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mathematics
statistics

Statistics 12th Edition James T. McClave, Terry T Sincich - Solutions

Calculate the range, variance, and standard deviation for the following samples: a. 4, 2, 1, 0, 1 b. 1, 6, 2, 2, 3, 0, 3 c. 8, −2, 1, 3, 5, 4, 4, 1, 3 d. 0, 2, 0, 0, −1, 1, −2, 1, 0, −1, 1, −1, 0, −3, −2, −1, 0, 1
Using only integers between 0 and 10, construct two data sets with at least 10 observations each such that the two sets have the same range, but different means. Construct a dot plot for each of your data sets, and mark the mean of each data set on its dot plot.
Compute s2, and s for each of the data sets listed. Where appropriate, specify the units in which your answer is expressed. a. 3, 1, 10, 10, 4 b. 8 feet, 10 feet, 32 feet, 5 feet c. −1, −4, −3, 1, −4, −4 d. 1/5 ounce, 1/5 ounce, 1/5 ounce, 2/5 ounce, 1/5 ounce, 4/5 ounce
Refer to the Reading in a Foreign Language (Apr. 2004) experiment to improve the Japanese reading comprehension levels of 14 University of Hawaii students, presented in Exercise. The data on number of books read and grade for each student are saved in the JAPANESE file. a. Find the range,
Refer to the Environmental Geology (Vol. 58, 2009) study of how far a block from a collapsing rock wall will bounce, Exercise. The rebound lengths (meters) for a sample of 13 rock bounces are reproduced in the table below and saved in the ROCKFALL file.a. Compute the range of the 13 rebound
Refer to Exercise and Fortune’s list of the 50 most powerful women in America. The data are stored in the WPOWER50 file. a. Find the range of the ages of these 50 women. b. Find the variance of the ages of these 50 women. c. Find the standard deviation of the ages for these 50 women. d.
Refer to Exercise and the U.S. Energy Information Administration’s data on the number of nuclear power plants operating in each of 20 states. The data are saved in the NUCLEAR file. a. Find the range, variance, and standard deviation of this data set. b. Eliminate the largest value from the
To what kind of data sets can Chebyshev’s rule be applied? How about the empirical rule?
For any set of data, what can be said about the percentage of the measurements contained in each of the following intervals? a. x-bar – s to x-bar + s b. x-bar – 2s to x-bar + 2s c. x-bar – 3s to x-bar + 3s
The following is a sample of 25 measurements. The data are saved in the LM2_94 file.a. Compute x-bar, s2, and s for this sample. b. Count the number of measurements in the intervals x-bar ± s, x-bar 2s, and x-bar 3s. Express each count as a percentage of the total number of measurements. c.
Refer to the Fortune list of the 50 most powerful women in America, saved in the WPOWER50 file. In Exercise you found the mean age of the 50 women in the data set, and in Exercise you found the standard deviation. Use these values to form an interval that will contain at least 75% of the ages in
Refer to Exercise and the Centers for Disease Control and Prevention listing of the sanitation scores for 186 cruise ships. The data are saved in the SHIPSANIT file. a. Find the mean and standard deviation of the sanitation scores. b. Calculate the intervals x-bar ± s, x-bar ± 2s, and x-bar ±
Researchers at Georgia State University investigated the personality characteristics of drug dealers in order to shed light on their motivation for participating in the illegal drug market (Applied Psychology in Criminal Justice, Sept. 2009). The sample consisted of 100 convicted drug dealers who
Many middle schools have initiated a program that provides every student with a free laptop (notebook) computer. Student usage of laptops at a middle school that participates in the initiative was investigated in American Secondary Education (Fall 2009). In a sample of 106 students, the researchers
Refer to the Evolutionary Ecology Research (July 2003) study of the patterns of extinction in the New Zealand bird population, presented in Exercise 2.20 (p. 37). Consider the data on the egg length (measured in millimeters) for the 132 bird species saved in the NZBIRDS file. a. Find the mean and
A study published in Applied Psycholinguistics (June 1998) compared the language skills of young children (16€“30 months old) from low-income and middle-income families. A total of 260 children€”65 in the low-income and 195 in the middle-income group€”completed the Communicative
Recall the American Heart Association Conference (Nov. 2005) study to gauge whether animal-assisted therapy can improve the physiological responses of heart failure patients. A team of nurses from the UCLA Medical Center randomly divided 76 heart patients into three groups. Each patient in group T
For a quantitative data set a. What is the 50th percentile called? b. Define QL. c. Define Qu.
For mound-shaped data, what percentage of measurements have a z -score between – 2 and 2?
Compare the z -scores to decide which of the following x values lie the greatest distance above the mean and the retest distance below the mean: a. x = 100, µ = 50, σ = 25 b. x = 1, µ = 4, σ = 1 c. x = 0, µ = 200, σ = 100 d. x = 10, µ = 5, σ = 3
According to the National Center for Education Statistics (2009), scores on a mathematics assessment test for United States eighth graders have a mean of 283, a 25th percentile of 259, a 75th percentile of 308, and a 90th percentile of 329. Interpret each of these numerical descriptive measures.
Refer to the sanitation levels of cruise ships presented in Exercise and saved in the SHIPSANIT file. a. Give a measure of relative standing for the Nautilus Explorer’s score of 74. Interpret the result. b. Give a measure of relative standing for the Rotterdam’s score of 92. Interpret the
Refer to the Reading in a Foreign Language (Apr. 2004) experiment to improve the Japanese reading comprehension levels of 14 University of Hawaii students, presented in Exercise. The data on number of books read and grade for each student are saved in the JAPANESE file. a. Find the mean and
The U.S. Environmental Protection Agency (EPA) sets a limit on the amount of lead permitted in drinking water. The EPA Action Level for lead is .015 milligram per liter (mg/L) of water. Under EPA guidelines, if 90% of a water system’s study samples have a lead concentration less than .015 mg/L,
In a study of how external clues influence performance, psychology professors at the University of Alberta and Pennsylvania State University gave two different forms of a midterm examination to a large group of introductory psychology students. The questions on the exam were identical and in the
Refer to the Southern Economic Journal (Apr. 2008) study of Ph.D. programs in economics, Exercise. The authors also made the following observation: “A noticeable feature of this skewness is that distinction between schools diminishes as the rank declines. For example, the top-ranked school,
With mound-shaped data, what proportion of the measurements have z-scores between –3 and 3?
Suppose a data set consisting of exam scores has a lower quartile QL = 60, a median M = 75, and an upper quartile QU = 85. The scores on the exam range from 18 to 100. Without having the actual scores available to you, construct as much of the box plot as possible.
Consider the following two sample data sets, saved in the LM2_132 file:a. Construct a box plot for each data set.b. Identify any outliers that may exist in the two data sets.
Refer to the Current Allergy & Clinical Immunology study of the use of local anesthetics in dentistry, presented in Exercise. Recall that the mean number of units (ampoules) of local anesthetics used per week by dentists was 79, with a standard deviation of 23. Consider a dentist who used 175 units
Tills are glacial drifts consisting of a mixture of clay, sand, gravel, and boulders. Engineers from the University of Washington€™s Department of Earth and Space Sciences studied the chemical makeup of buried tills in order to estimate the age of the glacial drifts in Wisconsin (American
Refer to the data on sanitation levels of cruise ships, presented in Exercise. These data are saved in the SHIPSANIT file. a. Use the box plot method to detect any outliers in the data. b. Use the z-score method to detect any outliers in the data. c. Do the two methods agree? If not, explain why.
Refer to the Environmental Geology (Vol. 58, 2009) study of how far a block from a collapsing rockwall will bounce, Exercise. The computer-simulated rebound lengths (in meters) for 13 block-soil impact marks left on a slope from an actual rock-fall (saved in the ROCKWELL file) are reproduced in the
Refer to the Archives of Pediatrics and Adolescent Medicine (Dec. 2007) study of honey as a remedy for coughing, Exercise. Recall that coughing improvement scores were recorded for children in three groups: the over-the-counter cough medicine dosage (DM) group, the honey dosage group, and the
A city librarian claims that books have been checked out an average of seven (or more) times in the last year. You suspect he has exaggerated the checkout rate (book usage) and that the mean number of checkouts per book per year is, in fact, less than seven. Using the computerized card catalog, you
Construct a scatterplot for the data in the table that follows. Do you detect a trend?
The Colorado Rockies play their major league home baseball games in Coors Field, Denver. Each year, the Rockies are among the leaders in team batting statistics (e.g., home runs, batting average, and slugging percentage). Many baseball experts attribute this phenomenon to the €œthin
Zoologists at the University of Western Australia conducted a study of the feeding behavior of black bream (a type of fish) spawned in aquariums. (Brain, Behavior and Evolution, April 2000). In one experiment, the zoologists recorded the number of aggressive strikes of two black bream feeding at
Refer to the American Journal of Physics (June 2010) study of sound waves in a spherical cavity, Exercise. The frequencies of sound waves (estimated using a mathematical formula) resulting from the first 24 resonances (echoes) after striking a basketball with a metal rod are reproduced in the table
In Geoforum (Vol. 37, Nov. 2006), Simon Fraser University professor Nicholas Blomley assessed whether the price of a geography journal is correlated with quality. He collected pricing data (cost for a 1-year subscription, in U.S. dollars) for a sample of 28 geography journals. In addition to cost,
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). Suppose that 50 gallons of methanol spills onto a level surface outdoors. The engineer uses derived empirical formulas (assuming a state
Construct a relative frequency histogram for the data summarized in the following table:
Refer to Exercise. For parts a–d, determine whether the three measurements 50, 70, and 80 are outliers.In exercisea. μ = 60, σ = 10b. μ = 60, σ = 5c. μ = 40, σ = 10d. μ = 40, σ = 100
For each of the data sets in parts a–d, compute x-bar, s2, and s. a. 13, 1, 10, 3, 3 b. 13, 6, 6, 0 c. 1, 0, 1, 10, 11, 11, 15 d. 3, 3, 3, 3 e. For each of the data sets in parts a–d, form the interval x-bar ± 2s and calculate the percentage of the measurements that fall into that
Chance (Spring 2000) reported on a study to estimate the number of pennies required to fill a coin collector’s album. The data used in the study were obtained by noting the mint date on each of a sample of 2,000 pennies. The distribution of mint dates is summarized in the following table: Mint
Each year, the National Highway Traffic Safety Administration (NHTSA) crash tests new car models to determine how well they protect the driver and front-seat passenger in a head-on collision. The NHTSA has developed a €œstar€ scoring system for the frontal crash test, with
The Condor (May 1995) published a study of competition for nest holes among collared flycatchers, a bird species. The authors collected the data for the study by periodically inspecting nest boxes located on the island of Gotland in Sweden. The nest boxes were grouped into 14 discrete locations
Refer to the Environmental Science & Technology (Jan. 2005) study of the factors related to MTBE contamination in 223 New Hampshire wells, presented in Exercise. The data are saved in the MTBE file. Two of the many quantitative variables measured for each well are the pH level (standard units) and
The distribution of scores on a nationally administered college achievement test has a median of 520 and a mean of 540. a. Explain why it is possible for the mean to exceed the median for this distribution of measurements. b. Suppose you are told that the 90th percentile is 660. What does this
Archaeologists gain insight into the social life of ancient tribes by measuring the distance (in centimeters) of each artifact found at a site from the €œcentral hearth€ (i.e., the middle of an artifact scatter). A graphical summary of these distances, in the form of a
Refer to the Forbes list of the 40 best-paid chief executive officers, Exercise. The salary and age of each CEO are saved in the FORBES40 file. a. Use a graph to portray the relationship between a CEO’s salary and age. Do you detect a trend? b. According to Chebyshev’s rule, what percentage
Three-way catalytic converters have been installed in new vehicles in order to reduce pollutants from motor vehicle exhaust emissions. However, these converters unintentionally increase the level of ammonia in the air. Environmental Science & Technology (Sept. 1, 2000) published a study on the
Astronomers theorize that cold dark matter caused the formation of galaxies and clusters of galaxies in the universe. The theoretical model for cold dark matter requires an estimate of the velocities of light emitted from galaxy clusters. The Astronomical Journal (July 1995) published a study of
Clinical observations suggest that specifically language-impaired (SLI) children have great difficulty with the proper use of pronouns. This phenomenon was investigated and reported in the Journal of Communication Disorders (Mar. 1995). Thirty children, all from low-income families, participated in
According to Benford’s law, certain digits (1, 2, 3, . . . , 9) are more likely to occur as the first significant digit in a randomly selected number than are other digits. For example, the law predicts that the number “1” is the most likely to occur (30% of the time) as the first digit. In a
US News & World Report reported on many factors contributing to the breakdown of public education. One study mentioned in the article found that over 90% of the nation’s school districts reported that their students were scoring “above the national average” on standardized tests. Using your
Suicide is the leading cause of death of Americans incarcerated in correctional facilities. To determine what factors increase the risk of suicide in urban jails, a group of researchers collected data on all 37 suicides that occurred over a 15-year period in the Wayne County Jail in Detroit,
The final grades given by two professors in introductory statistics courses have been carefully examined. The students in the first professor’s class had a grade point average of 3.0 and a standard deviation of .2. Those in the second professor’s class had grade points with an average of 3.0
According to the government, federal spending on K€“12 education has increased dramatically over the past 20 years, but student performance has stayed essentially the same. Hence, former President George Bush signed into law the No Child Left behind Act, a bill that promised improved
The following Venn diagram describes the sample space of a particular experiment and events A and B :a. Suppose the sample points are equally likely. Find P (A) and P (B). b. Suppose P(1) = P(2) = P(3) = P(4) = P(5) = 1/20 and P(6) = P(7) = P(8) = P(9) = P(10) = 3/20. Find P(A) and
Compute each of the following:a.b.c.d.e.
Two fair dice are tossed, and the up face on each die is recorded. a. List the 36 sample points contained in the sample space. b. Assign probabilities to the sample points. c. Find the probability of observing each of the following events: A: {A 3 appears on each of the two dice.} B: {The sum
A study of underwater sounds in a specific region of the Pacific Ocean focused on scarce sounds, such as humpback whale screams, dolphin whistles, and sounds from passing ships (Acoustical Physics, Vol. 56, 2010). During the month of September (non–rainy season), research revealed the following
Two species of rhinoceros native to Africa are black rhinos and white rhinos. The International Rhino Federation estimates that the African rhinoceros population consists of 3,610 white rhinos and 11,330 black rhinos. Suppose one rhino is selected at random from the African rhino population and its
According to a University of Florida veterinary researcher, the longer a beachgoer sits in wet sand or stays in the water, the higher the health risk (University of Florida News, Jan. 29, 2008). Using data collected at Fort Lauderdale, Hollywood, and Hobie Beach, the researcher discovered the
The Journal of Education and Human Development (Vol. 3, 2009) investigated the causes of plagiarism among six English-as-a-second language (ESL) students taking a master's course in linguistics. All students in the class wrote two essays, one in the middle and one at the end of the semester. After
Refer to the Environmental Science & Technology (Jan. 2005) study of methyl tert-butyl ether (MTBE) contamination in New Hampshire wells, presented in Exercise 2.21 (p. 37). Data collected for a sample of 223 wells are saved in the MTBE file. Recall that each well was classified according to
Consider the following question posed to Marilyn vos Savant in her weekly newspaper column, “Ask Marilyn”: I have two pairs of argyle socks, and they look nearly identical—one navy blue and the other black. [When doing the laundry] my wife matches the socks incorrectly much more often than
An individual's genetic makeup is determined by the genes obtained from each parent. For every genetic trait, each parent possesses a gene pair, and each parent contributes one-half of this gene pair, with equal probability, to his or her offspring, forming a new gene pair. The offspring's traits
Suppose P(A) = .4, P(B) = .7 and P(A B) = .3 . Find the following probabilities: a. P(Bc) b. P(Ac) c. P(A ( B2)
A pair of fair dice is tossed. Define the following events:A: {You will roll a 7 (i.e., the sum of the numbers of dots on the upper faces of the two dice is equal to 7).}B: {At least one of the two dice is showing a 4.}a. Identify the sample points in the events A, B, A  B, A  B, and Ac.b.
Consider the following Venn diagram, whereP(E1) = .10, P(E2) - .05, P(E3) = P(E4) = .2,P(E5) = .06, P(E6) - .3, P(E7) = .06, andP(E8) = .03:Find the following probabilities: a. P(Ac) b. P(Bc) c. P(Ac ˆ© B) d. P(A ˆª B) e. P(A ˆ© B) f. P(Ac ˆª Bc) g. Are
Three fair coins are tossed. We wish to find the probability of the event A: {Observe at least one head.}a. Express A as the union of three mutually exclusive events. Using the expression you wrote, find the probability of A.b. Express A as the complement of an event. Using the expression you
The Journal of Accounting Research (March 2008) published a study on relationship incentives and degree of optimism among analysts’ forecasts. Participants were analysts at either a large or small brokerage firm who made their forecasts either early or late in the quarter. Also, some analysts
The National Institute of Standards and Technology (NIST) mandates that for every 100 items scanned through the electronic checkout scanner at a retail store, no more than 2 should have an inaccurate price. A recent study of the accuracy of checkout scanners at Wal-Mart stores in California (Tampa
Sleep apnea is a common sleep disorder characterized by collapses of the upper airway during sleep. Chance (Winter 2009) investigated the role of sleep apnea in how people transition from one sleep stage to another. The various stages of sleep for a large group of sleep apnea patients were
The Alan Guttmacher Institute Abortion Provider Survey is a survey of all 238 known nonhospital abortion providers in the United States (Perspectives on Sexual and Reproductive Health, Jan./Feb. 2003). For one part of the survey, the 358 providers were classified according to case load (number of
A €œhandoff€ is a term used in wireless communications to describe the process of a cell phone moving from a coverage area of one base station to another. Each base station has multiple channels (called color codes) that allow it to communicate with the cell phone. The Journal
The Organizational Development Journal (Summer 2006) reported on the results of a survey of human resource officers (HROs) at major firms. The focus of the study was employee behavior, namely absenteeism, promptness to work, and turnover. The study found that 55% of the HROs had problems with
Passe-dix is a game of chance played with three fair dice. Players bet whether the sum of the faces shown on the dice will be above or below 10. During the late 16th century, the astronomer and mathematician Galileo Galilei was asked by the Grand Duke of Tuscany to explain why “the chance of
Give the multiplicative rule of probability for a. Two independent events. b. Any two events.
Defend or refute each of the following statements: a. Dependent events are always mutually exclusive. b. Mutually exclusive events are always dependent. c. Independent events are always mutually exclusive.
For two events A and B, P(A) = .4, P(B) = .2, and P(A|B) = .6. a. Find P (A ∩ B). b. Find P (B | A).
An experiment results in one of three mutually exclusive events A, B, and C. It is known that P(A) = .30, P(B) = .55, and P(C) = .15, Find each of the following probabilities: a. P(A ∪ B). b. P(A ∩ B)). c. P(A | B) d. P(B ∪ C)). e. Are B and C independent events? Explain.
An experiment results in one of five sample points with the following probabilities: P(E1) = .22, P(E2) = .31,P(E3) = .15, P(E4) = .22, and P(E5) = .1. The following events have been defined: A: {E1, E3} B: {E2, E3, E4} C: {E1, E5} Find each of the following probabilities: a. P (A) b. P (B) c.
A sample space contains six sample points and events A, B, and C, as shown in the Venn diagram on page 146. The probabilities of the sample points are P(1) = .20, P(2) = .05, P(3) = .30, P(4) = .10, P(5) = .10, and P(6) = .25.a. Which pairs of events, if any, are mutually exclusive? Why? b. Which
According to a September 2008 Harris poll, 68% of all American adults have a public library card. The percentages do differ by gender—62% of males have library cards compared to 73% of females. a. Consider the three probabilities: P(A) = .68, P(A|B) = .62, and P(A|C) = .73. Define events A, B,
Refer to the Journal of Behavioral Decision Making (Jan. 2007) study of the effect of guilt emotion on how a decision maker focuses on the problem, Exercise. The results (number responding in each category) for the 171 study participants are reproduced in the accompanying table. Suppose one of the
According to the Pew Internet & American Life Project (Oct. 2009), 54% of Internet users have a wireless connection to the Internet via a laptop, cell phone, game console, or other mobile device. Of these wireless users, 25% use Twitter to share updates about themselves. What is the probability
Refer to the Chance (Fall 2000) study of ancient pottery found at the Greek settlement of Phylakopi, presented in Exercise. Of the 837 pottery pieces uncovered at the excavation site, 183 were painted. These painted pieces included 14 painted in a curvilinear decoration, 165 painted in a geometric
Refer to the sleep apnea study published in Chance (Winter 2009), Exercise. Recall that the various stages of sleep for a large group of sleep apnea patients were monitored in 30-second €œepochs,€ and the sleep stage for the previous and current epoch was determined. A summary
Refer to the Aggressive Behavior (Jan./Feb. 2007) study of fallow deer bucks fighting during the mating season, presented in Exercise. Recall that researchers recorded 167 encounters between two bucks, one of which clearly initiated the encounter with the other. A summary of the fight status of the
A computer intrusion detection system (IDS) is designed to provide an alarm whenever someone intrudes (e.g., through unauthorized access) into a computer system. A probabilistic evaluation of a system with two independently operating intrusion detection systems (a double IDS) was published in the
Chance (Spring 2010) presented an article on the random mutation hypothesis developed by microbiologists. Under this hypothesis, when a wild-type organic cell (e.g., a bacteria cell) divides, there is a chance that at least one of the two daughter€ cells is a mutant. When a mutant cell
Process Safety Progress (Dec. 2004) published a risk analysis for a natural-gas pipeline between Bolivia and Brazil. The most likely scenario for an accident would be natural-gas leakage from a hole in the pipeline. The probability that the leak ignites immediately (causing a jet fire) is .01. If
Suppose you wish to sample n = 2 elements from a total of N = 10 elements. a. Count the number of different samples that can be drawn, first by listing them and then by using combinatorial mathematics. b. If random sampling is to be employed, what is the probability that any particular sample
Suppose that a population contains N = 200,000 elements. Use a computer or Table I of Appendix A to select a random sample of n = 10 elements from the population. Explain how you selected your sample.
In addition to its decennial enumeration of the population, the U.S. Census Bureau regularly samples the population for demographic information such as income, family size, employment, and marital status. Suppose the Bureau plans to sample 1,000 households in a city that has a total of 534,322
Researchers at the University of South Florida investigated the effects of diet on the physiology and behavior of rats (USF News, Oct. 17, 2009). One group of rats was fed a typical American diet (40% fat, 40% protein, 20% carbohydrates); a second group of rats was fed an Atkins-type diet (70% fat,
In auditing a firm’s financial statements, an auditor is required to assess the operational effectiveness of the accounting system. In performing the assessment, the auditor frequently relies on a random sample of actual transactions (Stickney and Weil, Financial Accounting: An Introduction to

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