Questions and Answers of Statistics For Engineering And The Sciences

Refer to the Evolutionary Ecology Research (July 2003) study of the New Zealand bird population prior to European contact, Exercise 1.12. Two quantitative variables measured for each of The 116 bird
The methodology for conducting a stress analysis of newly designed timber structures is well known. However, few data are available on the actual or allowable stress for repairing damaged structures.
Geneticists at Duke University Medical Center have identified the E2F1 transcription factor as an important component of cell proliferation control (Nature, Sept. 23, 1993). The researchers induced
An experiment was conducted to investigate the precision of measurements of a saturated solution of iodine after an extended period of continuous stirring. The data shown in the table represent
The theoretical relationship between heat flux and temperature gradient for homogeneous materials is well known and described by a Fourier equation. However, this relationship does not hold for
Marine biochemists at the University of Tokyo studied the properties of crustacean skeletal muscles (The Journal of Experimental Zoology, Sept. 1993). It is well known that certain muscles contract
Let y̅1 be the mean of a random sample of n1 observations from a Poisson distribution with mean λ1, and let y̅2 be the mean of a random sample of n2 observations from a Poisson distribution with
Let y1, y2, . . . , yn denote a random sample from a uniform distribution with probability densitya. Show that y̅ is a biased estimator of θ, and compute the bias.b. Find V(y̅).c. What function of
Refer to the IEICE Transactions on Information & Systems (Jan. 2005) comparison of two methods of testing electronic circuits, Exercise 8.50. Recall that each of 11 circuits was tested using the
Refer to The International Journal of Pavement Engineering (Sept. 2004) field study of concrete stress at a newly constructed highway, Exercise 8.51. The variable of interest was slab top transverse
Refer to the AIChE Journal (Jan. 2005) study of a new method for modeling multicomponent transport of gases, Exercise 8.53. Recall that 12 gas mixtures were prepared and the viscosity of each mixture
For the Wilcoxon signed ranks test, show that where n is the number of nonzero differences that are ranked. n(n + 1) T + T = 2
For the special case n = 2, with no ties in the data (that is, no differences of zero), list the eight different ways in which the two absolute differences can be ranked. The number of arrangements,
For the special case described in Exercise 15.32, show thatFind T+ for each of the eight arrangements of the ranks listed in Exercise 15.31; use the fact that any particular arrangement will occur
Refer to the Behavioral Neuroscience (Feb. 2004) study of the drug scopolamine’s effects on memory for word-pair associates, Exercise 14.13. Recall that a completely randomized design with three
Refer to the Landscape Ecology Engineering (January 2013) investigation of the impact of soil scouring on the characteristics of overturned and uprooted trees, Exercise 14.12. Recall that a
Food Chemistry (Vol. 106, 2008) published a study of the quality of commercial eggs produced from different housing systems for chickens. Four housing systems were investigated: (1) cage, (2) barn,
Refer to the data on DDT levels of contaminated fish saved in the DDT file. Suppose you want to compare the DDT levels of the three species of fish: (1) channel catfish, (2) smallmouth buffalofish,
Refer to the American Journal of Science (Jan. 2005) study of the chemical makeup of buried tills (glacial drifts) in Wisconsin, Exercise 14.11. Recall that till specimens were obtained from five
Phosphoric acid is chemically produced by reacting phosphate rock with sulfuric acid. An important consideration in the chemical process is the length of time required for the chemical reaction to
Use the sum of an arithmetic progression to show that for the Kruskal–Wallis H test,where k is the number of probability distributions being compared and n is the total sample size. п(п + 1) T +
Refer to the Applied Animal Behavior Science (June 2010) study of stress in cows prior to slaughter, Exercise 14.22. In the experiment, recall that the heart rate (beats per minute) of a cow was
The consequences of performing verbal and spatial-imagery tasks on visual search while driving were studied and the results published in the Journal of Experimental Psychology: Applied (Mar. 2000).
Refer to the Journal of Food Engineering (September, 2013) study of the cooling performances fruit container designs, Exercise 14.23. Recall that three container types were investigated— Standard,
Refer to the Soldering & Surface Mount Technology (Vol. 13, 2001) study to compare four soldering methods, Exercise 14.24. Recall that a measure of plastic hardening (Nm/m2) was obtained for each
An optical mark reader (OMR) is a machine that is able to “read” pencil marks that have been entered on a special form. A manufacturer of OMRs believes its product can operate equally well in a
For data sets that contain many missing values, methods for estimating the missing values — called imputation algorithms — may be applied. In the journal, Data & Knowledge Engineering (March
Refer to the Analytical Chemistry (May 2010) evaluation of a new method of typing blood, Exercise 10.6. Recall that blood drops were applied to the paper and the rate of absorption (called blood
Refer to the Engineering Structures (July 2013) study of the characteristics of fresh concrete, Exercise 10.38. Recall that the researchers investigated the linear effect of time needed for pressure
Refer to the Mining Engineering (Oct. 2004) study of a new iron-making technology, Exercise 10.25. Recall that the carbon content produced in a pilot plant test was compared to that from laboratory
Refer to Exercise 10.14 and the model of the thermal performance of integral-fin tubes used in the refrigeration and process industries (Journal of Heat Transfer, Aug. 1990). The data in the table
Show that for the special case where n = 3, -1 ≤ rs ≤ 1. List each of the 3! × 3! = 36 different arrangements of the x and y rankings and compute rs for each.
Show that for the special case where n = 3, E (rs) = 0. Use the results of Theoretical Exercise 15.60 and the fact that any of the arrangements has a probability of 1/36 of occurring.
Refer to Exercise 14.81 and the study to compare the speeds of three drill bits. Recall that five drilling sites were randomly assigned to each bit, and the rate of penetration (RoP) in feet per hour
The biting rate of a particular species of fly was investigated in a study reported in the Journal of the American Mosquito Control Association (Mar. 1995). Biting rate was defined as the number of
Refer to Exercise 15.63. The effect of wind speeds in kilometers per hour (kph) on the biting rate of the flies on Stanbury Island, Utah, was investigated by exposing samples of volunteers to one of
Refer to Exercise 8.104 and the study to compare human real-time scheduling to an automated approach that utilizes computerized robots and sensing devices (IEEE Transactions, Mar. 1993). Recall that
The building specifications in a certain city require that the sewer pipe used in residential areas have a median breaking strength of more than 2,500 pounds per lineal foot. A manufacturer who would
Refer to the EPA study of mercury poisoning in Maine lakes, Exercise 10.77. Lakes can be classified into three trophic states: Oligotrophic lakes have a balance between decaying vegetation and living
Refer to Exercise 14.77 and the study to determine the effects of acid rain on the acidity of soils in a natural ecosystem. Recall that experimental plots were irrigated with acid rain at two pH
A serious, drought-related problem for farmers is the spread of aflatoxin, a highly toxic substance caused by mold, which contaminates field corn. In higher levels of contamination, aflatoxin is
Refer to the Journal of Engineering for Industry (Aug. 1993) study of an automated warehouse, Exercise 10.73. Recall that the number of vehicles was varied and the congestion time (total time one
Refer to the Microcomputers in Civil Engineering study of lateral drift in a building, Exercise 14.76. The data shown in the table are the lateral displacements (in inches) estimated by three
A hybrid algorithm for solving a polynomial zero–one mathematical program was presented in IIE Transactions (June 1990). The algorithm incorporates a mixture of pseudo-Boolean concepts and
A preliminary study was conducted to obtain information on the background levels of the toxic substance polychlorinated biphenyl (PCB) in soil samples in the United Kingdom (Chemosphere, Feb. 1986).
Synthetic fibers (such as rayon, nylon, and polyester) account for approximately 70% of all fibers used by American mills in their production of textile products. An experiment was conducted to
Refer to the Corrosion Science (Sept. 1993) study on the resistivity of an amorphous iron– boron–silicon alloy after crystallization, Exercise 10.74. Five alloy specimens were annealed at 700°C,
Refer to Exercise 10.79 and the straight-line model relating the mean shear strength E(y) of masonry joints to pre compression stress, x. To test this model, a series of stress tests were performed
The EPA wants to determine whether temperature changes in the ocean’s water caused by a nuclear power plant will have a significant effect on the animal life in the region. Recently hatched
Oil producers are interested in finding high-strength nickel alloys that are corrosion-resistant. Nickel alloys are especially susceptible to hydrogen embrittlement, a process that results when the
Agent Orange, the code name for a herbicide developed for the U.S. armed forces in the 1960s, was found to be extremely contaminated with TCDD, or dioxin. During the Vietnam War, an estimated 19
In zoology, the phenomenon of fish moving excessively from one confined area to another is known as excessive transitory migration (ETM). To investigate the ETM of guppy populations, 40 adult female
Throughout this chapter we have omitted the theoretical derivations of the null distributions of the various nonparametric test statistics. However, we can use computer simulation to derive
Follow the steps outlined in Exercise 15.81 to find the approximate critical value (at α = .05) of Spearman’s test for rank correlation for the case n = 10. In part a you will need to randomly
Refer to the Software Quality Professional (Nov. 2004) evaluation of the performance of a software engineering team’s performance at Motorola, Inc., Exercise 5.42. Recall that the variable of
Refer to the Mining Engineering (Oct. 2004) study of a new technology for producing high-quality iron nuggets directly from raw iron ore and coal, Exercise 10.25. For one phase of the study, the
Refer to the Analytical Chemistry (Dec. 15, 2009) study of a method—called high performance liquid chromatography—of determining the amount of drug in a tablet, Exercise 5.45. Assume the data in
In Quality Engineering (Vol. 25, 2013), statisticians at Minitab, Inc., applied control chart methodology to monitor the time between discharges of male patients with hospital-acquired urinary tract
Each month, the quality control engineer at a bottle manufacturing company randomly selects one finished bottle from the production process at 20 points in time (days) and records the weight of each
Molded-rubber expansion joints, used in heating and air-conditioning systems, are designed to have internal diameters of 5 inches. To monitor the manufacturing process, one joint was randomly
A rheostat knob, produced by plastic molding, contains a metal insert. The fit of this knob into its assembly is determined by the distance from the back of the knob to the far side of a pin hole. To
Various interventions are available for nurses to help relieve patients’ pain (e.g., heat/cold applications, breathing exercises, massage). The journal Research in Nursing & Health (Vol. 35,
A corporation that manufactures field rifles for the Department of Defense operates a production line that turns out finished firing pins. To monitor the process, an inspector randomly selects five
Refer to the production of molded-rubber expansion joints used in heating and air conditioning systems, Exercise 16.6. To monitor the mean of the manufacturing process, eight joints (rather than one
Refer to the manufacture of a rheostat knob, Exercise 16.7. To monitor the process mean, five knobs from each hour’s production were randomly sampled and the distance from the back of the knob to
Refer to Exercise 16.8, where the desired circuit path widths were .5 to .85 micron. The manufacturer sampled four CPU chips six times a day (every 90 minutes from 8:00 A.M. until 4:30 P.M.) for five
Refer to the Research in Nursing & Health (Vol. 35, 2012) study of the effectiveness of a pain intervention, Exercise 16.9. Recall that pain levels (measured on a 100-point scale) were recorded
Refer to Exercise 16.11. Suppose the inspector wants to monitor the variation in firing pin lengths with an R-chart.a. Locate the center line for the R-chart.b. Locate upper and lower control limits
Construct an R-chart for the data of Exercise 16.12 to monitor the variation in the diameters of the molded-rubber expansion joints produced by the manufacturing process. Does the process appear to
A soft-drink bottling company is interested in monitoring the amount of cola injected into 16-ounce bottles by a particular filling head. The process is entirely automated and operates 24 hours a
Refer to Exercise 16.16 and the hourly data collected by BPI consulting.a. Construct an R-chart for the data. Is the process variation in control?b. Round each measurement in the data set to a whole
Examine the sequences of points in parts a–f for any trends.a. + + – – – – – + + + + b. – + – – – + + – + + + +c. – – – – – + + + + + – – d. – +++++
Refer to the x̅- and R-charts, Exercises 16.8 and 16.17. Conduct a runs analysis to detect any trend in the process. Data from Exercise 16.8 The central processing unit (CPU) of a microcomputer is a
Refer to the Research in Nursing & Health (Vol. 35, 2012) study of the effectiveness of a pain intervention, Exercises 16.9 and 16.18. Conduct a runs analysis on both the x̅-chart and the
Refer to the x̅- and -charts, Exercises 16.11 and 16.20. Conduct a runs analysis to detect any trend in the process.Data from Exercise 16.11A corporation that manufactures field rifles for the
Refer to the x̅- and R-charts, Exercises 16.12 and 16.21. Conduct a runs analysis to detect any trend in the process.Data from Exercise 16.12Refer to the production of molded-rubber expansion joints
Refer to the x̅- and R-charts, Exercises 16.15 and 16.24. Conduct a runs analysis to detect any trend in the process.Data from Exercise 16.15Refer to the manufacture of a rheostat knob, Exercise
Prestressed concrete cylinder pipe (PCCP) is a rigid pipe designed to take optimum advantage of the tensile strength of steel and the compressive strength and corrosive-inhibiting properties of
A manufacturer of computer terminal fuses wants to establish a control chart to monitor the production process. Each hour, for a period of 25 hours, during a time when the process is known to be in
An electronics company manufactures several types of cathode-ray tubes on a mass production basis. To monitor the process, 50 tubes of a certain type were randomly sampled from the production line
The number of imperfections (scratches, chips, cracks, and blisters) in manufactured custom wood cabinet panels is important both to the customer and to the custom builder. To monitor the
A quality control study was undertaken by the supervisor of a group of computer programmers. For each of the last 20 days, 25 program modules were randomly selected and inspected for coding errors.
Refer to Exercise 16.44. The numbers of alignment errors observed for each of the next 25 aircraft produced are shown in the table below.a. Add these 25 points to the c-chart of Exercise 16.44. Does
Electronics products (e.g., backplanes, complex motherboards for server systems, etc.) can have as many as thousands of opportunities for defects per printed circuit board (PCB). The defects can be
University of Waterloo (Canada) statistician S. H. Steiner applied control chart methodology to the manufacturing of a horseshoe-shaped metal fastener called a robotics clamp (Applied Statistics,
Refer to Exercise 16.11. Use all the sample information to find a 95% tolerance interval for 90% of the firing pin lengths. Assume the distribution of pin lengths is approximately normal.Data from
J. Namias used the techniques of statistical quality control to determine when to conduct a search for specific causes of consumer complaints at a beverage company (Journal of Marketing Research,
Refer to Exercise 16.15. Find a 99% tolerance interval for at least 95% of the distance measurements assuming each of the following:a. A normal distributionb. A non normal distributionData from
Many hand tools used by mechanics involve attachments that fit into sockets (e.g., a socket wrench). In the manufacturing of the tools, specifications require that the inside diameter of the socket
Refer to the Mining Engineering (Oct. 2004) study of a new technology for producing high quality iron nuggets, Exercise 16.2. The data on percent carbon change in produced nuggets for 33 time
A machine fills boxes with bran flakes. The target weight for the filled boxes is 24 ounces. To monitor the process, five boxes are randomly sampled from each day’s production and weighed. The data
A precision parts manufacturer produces bolts for use in military aircraft. The company sampled four consecutively produced bolts each hour on the hour for 25 consecutive hours and measured the
Consider a sampling plan with sample size n = 15 and acceptance number α = 1.a. Calculate the probability of lot acceptance for fractions defective p = .1, .2, .3, .4, and .5. Sketch the operating
Consider a sampling plan with sample size n = 5 and acceptance number a = 0.a. Calculate the probability of lot acceptance for fractions defective p = .1, .3, and .5. Sketch the operating
The tensile strengths of wires in a certain lot of size 400 are specified to exceed 5 kilograms. Consider an acceptance sampling plan based on a sample of n = 10 wires and acceptance number α = 1.a.
Refer to Exercise 16.61. Find the appropriate MIL-STD-105D normal (level) general inspection sampling plan for a lot size of 400 wires and an AQL of 2.5%.Data from Exercise 16.61The tensile strengths
Find the appropriate MIL-STD- 105D general inspection sampling plan for a lot size of 5,000 items and an AQL of 4% under each of the following inspection categories:a. Reduced (I) inspection levelb.
One of the operations in a plant consists of thread-grinding a fitting for an aircraft hydraulic system. To monitor the process, a production supervisor randomly sampled five fittings for each hour,
Suppose the process for manufacturing electrical shafts is in control. At the end of each hour, for a period of 20 hours, the manufacturer randomly selects one shaft and measures the diameter. The
Specifications require the nickel content of manufactured stainless steel hydraulic valves to be 13% by weight. To monitor the production process, four valves were selected from the production line

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