injection pressure (psi) for injection molding specimens of high amylose corn was determined for eight different specimens (higher pressure corresponds to greater processing difficulty), resulting in the following observations(from “Thermoplastic Starch Blends with a
34. Exposure to microbial products, especially endotoxin, may have an impact on vulnerability to allergic diseases. The article“Dust Sampling Methods for Endotoxin—An Essential, But Underestimated Issue” (Indoor Air, 2006: 20–27) considered various issues associated with determining
33. The article “The Pedaling Technique of Elite Endurance Cyclists” (Int. J. of Sport Biomechanics, 1991: 29–53)reported the accompanying data on single-leg power at a high workload:244 191 160 187 180 176 174 205 211 183 211 180 194 200a. Calculate and interpret the sample mean and
32. Fire load (MJ/m2) is the heat energy that could be released per square meter of floor area by combustion of contents and the structure itself. The article “Fire Loads in Office Buildings” (J. of Structural Engr., 1997: 365–368) gave the following cumulative percentages (read from a graph)
31. The cumulative frequency and cumulative relative frequency for a particular class interval are the sum of frequencies and relative frequencies, respectively, for that interval and all intervals lying below it. If, for example, there are four intervals with frequencies 9, 16, 13, and 12, then
30. A Pareto diagram is a variation of a histogram for categorical data resulting from a quality control study. Each category represents a different type of product nonconformity or production problem. The categories are ordered so that the one with the largest frequency appears on the far left,
29. Consider the following data on type of health complaint(J joint swelling, F fatigue, B back pain, M muscle weakness, C coughing, N nose running/irritation, O other) made by tree planters. Obtain frequencies and relative frequencies for the various categories, and draw a histogram.
28. Human measurements provide a rich area of application for statistical methods. The article “A Longitudinal Study of the Development of Elementary School Children’s Private Speech” (Merrill-Palmer Q., 1990: 443–463) reported on a study of children talking to themselves (private speech).
27. The paper “Study on the Life Distribution of Microdrills”(J. of Engr. Manufacture, 2002: 301–305) reported the following observations, listed in increasing order, on drill lifetime (number of holes that a drill machines before it breaks)when holes were drilled in a certain brass alloy.11
26. Automated electron backscattered diffraction is now being used in the study of fracture phenomena. The following information on misorientation angle (degrees) was extracted from the article “Observations on the Faceted Initiation Site in the Dwell-Fatigue Tested Ti-6242 Alloy:
28.1 1.45 60.1 1.78 21.0 1.32 31.2 1.49 23.7 1.37 22.3 1.35 13.7 1.14 18.6 1.27 15.5 1.19 46.0 1.66 21.4 1.33 36.3 1.56 25.8 1.41 26.6 1.42 19.1 1.28 16.8 1.23 26.2 1.42 38.4 1.58 34.8 1.54 32.0 1.51 72.8 1.86 62.3 1.79 43.5 1.64 48.9 1.69 28.0 1.45 17.4 1.24 21.4 1.33 17.9 1.25 38.8 1.59 20.7 1.32
25. A transformation of data values by means of some mathematical function, such as or 1/x, can often yield a set of numbers that has “nicer” statistical properties than the original data. In particular, it may be possible to find a function for which the histogram of transformed values is more
24. The accompanying data set consists of observations on shear strength (lb) of ultrasonic spot welds made on a certain type of alclad sheet. Construct a relative frequency histogram based on ten equal-width classes with boundaries 4000, 4200, . . . . [The histogram will agree with the one
23. In a study of warp breakage during the weaving of fabric(Technometrics, 1982: 63), 100 specimens of yarn were tested. The number of cycles of strain to breakage was determined for each yarn specimen, resulting in the following data:86 146 251 653 98 249 400 292 131 169 175 176 76 264 15 364 195
22. How does the speed of a runner vary over the course of a marathon (a distance of 42.195 km)? Consider determining both the time to run the first 5 km and the time to run between the 35-km and 40-km points, and then subtracting the former time from the latter time. A positive value of this
21. The article cited in Exercise 20 also gave the following values of the variables y number of culs-de-sac and z number of intersections:y 1 0 1 0 0 2 0 1 1 1 2 1 0 0 1 1 011 z 1 8 6 1 1 5 3 0 0 4 4 0 0 1 2 1404 y 1 1 0 0 0 1 1 2 0 1 2 2 1 1 0 2110 z 0 3 0 1 1 0 1 3 2 4 6 6 0 1 1 8 335 y 1 5 0
19. The number of contaminating particles on a silicon wafer prior to a certain rinsing process was determined for each wafer in a sample of size 100, resulting in the following frequencies:Number of particles 01234 567 Frequency 1 2 3 12 11 15 18 10 Number of particles 8 9 10 11 12 13 14 Frequency
18. In a study of author productivity (“Lotka’s Test,” Collection Mgmt., 1982: 111–118), a large number of authors were classified according to the number of articles they had published during a certain period. The results were presented in the accompanying frequency distribution:Number of
17. Temperature transducers of a certain type are shipped in batches of 50. A sample of 60 batches was selected, and the number of transducers in each batch not conforming to design specifications was determined, resulting in the following data:21240132053313247023 04213113412322845131
16. The article cited in Example 1.2 also gave the accompanying strength observations for cylinders:6.1 5.8 7.8 7.1 7.2 9.2 6.6 8.3 7.0 8.3 7.8 8.1 7.4 8.5 8.9 9.8 9.7 14.1 12.6 11.2a. Construct a comparative stem-and-leaf display (see the previous exercise) of the beam and cylinder data, and then
15. A Consumer Reports article on peanut butter (Sept. 1990)reported the following scores for various brands:Creamy 56 44 62 36 39 53 50 65 45 40 56 68 41 30 40 50 56 30 22 Crunchy 62 53 75 42 47 40 34 62 52 50 34 42 36 75 80 47 56 62 Construct a comparative stem-and-leaf display by listing stems
14. The accompanying data set consists of observations on shower-flow rate (L/min) for a sample of n 129 houses in Perth, Australia (“An Application of Bayes Methodology to the Analysis of Diary Records in a Water Use Study,”J. Amer. Stat. Assoc., 1987: 705–711):4.6 12.3 7.1 7.0 4.0 9.2 6.7
13. Allowable mechanical properties for structural design of metallic aerospace vehicles requires an approved method for statistically analyzing empirical test data. The article“Establishing Mechanical Property Allowables for Metals”(J. of Testing and Evaluation, 1998: 293–299) used the
12. The accompanying specific gravity values for various wood types used in construction appeared in the article “Bolted Connection Design Values Based on European Yield Model” (J. of Structural Engr., 1993: 2169–2186):.31 .35 .36 .36 .37 .38 .40 .40 .40.41 .41 .42 .42 .42 .42 .42 .43 .44.45
11. Every score in the following batch of exam scores is in the 60s, 70s, 80s, or 90s. A stem-and-leaf display with only the four stems 6, 7, 8, and 9 would not give a very detailed description of the distribution of scores. In such situations, it is desirable to use repeated stems. Here we could
10. Consider the strength data for beams given in Example 1.2.a. Construct a stem-and-leaf display of the data. What appears to be a representative strength value? Do the observations appear to be highly concentrated about the representative value or rather spread out?b. Does the display appear to
4. Indicate the units for stems and leaves someplace in the display?
3. Record the leaf for every observation beside the corresponding stem value.
2. List possible stem values in a vertical column.
1. Select one or more leading digits for the stem values. The trailing digits become the leaves.
9. In a famous experiment carried out in 1882, Michelson and Newcomb obtained 66 observations on the time it took for light to travel between two locations in Washington, D.C. A few of the measurements (coded in a certain manner) were 31, 23, 32, 36, 2, 26, 27, and 31.a. Why are these measurements
8. The amount of flow through a solenoid valve in an automobile’s pollution-control system is an important characteristic.An experiment was carried out to study how flow rate depended on three factors: armature length, spring load, and bobbin depth. Two different levels (low and high) of each
7. A certain city divides naturally into ten district neighborhoods.How might a real estate appraiser select a sample of singlefamily homes that could be used as a basis for developing an equation to predict appraised value from characteristics such as age, size, number of bathrooms, distance to
6. The California State University (CSU) system consists of 23 campuses, from San Diego State in the south to Humboldt State near the Oregon border. A CSU administrator wishes to make an inference about the average distance between the hometowns of students and their campuses. Describe and discuss
5. Many universities and colleges have instituted supplemental instruction (SI) programs, in which a student facilitator meets regularly with a small group of students enrolled in the course to promote discussion of course material and enhance subject mastery. Suppose that students in a large
4.a. Give three different examples of concrete populations and three different examples of hypothetical populations.b. For one each of your concrete and your hypothetical populations, give an example of a probability question and an example of an inferential statistics question.
3. Consider the population consisting of all computers of a certain brand and model, and focus on whether a computer needs service while under warranty.a. Pose several probability questions based on selecting a sample of 100 such computers.b. What inferential statistics question might be answered
2. For each of the following hypothetical populations, give a plausible sample of size 4:a. All distances that might result when you throw a footballb. Page lengths of books published 5 years from nowc. All possible earthquake-strength measurements (Richter scale) that might be recorded in
1. Give one possible sample of size 4 from each of the following populations:a. All daily newspapers published in the United Statesb. All companies listed on the New York Stock Exchangec. All students at your college or universityd. All grade point averages of students at your college or university
=+1. The May 1, 2009, issue of The Montclarian reported the following sales figures ($ 1000s) for a sample of homes in Alameda, California, that were sold the previous month:590 815 575 608 350 1285 408 540 555 679
=+a. Calculate and interpret the sample mean and median.
=+b. Suppose the sixth observation had been 985 rather than 1285. How would the mean and median change?
=+c. Calculate a 20% trimmed mean by first trimming the two smallest and two largest observations.
=+d. Calculate a 15% trimmed mean.
=+2. Exposure to microbial products, especially endotoxin, may affect human vulnerability to allergic diseases. The article “Dust Sampling Methods for Endotoxin—An Essential but Underestimated Issue” (Indoor Air, 2006: 20–27) considered various issues associated with determining endotoxin
=+a. Determine the sample mean for each sample.How do they compare?
=+b. Determine the sample median for each sample.How do they compare? Why is the median for the urban sample so different from the mean for that sample?
=+c. Calculate the trimmed mean for each sample by deleting the smallest and largest observation.What are the corresponding trimming percentages? How do the values of these trimmed means compare to the corresponding means and medians?
=+3. The production of Bidri is a traditional craft of India.Bidriware (bowls, vessels, and so on) is cast from an alloy containing primarily zinc along with some copper. Consider the following observations on copper content (%) for a sample of Bidri artifacts in London’s Victoria and Albert
=+a. Construct a stem-and-leaf display of the data.How does it suggest that the sample mean and median will compare?
=+b. Calculate the values of the sample mean and median. Hint: ^xi 5 95.0.
=+c. By how much could the largest observation,
=+10.1, be increased without affecting the value of the sample median? By how much could this value be decreased without affecting the value of the sample median?
=+4. Suppose that after computing xn based on n sample observations x1, . . . , xn, another observation xn11 becomes available. What is the relationship between the mean of the first n observations, the new observation, and the mean of all n11 observations?The mean of the 10 observations in
=+5. In the article “Evaluation of Optimal Power Options for Base Transceiver Stations of Mobile Telephone Networks Cameroon” (Solar Energy, 2012: 2935–2949), researchers recorded site specific information for remote telecommunications stations throughout Cameroon. The following
=+ Without doing any computation, how do you think the sample mean compares to the sample median?What would you report as representative, or typical, of the daily energy demand for these stations? What prompted your choice?
=+6. Blood pressure values are often reported to the nearest 5 mmHg (100, 105, 110, and so on). Suppose the actual blood pressure values for nine randomly selected individuals are 118.6 127.4 138.4 130.0 113.7 122.0 108.3 131.5 133.2
=+a. What is the median of the reported blood pressure values?
=+b. Suppose the blood pressure of the second individual is 127.6 rather than 127.4 (a small change in a single value). How does this affect the median of the reported values? What does this say about the sensitivity of the median to rounding or grouping in the data?
=+7. An experiment to study the lifetime (hr) for a certain type of component involved putting ten components into operation and observing them for 100 hours. Eight of the components failed during that period, and those lifetimes were recorded.Denote the lifetimes of the two components still
=+57, 17, 1001, and 29. Which of the measures of center discussed in this section can be calculated, and what are the values of those measures? Note:
=+The data from this experiment is said to be “censored on the right”; patient lifetimes in medical experimentation are sometimes obtained in this way.
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