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applied statistics and probability for engineers

Questions and Answers of Applied Statistics And Probability For Engineers

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
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
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
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
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
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
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
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.
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
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.
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
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
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
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
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
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
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
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
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
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
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
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
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)
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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.
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
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
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
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”
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
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
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
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
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
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
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
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
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
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
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
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
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
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
13. Allowable mechanical properties for structural design of metallic aerospace vehicles requires an approved method for statistically analyzing empirical test data. The article“Establishing
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
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
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
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
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
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
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
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
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
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
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
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
=+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
=+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
=+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
=+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
=+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,
=+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
=+ 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?
=+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
=+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
=+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
=+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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