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Questions and Answers of
Statistics
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
A transformation of data values by means of some mathematical function, such as x or 1/x, can often yield a set of numbers that has "nicer" statistical properties than the original data.
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
The article "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
The accompanying frequency distribution on deposited energy (mJ) was extracted from the article "Experimental Analysis of Laser-Induced Spark Ignition of Lean Turbulent Premixed Flames" (Combustion
The following categories for type of physical activity involved when an industrial accident occurred appeared in the article "Finding Occupational Accident Patterns in the Extractive Industry Using a
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
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 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
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
The May 1, 2009, issue of The Montclarian reported the following home sale amounts for a sample of homes in Alameda, CA that were sold the previous month (1000s of $):590 815 575 608 350 1285 408 540
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
Mercury is a persistent and dispersive environmental contaminant found in many ecosystems around the world. When released as an industrial by-product, it often finds its way into aquatic systems
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
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
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
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
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
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.In Exercise 27The article "Study on the Life
A sample of n 5 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
a. If a constant c is added to each xi in a sample, yielding yi = xi + c, 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
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
Poly(3-hydroxybutyrate) (PHB), a semicrystalline polymer that is fully biodegradable and biocompatible, is obtained from renewable resources. From a sustainability perspective, PHB offers many
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
The article "Effects of Short-Term Warming on Low and High Latitude Forest Ant Communities" (Ecoshpere, May 2011, Article 62) described an experiment in which observations on various characteristics
Zinfandel is a popular red wine varietal produced almost exclusively in California. It is rather controversial among wine connoisseurs because its alcohol content varies quite substantially from one
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:a. Determine the value of the sample standard
A study of the relationship between age and various visual functions (such as acuity and depth perception) reported the following observations on the area of sclera lamina (mm2) from human optic
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
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 oxidation-induction time (min) for
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
A mutual fund is a professionally managed investment scheme that pools money from many investors and invests in a variety of securities. Growth funds focus primarily on increasing the value of
Grip is applied to produce normal surface forces that compress the object being gripped. Examples include two people shaking hands, or a nurse squeezing a patient's forearm to stop bleeding. The
Here is a stem-and-leaf display of the escape time data introduced in Exercise 36 of this chapter.a. Determine the value of the fourth spread. b. Are there any outliers in the sample? Any extreme
The following data on distilled alcohol content (%) for a sample of 35 port wines was extracted from the article "A Method for the Estimation of Alcohol in Fortified Wines Using Hydrometer
A sample of 20 glass bottles of a particular type was selected, and the internal pressure strength of each bottle was determined. Consider the following partial sample information: Median =
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
Blood cocaine concentration (mg/L) was determined both for a sample of individuals who had died from cocaine-induced excited delirium (ED) and for a sample of those who had died from a cocaine
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
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
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.
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.
A sample of 77 individuals working at a particular office was selected and the noise level (dBA) experienced by each individual was determined, yielding the following data ("Acceptable Noise Levels
Fretting is a wear process that results from tangential oscillatory movements of small amplitude in machine parts. The article "Grease Effect on Fretting Wear of Mild Steel" (Industrial Lubrication
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
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
Aortic stenosis refers to a narrowing of the aortic valve in the heart. The article "Correlation Analysis of Stenotic Aortic Valve Flow Patterns Using Phase Contrast MRI" (Annals of Biomed. Engr.,
a. For what value of c is the quantity ∑(xi - c)2 minimized? b. Using the result of part (a), which of the two quantities ∑(xi - )2 and ∑(xi - μ)2 will be smaller than the other (assuming
a. Let a and b be constants and let yi = axi + b for i = 1, 2, . . . , n. What are the relationships between and and between sx2 and sy2? b. A sample of temperatures for initiating a certain
A certain city divides naturally into ten district neighborhoods. How might a real estate appraiser select a sample of single-family homes that could be used as a basis for developing an equation to
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
Here is a description from Minitab of the strength data given in Exercise 13.a. Comment on any interesting features (the quartiles and fourths are virtually identical here). b. Construct a boxplot of
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 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
Specimens of three different types of rope wire were selected, and the fatigue limit (MPa) was determined for each specimen, resulting in the accompanying data.a. Construct a comparative boxplot, and
The three measures of center introduced in this chapter are the mean, median, and trimmed mean. Two additional measures of center that are occasionally used are the midrange, which is the average of
The authors of the article "Predictive Model for Pitting Corrosion in Buried Oil and Gas Pipelines" (Corrosion, 2009: 332-342) provided the data on which their investigation was based.a. Consider the
Consider a sample x1, x2,..., xn and suppose that the values of , s2, and s have been calculated. a. Let yi = xi - for i = 1,..., n. How do the values of s2 and s for the yi's compare to the
Let n and sn2 denote the sample mean and variance for the sample x1,..., xn and let n+1 and s2n+1 denote these quantities when an additional observation xn+1 is added to the sample.a. Show how n+1
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:
Lengths of bus routes for any particular transit system will typically vary from one route to another. The article "Planning of City Bus Routes" (J. of the Institution of Engineers, 1995: 211-215)
A study carried out to investigate the distribution of total braking time (reaction time plus accelerator-to-brake movement time, in ms) during real driving conditions at 60 km/hr gave the following
The sample data x1, x2,..., xn sometimes represents a time series, where xt = the observed value of a response variable x at time t. Often the observed series shows a great deal of random variation,
Consider numerical observations x1,..., xn. It is frequently of interest to know whether the xi s are (at least approximately) symmetrically distributed about some value. If n is at least moderately
Consider a sample x1, ... , xn with n even. Let L and U denote the average of the smallest n/2 and the largest n/2 observations, respectively. Show that the mean absolute deviation from the median
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
Four universities-1, 2, 3, and 4-are participating in a holiday basketball tournament. In the first round, 1 will play 2 and 3 will play 4. Then the two winners will play for the championship, and
a. In Example 2.10, identify three events that are mutually exclusive. b. Suppose there is no outcome common to all three of the events A, B, and C. Are these three events necessarily mutually
Jay and Maurice are playing a tennis match. In one particular game, they have reached deuce, which means each player has won three points. To finish the game, one of the two players must get two
A system consists of two components. The probability that the second component functions in a satisfactory manner during its design life is .9, the probability that at least one of the two components
The accompanying table categorizing each student in a sample according to gender and eye color appeared in the article "Does Eye Color Depend on Gender? It Might Depend on Who or How You Ask" (J. of
a. A certain company sends 40% of its overnight mail parcels via express mail service E1. Of these parcels, 2% arrive after the guaranteed delivery time (denote the event "late delivery" by L). If a
A company uses three different assembly lines-A1, A2, and A3-to manufacture a particular component. Of those manufactured by line A1, 5% need rework to remedy a defect, whereas 8% of A2's components
Disregarding the possibility of a February 29 birthday, suppose a randomly selected individual is equally likely to have been born on any one of the other 365 days. a. If ten people are randomly
A subject is allowed a sequence of glimpses to detect a target. Let Gi = {the target is detected on the ith glimpse}, with pi = P(Gi). Suppose the Giʹs are independent events, and write an
In a Little League baseball game, team A's pitcher throws a strike 50% of the time and a ball 50% of the time, successive pitches are independent of one another, and the pitcher never hits a batter.
Four engineers, A, B, C, and D, have been scheduled for job interviews at 10 a.m. on Friday, January 13, at Random Sampling, Inc. The personnel manager has scheduled the four for interview rooms 1,
A particular airline has 10 a.m. flights from Chicago to New York, Atlanta, and Los Angeles. Let A denote the event that the New York flight is full and define events B and C analogously for the
A personnel manager is to interview four candidates for a job. These are ranked 1, 2, 3, and 4 in order of preference and will be interviewed in random order. However, at the conclusion of each
Consider four independent events A1, A2, A3, and A4, and let pi = P(Ai) for i = 1,2,3,4. Express the probability that at least one of these four events occurs in terms of the pis, and do the same for
A box contains the following four slips of paper, each having exactly the same dimensions: (1) win prize 1; (2) win prize 2; (3) win prize 3; (4) win prizes 1, 2, and 3. One slip will be randomly
Show that if A1, A2, and A3 are independent events, then P(A1 | A2 ⋂ A3) = P(A1).
Consider randomly selecting a student at a large university, and let A be the event that the selected student has a Visa card and B be the analogous event for MasterCard. Suppose that P(A) = .6 and
A computer consulting firm presently has bids out on three projects. Let Ai = {awarded project i}, for i = 1, 2, 3, and suppose that P(A1) = .22, P(A2) = .25, P(A3) = .28, P(A1 ∩ A2) = .11, P(A1
Suppose that 55% of all adults regularly consume coffee, 45% regularly consume carbonated soda, and 70% regularly consume at least one of these two products. a. What is the probability that a
Consider the type of clothes dryer (gas or electric) purchased by each of five different customers at a certain store. a. If the probability that at most one of these purchases an electric dryer is
An individual is presented with three different glasses of cola, labeled C, D, and P. He is asked to taste all three and then list them in order of preference. Suppose the same cola has actually been
Let A denote the event that the next request for assistance from a statistical software consultant relates to the SPSS package, and let B be the event that the next request is for help with SAS.
A wallet contains five $10 bills, four $5 bills, and six $1 bills (nothing larger). If the bills are selected one by one in random order, what is the probability that at least two bills must be
Human visual inspection of solder joints on printed circuit boards can be very subjective. Part of the problem stems from the numerous types of solder defects (e.g., pad non-wetting, knee visibility,
Suppose that vehicles taking a particular freeway exit can turn right (R), turn left (L), or go straight (S). Consider observing the direction for each of three successive vehicles. a. List all
A certain factory operates three different shifts. Over the last year, 200 accidents have occurred at the factory. Some of these can be attributed at least in part to unsafe working conditions,
An insurance company offers four different deductible levels-none, low, medium, and high-for its homeowner's policyholders and three different levels-low, medium, and high-for its automobile
The route used by a certain motorist in commuting to work contains two intersections with traffic signals. The probability that he must stop at the first signal is .4, the analogous probability for
The computers of six faculty members in a certain department are to be replaced. Two of the faculty members have selected laptop machines and the other four have chosen desktop machines. Suppose that
Show that if one event A is contained in another event B (i.e., A is a subset of B), then P(A) ≤ P(B). For general A and B, what does this imply about the relationship among P(A ⋂ B), P(A) and
The three most popular options on a certain type of new car are a built-in GPS (A), a sunroof (B), and an automatic transmission (C). If 40% of all purchasers request A, 55% request B, 70% request C,
A certain system can experience three different types of defects. Let Ai (i = 1,2,3) denote the event that the system has a defect of type i. Suppose that P(A1) = .12 P(A2) = .07 P(A3) = .05 P(A1 ⋃
An academic department with five faculty members-Anderson, Box, Cox, Cramer, and Fisher-must select two of its members to serve on a personnel review committee. Because the work will be
In Exercise 5, suppose that any incoming individual is equally likely to be assigned to any of the three stations irrespective of where other individuals have been assigned. What is the probability
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