Questions and Answers of Statistics For Engineering And The Sciences

A craps player who has experienced a long run of bad luck at the craps table wants to test whether the casino dice are “loaded,” i.e., whether the proportion of “sevens” occurring in many
Pesticides applied to an extensively grown crop can result in inadvertent areawide air contamination. Environmental Science & Technology (Oct. 1993) reported on air deposition residues of the
A large steel corporation conducted an experiment to compare the average iron contents of two consignments of lumpy iron ore. In accordance with industrial standards, n increments of iron ore were
The Journal of Environmental Engineering (Feb. 1986) reported on a heat transfer model designed to predict winter heat loss in wastewater treatment clarifiers. The analysis involved a comparison of
Jitter is a term used to describe the variation in conduction time of a modular pulsed-water power system. Low throughput jitter is critical to successful waterline technology. An investigation of
By law, all new cars must be equipped with both driver-side and passenger side safety air bags. There is concern, however, over whether air bags pose a danger for children sitting on the Passenger
According to a study conducted by the California Division of Labor Research and Statistics, roofing is one of the most hazardous occupations. Of 2,514 worker injuries that caused absences for a full
In Ireland, the majority of commercial forests are located in remote areas on predominantly peat soils. These roads exhibit rapid deterioration when traversed by logging vehicles or other heavy
Chemical engineers at the University of Murcia (Spain) conducted a series of experiments to determine the most effective membrane to use in a passive sampler (Environmental Science & Technology,
Let y1, y2, y3, . . . , yn, represent a random sample of size n selected from a normal probability distribution with unknown mean μ and variance σ2 = 1. Then the sample mean, y̅ , has a normal
Let y1, y2, y3, . . . , yn, represent a random sample of size n selected from a Poisson probability distribution with unknown mean λ. Let X represent the sum of the Poisson values, X = ∑Yi
In fields that require high precision surface height maps, white light interferometry (WLI) has become the standard inspection tool. Because WLI generates two-dimensional height profiles, and
Refer to the American Journal of Science (Jan. 2005) study of the chemical makeup of buried glacial drifts (or tills) in Wisconsin, Exercise 7.64. The data on the ratios of aluminum (Al) to beryllium
Refer to the Environmental Science & Technology (Jan. 2005) study of contaminated well sites located near a New Jersey gasoline service station, Exercise 7.29. The data (parts per billion) on the
Refer to the Composites Fabrication Magazine (Sept. 2004) study of the strength of fiber-reinforced polymer (FRP) composite materials, Exercise 2.47. Recall that 10 specimens of pultruded FRP strips
When determining the sample size required to estimate p, show that the sample size n is largest when p = .5.
Refer to the JOM (Jan. 2003) comparison of a new high-strength RAA aluminum alloy to the current strongest aluminum alloy, Exercise 7.43. Suppose the researchers want to estimate the difference
Refer to the Environmental Science & Technology (Jan. 2005) study of methyl tert-butyl ether (MTBE) contamination in New Hampshire wells, Exercise 7.66. How many public and how many private wells
Refer to Exercise 7.35. Suppose that we want to estimate the average decay rate of fine particles produced from oven cooking or toasting to within .04 with 95% confidence. How large a sample should
Refer to the Journal of Chemical Ecology (March 2013) study of the effectiveness of pheromones to attract two different strains of fall armyworms, Exercise 7.68. Recall that both corn-strain and
Refer to the Computers & Security (July 2013) study of security issues with Microsoft products, Exercise 7.58. Determine the number of security bulletins to be sampled in order for Microsoft to
Refer to The International Journal of Robotics Research (Dec. 2004) algorithm for estimating the sensor motion of a robotic arm, Exercise 2.64. A key variable is the error of estimating arm rotation
Refer to the Journal of Food Engineering (Sep. 2013) study of the characteristics of fried sweet potato chips, Exercise 7.78. Recall that a sample of 6 sweet potato slices fried at 130º using a
Refer to the Landscape & Ecology Engineering (Jan. 2013) study of hippopotamus grazing patterns in Kenya, Exercise 7.41. Recall that plots of land were sampled in two areas — a national reserve
Refer to Exercise 7.39 and the Analytical Chemistry (Dec. 15, 2009) study in which scientists used high-performance liquid chromatography to determine the amount of drug in a tablet. Recall that 25
Refer to the Environmental Geology (Vol. 58, 2009) simulation study of how far a block from a collapsing rock wall will bounce down a soil slope, Exercise 2.29. Rebound lengths (in meters) were
The Occupational Safety & Health Administration requires companies that handle hazardous chemicals to complete material safety data sheets (MSDS). These MSDS have been criticized for being too
Use the pivotal statistic T given in Exercise 7.22 to derive a (1 - α)100% small-sample confidence interval for (μ1 - μ2).Data from Exercise 7.22Refer to Exercises 7.20 and 7.21. The pooled
Refer to Exercises 7.20 and 7.21. The pooled estimator of the common variance σ2 is given byShow thathas a Student’s T distribution with (n1 + n2 - 2) df. Recall that T = Z/√x2/v has a
Let y1, y2, . . . , yn be a random sample of n observations from an exponential distribution with mean β. Derive a large-sample confidence interval for β. Start with the pivotal statisticand show
Suppose the random variable Y has a binomial distribution with parameters n and p.a. Show that p̂ = y/n is an unbiased estimator of p.b. Find the variance of p̂.
Let y1, y2, y3, . . . , yn be a random sample from a Poisson distribution with mean λ, i.e., E (yi) = λ, i = 1, 2, .... n. Consider four estimators of λ:a. Which of the four estimators are
Let y1, y2, y3 be a random sample from an exponential distribution with mean θ, i.e., E (yi) = θ, i = 1, 2, 3. Consider three estimators of θ:a. Show that all three estimators are
The continuous random variable Y is said to have a lognormal distribution with parameters μ and σ if its probability density function, f(y), satisfiesShow that X = ln (Y) has a normal distribution
Use Theorem 6.7 to draw a random sample of n = 5 observations from a population with probability density function given by 2ye- if 0 < y < f(y) : elsewhere
Use Theorem 6.7 to draw a random sample of n = 5 observations from a population with probability density function given by S2(y – 1) if 1 sy < 2 f(y) lo elsewhere
Let Y1 and Y2 be a random sample of n = 2 observations from a normal distribution with mean μ and variance σ2. a. Show thathas a standard normal distribution. b. Given the result in part
The lifetime Y of an electronic component of a laptop computer has a Rayleigh density, given byFind the probability density function for W = Y2, and identify the type of density function. 2y -3/B if
Let X and Y be two continuous random variables with joint density f(x, y). Show that f2(y Ι x)f1(x) = f1(x Ι y)f2(y)
The waiting time Y until delivery of a new component for a data-processing unit is uniformly distributed over the interval from 1 to 5 days. The cost C (in hundreds of dollars) of this delay to the
Refer to the problem of transporting neutral particles in a nuclear fusion reactor, described in Exercise 3.36. Recall that particles released into a certain type of evacuated duct collide with the
Let Y̅1 and Y̅2 be the means of independent random samples of sizes n1 and n2 selected from normally distributed populations with parameters (μ1, σ2) and (μ2, σ2), respectively. Ifshow
University of Maryland engineers investigated the life lengths of several commercial avionics, including flight control systems, autopilots, flight director systems, and symbol generators. (The
Use the results of Exercise 4.39 and the fact thatto find E(Y2) for a binomial random variable. ELY(Y – 1)] - E(Y² – Y) = E(Y²) – E(Y) = E(Y?) – H
Prove Theorem 4.3.
Prove Theorem 4.2. The proof follows directly from Definition 4.5.
Prove Theorem 4.1. Use the fact that ∑all P(y) = 1
Digital signal and image processing (DSIP) has a wide variety of applications, including entertainment (video on demand), telemedicine, security/surveillance, military target recognition, wireless
Refer to the Human Factors (Dec. 1988) study of color brightness as a body orientation clue, Exercise 7.65. Ninety college students, reclining on their backs in the dark, were disoriented when
The American Association of Engineering Societies (AAES) hired Harris Interactive to conduct a survey of the American public’s knowledge of and interest in engineering. (AAES/Harris Poll
Because of erratic rainfall patterns and low water-holding capacities of soils in Florida, supplemental irrigation is required for producing most crops. A research team has developed five alternative
For the multinomial probability distribution, show thatCov (ni, nj) = -npipjFirst show that E (ninj) = n(n - 1)pipj.
Refer to the American Association of Engineering Societies (AAES) survey of the public’s knowledge of engineering, Exercise 9.7. Responses to the statement, “Engineers are responsible for
A group of environmental engineers are studying mushroom-like slime molds as a potential food source for insects. (Journal of Natural History, May 2010.) In particular, they investigated which of six
Refer to the Human Factors (Dec. 1988) study of orientation clues, Exercise 9.6. Conduct a test to compare the proportions of subjects that fall in the three disk-orientation categories. Assume you
Geneticists at Australian National University are studying whether the cognitive effects of Alzheimer’s disease can be detected at an early age (Neuropsychology, Jan. 2007.) One portion of the
A contract engineer at DuPont Corp. studied the rate at which a spilled volatile liquid will spread across a surface (Chemical Engineering Progress, Jan. 2005). Assume 50 gallons of methanol spills
A study was conducted to model the thermal performance of integral-fin tubes used in the refrigeration and process industries (Journal of Heat Transfer, Aug. 1990). Twenty-four specially manufactured
Show that Note thatsince Σ(xi - x̅) = 0. T(x - I) Bo = y - Bx = 2
An innovative new ironmaking technology (called ITmk3) produces high-quality iron nuggets directly from raw iron ore and coal. Mining Engineering (Oct. 2004) published the results of pilot tests
Refer to the Wind Engineering (Jan. 2004) study of two types of timber radiata pine and hoop pine—used in high-efficiency small wind turbine blades, Exercise 10.16. Data on stress (y) and the
The standard method of determining the water content of soil involves the removal of the soil and estimation of soil volume. Forest Engineering (July 1999) presented a method that does not require
Use the result of Exercise 10.51 to show that rVn - 2 s/VSSx
A general proof of the fact that χ 2 possesses approximately a chi-square sampling distribution when n is large is beyond the scope of this text. However, it can be justified for the binomial case
In Tectonics (Oct. 2004), geologists published their research on the formation of oroclines (curved mountain belts) in the central Appalachian mountains. A comparison was made of two nappes (sheets
Refer to the Environmental Science & Technology (Jan. 2005) study of methyl tert-butyl ether (MTBE) contamination in public and private New Hampshire wells, Exercise 2.12. Recall that data on
Refer to the AAES survey of the American public’s knowledge of and interest in engineering, Exercise 9.7. Another survey question asked, “What media sources do you use to follow stories about
The PROMISE Software Engineering Repository, hosted by the School of Information Technology and Engineering, University of Ottawa, provides researchers with data sets for building predictive software
According to the Highway Loss Data Institute (HLDI), “hybrid [automobiles] have a safety edge over their conventional twins when it comes to shielding their occupants from injuries in crashes”.
Westinghouse Electric Company has experimented with different means of evaluating the performance of solder joint inspectors. One approach involves comparing an individual inspector’s
When bonding teeth, orthodontists must maintain a dry field. A new bonding adhesive (called Smart bond) has been developed to eliminate the necessity of a dry field. However, there is concern that
Seldane-D, produced by Marion Merrell Dow, Inc., is an over-the-counter drug designed to relieve sneezing, nasal congestion, and other symptoms of allergic rhinitis. General adverse effects of
Refer to the Disasters (Vol. 28, 2004) study of the effects of a tropical cyclone on the quality of drinking water on a remote Pacific island, Exercise 1.11. One part of the study evaluated the
Refer to the Trends in Biomaterials & Artificial Organs (Jan. 2003) study of a new bonding adhesive for teeth, Exercise 9.33. Recall that the new adhesive (called Smart bond) was compared to the
Refer to the study on predicting defects in software code written in C language for a NASA spacecraft instrument, Exercise 9.29. The SPSS contingency table for the two categorical variables, actual
Refer to the NAWIC Journal of Professional Issues in Engineering Education & Practice (April 2013) study of the job satisfaction of members of the National Association of Women in Construction
A traffic study found that of 972 automobiles entering a busy intersection during the period from 4 P.M. to 7 P.M., 357 turned left, 321 turned right, and 294 drove straight through the
Compressed work weeks are defined as “alternative work schedules in which a trade is made between the number of hours worked per day, and the number of days worked per week, in order to work the
Researchers at the Oak Ridge (Tennessee) National Laboratory have developed an algorithm to estimate the numbers of expected and excess cases of thyroid cancer occurring in the lifetime of those
Four pesticides used in dormant California orchards are chlorpyrifos, diazinon, methidathion, and parathion. Environmental Science & Technology (Oct. 1993) reported the number of applications of
Refer to the Nature (Sept. 1993) study of animal and plant species “hot spots” in Great Britain, Exercise 3.81. A hot spot is defined as a 10-km square area that is species-rich, i.e., that is
Refer to the survey of agricultural engineers, Exercise 9.8. Do the data present sufficient evidence to indicate a preference for one or more of the five water-management strategies? Test using α =
Dear enemy recognition (DER) is the term used by naturalists and ecologists for the aggressive behavior of birds, mammals, and ants when their territorial boundaries are violated by one of their own
Video engineers use time compression to shorten the time required for broadcasting a television commercial. But can shorter commercials be effective? To answer this question, 200 college students
A decision support system (DSS) is a computerized system designed to aid in the management and analysis of large data sets. Ideally, a DSS should include four components: (1) a data extraction
An experiment was conducted to compare the fidelity and selectivity of radio receivers. Thirty receivers were tested and classified as low or high in each of the two categories. Do the data in the
A waterborne nonbacterial gastroenteritis outbreak occurred in Colorado as a result of a long-standing filter deficiency and malfunction of a sewage treatment plant. A study was conducted to
Does the propensity for worker injuries depend on the length of time that a worker has been on the job? An analysis of 714 worker injuries by one manufacturer gave the results shown in the table for
The scarce and essential metal, manganese, has been found in abundance in nodules on the deep seafloor. To investigate the relationship between the magnetic age of Earth’s crust on the ocean floor
The equation for a straight line (deterministic) is y = β̂o + β̂1xIf the line passes through the point (0, 1), then x = 0, y = 1must satisfy the equation. That is, 1 = βo +
In each case find the equation of the line that passes through the points. Graph each line.a. (0, 2) and (2, 6)b. (0, 4) and (2, 6)c. (0, -2) and (-1, -6)d. (0, -4) and (3, -7)
Plot the following lines; give the y-intercept and slope of each. a. y = 3 + 2xb. y = 1 + xc. y = - 2 + 3xd. y = 5xe. y = 4 - 2x
In Analytical Chemistry (May 2010), chemical engineers tested a new method of typing blood using lost cost paper. Blood drops were applied to the paper and the rate of absorption (called blood
Pipes used in a water distribution network are susceptible to breakage due to a variety of factors. When pipes break, engineers must decide whether to repair or replace the broken pipe. A team of
Accurate measurements of rainfall are critical for many hydrological and meteorological projects. Two standard methods of monitoring rainfall use rain gauges and weather radar. Both, however, can be
A common byproduct of burning municipal solid waste is bottom ash. The use of bottom ash waste in the building of asphalt roads was investigated in the Journal of Civil Engineering and Construction
The maximum likelihood estimator of the mean m of a normal distribution is the sample mean . Consider the model E(y) = μ. Show that the least-squares estimator of μ is also y̅. Minimize SSE =
Consider the pair of simultaneous linear equations:Derive the formulas for the least-squares estimates, β̂o and β̂1. nBo + BiE = Ey Bo Ex + BI E = Exyi
We showed in Example 10.2 that β̂1, the least-squares estimator of the slope b1, is an unbiased estimator of β1, i.e., E(β̂1) = β1. Use the result from Exercise 10.17 to show that E(β̂o) =
In Exercise 10.19, you showed that β̂o could be written as a linear function of independent random variables. Use Theorem 6.8 to show that THEOREM 6.8 The Expected Value E(C) and variance V(O* of a

Showing 100 - 200 of 1103