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Statistics 13th Edition James T. McClave - Solutions
The postmortem interval (PMI) is defined as the time elapsed (in days) between death and an autopsy. Knowledge of the PMI is considered essential to conducting medical research on human cadavers. The data in the accompanying table are the PMIs of 22 human brain specimens obtained at autopsy in a
A high concentration of calcium and gypsum in water can affect the water quality and limit mineral flotation. In Minerals Engineering (Vol. 46-47, 2013), chemical and materials engineers published a study of the impact of calcium and gypsum on the flotation properties of silica in water. Solutions
Refer to the American Journal of Archaeology (Jan. 2014) study of sword shaft graves in ancient Greece, Exercise 2.37 (p. 50). The number of sword shafts buried at each of 13 recently discovered grave sites is reproduced in the following table.a. Calculate the mean of the data. Interpret the
In Environmental Geology (Vol. 58, 2009) computer simulation was employed to estimate how far a block from a collapsing rock wall will bounce-called rebound length-down a soil slope. Based on the depth, location, and angle of block-soil impact marks left on the slope from an actual rock fall, the
Refer to the British Journal of Music Education (Mar. 2014) study of music performanceanxiety, Exercise 2.39 (p. 50). Scores on the Performance Anxiety Inventory (PAI) scale for participants in eight different studies are reproduced in the table.a. Find and interpret the mean of the PAI scores.b.
Refer to the Business and Society (Mar. 2011) study on the sustainability behaviors of CPA corporations, Exercise 2.36 (p. 50). Recall that the level of support for corporate sustainability (measured on a quantitative scale rangingfrom 0 to 160 points) was obtained for each of 992 senior managers
Refer to the Archives of Pediatrics and Adolescent Medicine (Dec. 2007) study of honey as a remedy for coughing, Exercise 2.40 (p. 51). Recall that the 105 ill children in the sample were randomly divided into three groups: those who received a dosage of an over-the-counter cough medicine (DM),
Refer to the American Journal of Physical Anthropology (Vol. 142, 2010) study of the characteristics of cheek teeth (e.g., molars) in an extinct primate species, Exercise 2.38 (p. 50). The data on dentary depth of molars (in millimeters) for 18 cheek teeth extracted from skulls are reproduced
Refer to the Minerals Engineering (Vol. 46-47, 2013) study of the impact of calcium and gypsum on the flotation properties of silica in water, Exercise 2.48 (p. 53). The zeta potential (mV) was determined for each of 50 liquid solutions prepared without calcium/gypsum and for 50 liquid solutions
Myopia (i.e., nearsightedness) is a visual condition that affects over 100 million Americans. Two treatments that may slow myopia progression are the use of (1) corneal reshaping contact lenses and (2) bifocal soft contact lenses. In Optometry and Vision Science (Jan., 2013), university optometry
What is the range of a data set?
Describe the sample variance in words rather than with a formula. Do the same with the population variance.
Calculate the range, variance, and standard deviation for the following samples:a. 39, 42, 40, 37, 41b. 100, 4, 7, 96, 80, 3, 1, 10, 2c. 100, 4, 7, 30, 80, 30, 42, 2 Discuss.
Aquatic Biology (Vol. 9, 2010) reported on a study of green sea turtles inhabiting the Grand Cayman South Sound lagoon. The data on curved carapace (shell) length (in centimeters) for 76 captured turtles are saved in the TURTLES file. Descriptive statistics for the data are shown on the
Refer to the American Journal of Archaeology (Jan. 2014) study of sword shaft graves in ancient Greece, Exercise 2.60 (p. 61). The number of sword shafts buried at each of 13 recently discovered grave sites is reproduced in the following table.a. Calculate the range of the sample data.b. Calculate
Refer to the British Journal of Music Education (Mar. 2014) study of music performance anxiety, Exercise 2.62 (p. 61). Scores (measured in points) on the Performance Anxiety Inventory (PAI) scale for participants in eight different studies are reproduced in the table.a. Find the variance of the
Refer to the Archives of Pediatrics and Adolescent Medicine (Dec. 2007) study of honey as a remedy for coughing, Exercise 2.64 (p. 62). The coughing improvement scores for the patients in the over-the-counter cough medicine dosage (DM) group, honey dosage group, and control group are reproduced in
The characteristics of cheek teeth (e.g., molars) can provide anthropologists with information on the dietary habits of extinct mammals. The cheek teeth of an extinct primate species were the subject of research reported in the American Journal of Physical Anthropology (Vol. 142, 2010). A total of
Refer to the American Journal of Physical Anthropology (Vol. 142, 2010) study of the characteristics of cheek teeth (e.g., molars) in an extinct primate species, Exercise 2.65 (p. 62). The data on dentary depth of molars (in millimeters) for 18 cheek teeth extracted from skulls are reproduced in
To what kinds of data sets can the empirical rule be applied?
Use the applet entitled Mean versus Median to find the mean and median of each of the three data sets presented in Exercise 2.59. For each data set, set the lower limit to a number less than all of the data, set the upper limit to a number greater than all of the data, and then click on Update.
Use the applet Mean versus Median to illustrate your descriptions in Exercise 2.54. For each part a, b, and c, create a data set with 10 items that has the given property. Using the applet, verify that the mean and median have the relationship you described in Exercise 2.54.
Use the applet Mean versus Median to study the effect that an extreme value has on the difference between the mean and median. Begin by setting appropriate limits and plotting the following data on the number line provided in the applet: 0 6 7 7 8 8 8 9 9 10 a. Describe the shape of the
Use the applet entitled Standard Deviation to find the standard deviation of each of the four data sets listed in Exercise 2.80. For each data set, set the lower limit to a number less than all of the data, set the upper limit to a number greater than all of the data, and then click on Update.
Use the applet Standard Deviation to study the effect that multiplying or dividing each number in a data set by the same number has on the standard deviation. Begin by setting appropriate limits and plotting the given data on the number line provided in the applet.0 1 1 1 2 2 3 4a. Record the
Use the applet Standard Deviation to study the effect that an extreme value has on the standard deviation. Begin by setting appropriate limits and plotting the following data on the number line provided in the applet:0 6 7 7 8 8 8 9 9 10a. Record the standard deviation. Replace the extreme value of
What is an experiment?
Consider an experiment in which 10 identical small boxes are placed side by side on a table. A crystal is placed at random inside one of the boxes. A self-professed "psychic" is asked to pick the box that contains the crystal. a. If the "psychic" simply guesses, what is the probability that she
Give a scenario where the permutations rule applies.
What is the difference between the permutations rule and the combinations rule?
Use the multiplicative rule to determine the number of sample points in the sample space corresponding to the experiment of tossing a coin the following number of times: a. 2 times b. 3 times c. 5 times d. n times
An experiment consists of choosing objects without regard to order. How many sample points are there if you choose the following?a. 3 objects from 7b. 2 objects from 6c. 2 objects from 30d. 8 objects from 10e. r objects from
Refer to the American Journal of Physical Anthropology (Vol. 142, 2010) study of the dietary habits of extinct mammals, Exercise 3.25 (p. 130). Recall that 18 cheek teeth extracted from skulls of an extinct primate species discovered in western Wyoming were analyzed. Each tooth was classified
Refer to the Journal of Consumer Research (March 2003) study of how people attempt to influence the choices of others. Exercise 3.27 (p. 122). Recall that students selected three portable grill displays to be compared from an offering of five different grill displays. a. Use a counting rule to
Suppose you are to choose a basketball team (five players) from eight available athletes.a. How many ways can you choose a team (ignoring positions)?b. How many ways can you choose a team composed of two guards, two forwards, and a center?c. How many ways can you choose a team composed of one each
Refer to the Engineering Management Research (May 2012) study of using a simulation game to teach a production course, Exercise 3.32 (p. 131). Recall that a purchase order card in the simulated game consists of a choice of one of two color television brands (A or B), one of two colors (red or
An article published in BMC Public Health (Vol. 10, 2010) studied the effectiveness of gold kiwifruit as an iron supplement in women with an iron deficiency. Fifty women were assigned to receive an iron- fortified breakfast cereal with a banana, and 50 women were assigned to receive an
Successful companies such as Amway, Herbalife, and NuSkin employ multilevel marketing (MLM) schemes to distribute their products. In MLM, each distributor recruits several additional distributors to work at the first level. Each of these first-level distributors, in turn, recruits distributors to
A mathematics assignment problem in which each element from one set is matched with one and only one element from another set is often referred to as a "marriage" problem. Mathematical Social Sciences (May 2014) considered the following marriage problem. After passing their preliminary exams,
In the Journal of Quality in Maintenance Engineering (Vol. 9, 2003), researchers used an analytic hierarchy process to help build a preferred maintenance organization for ARTHUR, the Norwegian Army's high-tech radar system. The process requires the builder to select alternatives in three different
A college professor hands out a list of 10 questions, 5 of which will appear on the final examination for the course. One of the students taking the course is pressed for time and can prepare for only 7 of the 10 questions on the list. Suppose the professor chooses the 5 questions at random from
Granular media are substances made up of many distinct grains-including sand, rice, ball bearings, and flour. The properties of these materials were theoretically modeled in Engineering Computations: International Journal for Computer-Aided Engineering and Software (Vol. 30, No. 2, 2013). The model
Consider 5-card poker hands dealt from a standard 52-card bridge deck. Two important events are A: {You draw a flush.} B: {You draw a straight.} [Note: A flush consists of any 5 cards of the same suit. A straight consists of any 5 cards with values in sequence. In a straight, the cards may be of
Why is Bayes's rule unnecessary for finding P(B\A) if events A and B are independent?
Use the symbols ∩, ∪, |, and c to convert the following statements into compound events involving events A and B, where A = 5You purchase a notebook computer6 and B = {You vacation in Europe}: a. You purchase a notebook computer or vacation in Europe. b. You will not vacation in Europe. c. You
Given that P(A ∩ B) = .4 and P(A\B) = .8, find P (B).
A fair die is tossed, and the up face is noted. If the number is even, the die is tossed again; if the number is odd, a fair coin is tossed. Consider the following events: A: {A head appears on the coin.} B: {The die is tossed only one time.} a. List the sample points in the sample space. b. Give
Two events, A and B, are independent, with P(A) = .3 and P(B) = .1.a. Are A and B mutually exclusive? Why?b. Find P(A\B) and P(B\A).c. Find P(A ∪ B).
Simulate the experiment described in Exercise 3.15, using any five identically shaped objects, two of which are one color and three another. Mix the objects, draw two, record the results, and then replace the objects. Repeat the experiment a large number of times (at least 100). Calculate the
The Wall Street Journal (Sept. 1, 2000) reported on an independent study of postal workers and violence at post offices. In a sample of 12,000 postal workers, 600 were physically assaulted on the job in a recent year. Use this information to estimate the probability that a randomly selected postal
Refer to the National Highway Traffic Safety Administration (NHTSA) crash tests of new car models, presented in Exercise 2.190 (p. 107). Recall that the NHTSA has developed a "star" scoring system, with results ranging from one star (*) to five stars (*****). The more stars in the rating, the
The current status of the beech tree species in East Central Europe was evaluated by Hungarian university professors in Applied Ecology and Environmental Research (Vol. 1, 2003). Of 188 beech trees surveyed, 49 had been damaged by fungi. Depending on the species of fungus, damage will occur on
According to a 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, and C. b. Assuming
Process Safety Progress (Sept. 2004) reported on an emergency response system for incidents involving toxic chemicals in Taiwan. The system has logged over 250 incidents since being implemented. The next table gives a breakdown of the locations where these incidents occurred. Consider the location
The Journal of the American Law and Economics Association (Vol. 3, 2001) published the results of a study of appeals of federal civil trials. The accompanying table, extracted from the article, gives a breakdown of 2,143 civil cases that were appealed by either the plaintiff or the defendant. The
Roulette is a very popular game in many American casinos. In Roulette, a ball spins on a circular wheel that is divided into 38 arcs of equal length, bearing the numbers 00, 0, 1, 2 ... 35, 36. The number of the arc on which the ball stops is the outcome of one play of the game. The numbers are
The National Resident Matching Program (NRMP) is a service provided to match graduating medical students with residency appointments at hospitals. After students and hospital officials have evaluated each other, they submit rank-order lists of their preferences to the NRMP. Using a matching
In college basketball games, a player may be afforded the opportunity to shoot two consecutive foul shots (free throws). a. Suppose a player who makes (i.e., scores on) 80% of his foul shots has been awarded two free throws. If the two throws are considered independent, what is the probability that
The level of crop damage by wild boars in southern Italy was investigated in Current Zoology (Apr. 2014). In the study, crop damage occurred when the wild boars partially or completely destroyed agricultural crops in privately owned lands. The researchers identified 157 incident of crop damage in
Consider the two systems shown in the schematic below. System A operates properly only if all three components operate properly. (The three components are said to operate in series.) The probability of failure for system A components 1, 2, and 3 is .12, .09, and .11, respectively. Assume that the
Refer to University of New Mexico professor Jane Hood's study of the fieldwork methods used by qualitative sociologists, presented in Exercise 2.195 (p. 108). Recall that she discovered that fieldwork methods could be classified into four distinct categories: Interview, Observation plus
Refer to the Conservation Ecology (Dec. 2003) study of the causes of forest fragmentation, presented in Exercise 2.166 (p. 97). Recall that the researchers used advanced high-resolution satellite imagery to develop fragmentation indexes for each forest. A 3 × 3 grid was superimposed over an
One of the problems encountered with organ transplants is the body's rejection of the transplanted tissue. If the antigens attached to the tissue cells of the donor and receiver match, the body will accept the transplanted tissue. Although the antigens in identical twins always match, the
Originally, M&Ms Plain Chocolate Candies came in only a brown color. Today, M&Ms in standard bags come in six colors: brown, yellow, red, blue, orange, and green. According to Mars Corporation, today 24% of all M&Ms produced are blue, 20% are orange, 16% are green, 14% are yellow, 13%
Seventy-five percent of all women who submit to pregnancy tests are really pregnant. A certain pregnancy test gives a false positive result with probability .02 and a valid positive result with probability .99. If a particular woman's test is positive, what is the probability that she really is
According to a morning news program, a very rare event recently occurred in Dubuque, Iowa. Each of four women playing bridge was astounded to note that she had been dealt a perfect bridge hand. That is, one woman was dealt all 13 spades, another all 13 hearts, another all the diamonds, and another
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 5,055 white rhinos and 20,405 black rhinos. Suppose one rhino is selected at random from the African rhino population and its
Answer the following question posed in the Atlanta Journal-Constitution: When a meteorologist says, "The probability of rain this afternoon is .4," does it mean that it will be raining 40% of the time during the afternoon?
Refer to the Journal of Transportation Engineering (May 2013) investigation of railroad track allocation at a railway station with 11 tracks, Exercise 2.16 (p. 40). A simple algorithm designed to minimize waiting time and bottlenecks is one in which engineers randomly assign one of the 11 tracks to
Define the sample space?
Nausea and vomiting after surgery are common side effects of anesthesia and painkillers. Six different drugs, varying in cost, were compared for their effectiveness in preventing nausea and vomiting (New England Journal of Medicine, June 10, 2004). The medical researchers looked at all possible
Define in words mutually exclusive events?
Define in words the union of two events?
Define in words the intersection of two events?
Define in words the complement of an event?
State the rule of complements?
State the additive rule of probability for mutually exclusive events?
State the additive rule of probability for any two events?
Consider the following Venn diagram, whereP(E2) = P(E3) = 1/5, P(E4) = P(E5) = 1/20,P(E6) = 1/10, P(E7) = 1/5:Find each of the following probabilities: a. P(A) b. P(B) c. P(A ( B) d. P(A ( B) e. P(Ac) f. P(Bc) g. P(A ( Ac) h. P(Ac ( B)
Give two probability rules for sample points?
According to the Pew Research Internet Project (Dec. 2013) survey, the two most popular social networking sites in the United States are Facebook and LinkedIn. Of all adult Internet users, 71% have a Facebook account, 22% have a LinkedIn account, and 18% visit both Facebook and LinkedIn.a. Draw a
Gene expression profiling is a state-of-the-art method for determining the biology of cells. In Briefings in Functional Genomics and Proteomics (Dec. 2006), biologists reviewed several gene expression profiling methods. The biologists applied two of the methods (A and B) to data collected on
A study of attempted suicide methods was published in the journal Death Studies (Vol. 38, 2014). Data for 59 suicide victims who had previously attempted suicide were collected. The table gives a breakdown of the number of suicide victims according to method used and gender. Suppose one of the
In Aggressive Behavior (Jan./Feb. 2007), zoologists investigated the likelihood of fallow deer bucks fighting during the mating season. During the observation period, the researchers recorded 205 encounters between two bucks. Of these, 167 involved one buck clearly initiating the encounter with the
The ability of a mouse to recognize the odor of a potential predator (e.g., a cat) is essential to the mouse's survival. The chemical makeup of these odors-called kairomones-was the subject of a study published in Cell (May 14, 2010). Typically, the sources of these odors are major urinary proteins
Wireless identity theft is a technique of stealing an individual's personal information from radio-frequency-enabled cards (e.g., credit or debit cards). Upon capturing this data, thieves are able to program their own cards to respond in an identical fashion via cloning. A method for detecting
Explain the difference between an unconditional probability and a conditional probability?
How do you find the probability of an event made up of several sample points?
Give a scenario where the combinations rule is appropriate for counting the number of sample points?
According to Global Research News (Mar. 4, 2014), one-fourth of all rough diamonds produced in the world are blood diamonds. (Any diamond that is mined in a war zone-often by children-in order to finance a warlord's activity, an insurgency, or an invading army's effort is considered a blood
Refer to the Current Zoology (Apr. 2014) study of crop damage by wild boars, Exercise 3.18 (p. 129). Recall that researchers identified 157 incidents of crop damage in the study area caused by wild boars over a five-year period. The table giving the types of crops destroyed and corresponding
In addition to standard exercise electrocardiography (SEE), two widely applied methods of stress testing of cardiac patients are stress echocardiography (SE) and single-photon emission computed tomography (SPECT). These methods were evaluated in the American Journal of Medical Quality (Mar./Apr.
The Harvard School of Public Health conducted a study of privately held firearm stock in the United States. In a representative household telephone survey of 2,770 adults, 26% reported that they own at least one gun (Injury Prevention, Jan. 2007). Of those that own a gun, 5% own a handgun. Suppose
According to psychological theory, each negative emotion one has is linked to some thought (appraisal) about the environment. This theory was tested in the journal Cognition and Emotion (Vol. 24, 2010). Undergraduate students were asked to respond to events that occurred within the past 15 minutes.
Refer to the University of Florida study of health risks to beachgoers, Exercise 3.24 (p. 130). According to the study, 6 out of 1,000 people exposed to wet sand for a 10-minute period will acquire gastroenteritis and 7 out of 1,000 people exposed to ocean water for a 10-minute period will acquire
According to Sociology of Education (Apr. 2014), compensatory advantage occurs when individuals from privileged backgrounds are less dependent on prior negative outcomes than individuals from disadvantaged families. The researcher applied this theory to educational success. Let St represent the
Refer to the Evolutionary Ecology Research (July 2003) study of the patterns of extinction in the New Zealand bird population, presented in Exercise 2.24 (p. 42). Consider the data on extinction status (extinct, absent from island, present) for the 132 bird species. The data are summarized in the
In Ageing Research Reviews (May 2014), nutritionists published a study of the health issues faced by aging adults. Three of the most common health conditions are obesity (high body fat mass), osteoporosis (low bone mineral density in neck and spine), and sarcopenia (low skeletal muscle mass index).
University of Florida researchers in the Department of Materials Science and Engineering have invented a technique that rapidly detects traces of TNT (Today, Spring 2005). The method, which involves shining a laser on a potentially contaminated object, provides instantaneous results and gives no
Use the applet entitled Simulating the Probability of Rolling a 6 to explore the relationship between the proportion of sixes rolled on several rolls of a die and the theoretical probability of rolling a 6 on a fair die. a. To simulate rolling a die one time, click on the Roll button on the screen
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