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A First Course In Statistics 12th Edition James T McClave, Terry T Sincich - Solutions
Treating psoriasis with the “Doctorfish of Kangal.” Psoriasis is a skin disorder with no known cure. An alternative treatment for psoriasis is ichthyotherapy, also known as therapy with the “Doctorfish of Kangal.” Fish from the hot pools of Kangal, Turkey, feed on the skin scales of
Voltage sags and swells. Refer to the Electrical Engineering(Vol. 95, 2013) study of power quality (measured by “sags”and “swells”) in Turkish transformers, Exercise 2.127(p. 106). For a sample of 103 transformers built for heavy industry, the mean and standard deviation of the number of
Corporate sustainability of CPA firms. Refer to the Business and Society (Mar. 2011) study on the sustainability behaviors of CPA corporations, Exercise 2.105 (p. 101). Numerical descriptive measures for level of support for corporate sustainability for the 992 senior managers are repeated in the
Research on brain specimens. Refer to the Brain and Language data on postmortem intervals (PMIs) of 22 human brain specimens, presented in Exercise 2.45 (p. 76).The mean and standard deviation of the PMI values are 7.3 and 3.18, respectively.a. Find the z-score for the PMI value of 3.3.b. Is the
Dentists’ use of anesthetics. Refer to the Current Allergy& Clinical Immunology study of the use of local anesthetics in dentistry, presented in Exercise 2.103 (p. 101). Recall that the mean number of units (ampoules) of local anesthetics used per week by dentists was 79, with a standard
Blond hair types in the Southwest Pacific. A mutation of a pigmentation gene is theorized to be the cause of blondhair genotypes observed in several Southwest Pacific islands. The distribution of this mutated gene was investigated in the American Journal of Physical Anthropology(Apr. 2014). For
Consider the following sample data set.171 152 170 168 169 171 190 183 185 140 173 206 172 174 169 199 151 180 167 170 188a. Construct a box plot.b. Identify any outliers that may exist in the data.Applet Exercise 2.7 Use the applet Standard Deviation to determine whether an item in a data set may
Consider the following sample data set. Construct a box plot for the data and use it to identify any outliers.121 171 158 173 184 163 157 85 145 165 172 196 170 159 172 161 187 100 142 166 171
A sample data set has a mean of 57 and a standard deviation of 11. Determine whether each of the following sample measurements is an outlier.a. 65b. 21c. 72d. 98
Consider the following horizontal box plot:0 2 4 6 8 10 12 14 16* * *a. What is the median of the data set (approximately)?b. What are the upper and lower quartiles of the data set(approximately)?c. What is the interquartile range of the data set(approximately)?d. Is the data set skewed to the
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.
Define an outlier.Learning the Mechanics
What does the central line parallel to the hinges of a boxplot indicate?
What is the percentage of population that lies outside the interquartile range?
GPAs of students. At one university, the students are given z-scores at the end of each semester, rather than the traditional GPAs. The mean and standard deviation of all students’ cumulative GPAs, on which the z-scores are based, are 2.7 and .5, respectively.a. Translate each of the following
Ranking Ph.D. programs in economics (cont’d). Refer to the Southern Economic Journal (Apr. 2008) study of Ph.D. programs in economics, Exercise 2.129.The authors also made the following observation:“A noticeable feature of this skewness is that distinction between schools diminishes as the rank
Ranking Ph.D. programs in economics. The Southern Economic Journal (Apr. 2008) published a guide to graduate study in economics by ranking the Ph.D. programs at 129 colleges and universities. Each program was evaluated according to the number of publications published by faculty teaching in the
Blue versus red exam study. 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
Voltage sags and swells. The power quality of a transformer is measured by the quality of the voltage. Two causes of poor power quality are “sags” and “swells.” A sag is an unusual dip, and a swell is an unusual increase in the voltage level of a transformer. The power quality of
Lead in drinking water. 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
Extinct New Zealand birds. Refer to the Evolutionary Ecology Research (July 2003) study of the patterns of extinction in the New Zealand bird population, first presented in Exercise 2.24 (p. 66). Again, consider the data on the egg length (measured in millimeters) for the 132 bird species.a. Find
Motivation of drug dealers. Refer to the Applied Psychology in Criminal Justice (Sept. 2009) study of convicted drug dealers’ motivations, Exercise 2.102 (p. 101).Recall that the sample of drug dealers had a mean Wanting Recognition (WR) score of 39 points, with a standard deviation of 6
Sanitation inspection of cruise ships. Refer to the sanitation levels of cruise ships presented in Exercise 2.41 (p. 75).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 Star Princess’score of 92.
Stability of compounds in new drugs. Refer to the Pfizer Global Research and Development study (reported in ACS Medicinal Chemistry Letters, Vol. 1, 2010) of the metabolic stability of drugs, Exercise 2.35 (p. 73). Recall that the stability of each of 416 drugs was measured by the fup/fumic
Age distribution. According to a demographic survey of India, 69% of the estimated population of 1.25 billion are aged above 14 years. Give a percentile ranking for the age of 14 years in the distribution of all ages across the overall population of India.
Analysis of students’ performance. 250 students appeared for a test of 500 marks. The scores they obtained have a mean of 383, a first quartile of 355, a third quartile of 402, and a 90th percentile of 437. Interpret each of these numerical descriptive measures.
Suppose that 40 and 90 are two elements of a population data set and that their z-scores are -2 and 3, respectively.Using only this information, is it possible to determine the population’s mean and standard deviation? If so, find them. If not, explain why it’s not possible.Applying the
What will be the z-score of an observation x = 10 if it is picked from a distribution with the following means (m)and standard deviations (s)?a. m = 30 and s = 10b. m = -10 and s = 10c. m = 30 and s = 20d. m = 20 and s = 30
Compute the z-score corresponding to each of the following values of x:a. x = 40, s = 5, x = 30b. x = 90, m = 89, s = 2c. m = 50, s = 5, x = 50d. s = 4, x = 20, x = 30e. In parts a–d, state whether the z-score locates x within a sample or within a population.f. In parts a–d, state whether each
For a mound-shaped data, what percentage of the measurements will have negative z-score?Learning the Mechanics
Give the percentage of measurements in a data set that are above and below each of the following percentiles:a. 75th percentileb. 50th percentilec. 20th percentiled. 84th percentile
Land purchase decision. A buyer for a lumber company must decide whether to buy a piece of land containing 5,000 pine trees. If 1,000 of the trees are at least 40 feet tall, the buyer will purchase the land; otherwise, he won’t. The owner of the land reports that the height of the trees has a
Animal-assisted therapy for heart patients. A study was presented at the American Heart Association Conference(Nov. 2005) 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
Shopping vehicle and judgment. While shopping at the grocery store, are you more likely to buy a vice product(e.g., a candy bar) when pushing a shopping cart or carrying a shopping basket? This was the question of interest in a study published in the Journal of Marketing Research(Dec. 2011). The
Permeability of sandstone during weathering. Refer to the Geographical Analysis (Vol. 42, 2010) study of the decay properties of sandstone when exposed to the weather, Exercises 2.69 and 2.90 (pp. 87 and 94). Recall that slices of sandstone blocks were measured for permeability under three
Velocity of Winchester bullets. The American Rifleman reported on the velocity of ammunition fired from the FEG P9R pistol, a 9-mm gun manufactured in Hungary.Field tests revealed that Winchester bullets fired from the pistol had a mean velocity (at 15 feet) of 936 feet per second and a standard
Extinct New Zealand birds. 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. 66). Consider the data on the egg length(measured in millimeters) for the 132 bird species saved in the NZBIRDS
Hand washing versus hand rubbing. As an alternative to hand washing, some hospitals allow health workers to rub their hands with an alcohol-based antiseptic. The British Medical Journal (Aug. 17, 2002) reported on a study to compare the effectiveness of washing the hands with soap and rubbing the
Characteristics of antiwar demonstrators. The characteristics of antiwar demonstrators in the United States were examined in the American Journal of Sociology(Jan. 2014). Using data collected for over 5,000 antiwar demonstrators over a recent 3-year period, the researchers found that the mean
Corporate sustainability of CPA firms. Refer to the Business and Society (Mar. 2011) study on the sustainability behaviors of CPA corporations, Exercise 2.36 (pp. 74).Recall that the level of support for corporate sustainability(measured on a quantitative scale ranging from 0 to 160 points) was
Irrelevant speech effects. Refer to the Acoustical Science& Technology (Vol. 35, 2014) study of irrelevant speech effects, Exercise 2.34 (p. 73). Recall that subjects performed a memorization task under two conditions: (1) with irrelevant background speech and (2) in silence. The difference in the
Dentists’ use of anesthetics. A study published in Current Allergy & Clinical Immunology (Mar. 2004) investigated allergic reactions of dental patients to local anesthetics. Based on a survey of dental practitioners, the study reported that the mean number of units (ampoules) of local anesthetics
Motivation of drug dealers. 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
Sanitation inspection of cruise ships. Refer to Exercise 2.41(p. 75) and the Centers for Disease Control and Prevention listing of the sanitation scores for 186 cruise ships. The data are saved in the SANIT file.a. Find the mean and standard deviation of the sanitation scores.b. Calculate the
Do social robots walk or roll? Refer to the International Conference on Social Robotics (Vol. 6414, 2010) study on the current trend in the design of social robots, Exercise 2.7(p. 62). Recall that in a random sample of social robots obtained through a Web search, 28 were built with wheels. The
Given a data set with a largest value of 760 and a smallest value of 135, what would you estimate the standard deviation to be? Explain the logic behind the procedure you used to estimate the standard deviation. Suppose the standard deviation is reported to be 25. Is this number
The following is a sample of 25 measurements.7 6 6 11 8 9 11 9 10 8 7 7 5 9 10 7 7 7 7 9 12 10 10 8 6a. Compute x, s2, and s for this sample.b. Count the number of measurements in the intervals x { s, x { 2s, and x { 3s. Express each count as a percentage of the total number of measurements.c.
For a set of data with a mound-shaped relative frequency distribution, what can be said about the percentage of the measurements contained in each of the intervals specified in Exercise 2.96?Learning the Mechanics
For any set of data, what can be said about the percentage of the measurements contained in each of the following intervals?a. x - s to x + sb. x - 2s to x + 2sc. x - 3s to x + 3s
The output from a statistical computer program indicates that the mean and standard deviation of a data set consisting of 200 measurements are $1,500 and $300, respectively.a. What are the units of measurement of the variable of interest? On the basis of the units, what type of data is this,
As per Chebyshev’s rule how many measurements fall within(m - 2s, m + 2s)
Active nuclear power plants. Refer to Exercise 2.72 (p. 88)and the U.S. Energy Information Administration’s data on the number of nuclear power plants operating in each of 20 states.a. Find the range, variance, and standard deviation of this data set.b. Eliminate the largest value from the data
Cheek teeth of extinct primates. 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. 86). The data on dentary depth of molars (in millimeters) for 18 cheek teeth extracted
Permeability of sandstone during weathering. Refer to the Geographical Analysis (Vol. 42, 2010) study of the decay properties of sandstone when exposed to the weather, Exercise 2.69 (p. 87). Recall that slices of sandstone blocks were tested for permeability under three conditions: no exposure to
Is honey a cough remedy? Refer to the Archives of Pediatrics and Adolescent Medicine (Dec. 2007) study of honey as a remedy for coughing, Exercise 2.64(p. 86). The coughing improvement scores for the patients in the over-the-counter cough medicine dosage(DM) group, honey dosage group, and control
Characteristics of a rockfall. Refer to the Environmental Geology (Vol. 58, 2009) study of how far a block from a collapsing rock wall will bounce, Exercise 2.61 (p. 85).The rebound lengths (meters) for a sample of 13 rock bounces are reproduced in the table below.10.94 13.71 11.38 7.26 17.83 11.92
Music performance anxiety. Refer to the British Journal of Music Education (Mar. 2014) study of music performance anxiety, Exercise 2.62 (p. 85). Scores (measured in points) on the Performance Anxiety Inventory (PAI) scale for participants in eight different studies are reproduced in the table.54
Shaft graves in ancient Greece. Refer to the American Journal of Archaeology (Jan. 2014) study of sword shaft graves in ancient Greece, Exercise 2.60 (p. 85). The number of sword shafts buried at each of 13 recently discovered grave sites is reproduced in the following table.1 2 3 1 5 6 2 4 1 2 4 2
Shell lengths of sea turtles. 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
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, 4b. 8 feet, 10 feet, 32 feet, 5 feetc. -1, -4, -3, 1, -4, -4d. 1/5 ounce, 1/5 ounce, 1/5 ounce, 2/5 ounce, 1/5 ounce, 4/5 ounce Use the applet entitled
Consider the following sample of five measurements: 2, 1, 1, 0, 3.a. Calculate the range, s2, and s.b. Add 3 to each measurement and repeat part a.c. Subtract 4 from each measurement and repeat part a.d. Considering your answers to partsa, b, andc, what seems to be the effect on the variability of
Using only integers between −10 and 10, construct two data sets each with 10 observations such that the two sets have the same range, but different means. Moreover, the two data sets should not have any common units.
Using only integers between −10 and 10, construct two data sets each with 10 observations such that the two sets have the same mean, but different variances. The two data sets should not have any common units.
Calculate the range, variance, and standard deviation for the following samples:a. 4, 2, 1, 0, 1b. 1, 6, 2, 2, 3, 0, 3c. 8, -2, 1, 3, 5, 4, 4, 1, 3d. 0, 2, 0, 0, -1, 1, -2, 1, 0, -1, 1, -1, 0, -3, -2, -1, 0, 1
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
If data set A has more variance than data set B, which one would have the lower standard deviation?Learning the Mechanics
What is advantage of the range as a measure of variability?
What is the range of a data set?
Active nuclear power plants. The U.S. Energy Information Administration monitors all nuclear power plants operating in the United States. The table below lists the number of active nuclear power plants operating in each of a sample of 20 states.a. Find the mean, median, and mode of this data set.b.
Contact lenses for myopia. Myopia (i.e., nearsightedness)is a visual condition that affects over 100 million Americans. Two treatments that may slow myopia SILICA MYoPIA State Number of Power Plants State Number of Power Plants Alabama 5 New Hampshire 1 Arizona 3 New York 6 California 4 North
Mineral flotation in water study. 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. 77). The zeta potential (mV) was determined for each of 50 liquid solutions prepared without
Permeability of sandstone during weathering. Natural stone, such as sandstone, is a popular building construction material. An experiment was carried out in order to better understand the decay properties of sandstone when exposed to the weather (Geographical Analysis, Vol. 42, 2010). Blocks of
Mongolian desert ants. The Journal of Biogeography (Dec.2003) published an article on the first comprehensive study of ants in Mongolia (Central Asia). Botanists placed seed baits at 11 study sites and observed the ant species attracted to each site. Some of the data recorded at each study site are
Symmetric or skewed? Would you expect the data sets that follow to possess relative frequency distributions that are symmetric, skewed to the right, or skewed to the left? Explain.a. The salaries of all persons employed by a large universityb. The grades on an easy testc. The grades on a difficult
Ranking driving performance of professional golfers.A group of Northeastern University researchers developed a new method for ranking the total driving performance of golfers on the Professional Golf Association (PGA) tour(The Sport Journal, Winter 2007). The method requires knowing a golfer’s
Cheek teeth of extinct primates. 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. 74). The data on dentary depth of molars (in millimeters) for 18 cheek teeth extracted
Is honey a cough remedy? Refer to the Archives of Pediatrics and Adolescent Medicine (Dec. 2007) study of honey as a remedy for coughing, Exercise 2.40 (p. 75).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
Corporate sustainability of CPA firms. Refer to the Business and Society (Mar. 2011) study on the sustainability behaviors of CPA corporations, Exercise 2.36(p. 74). Recall that the level of support for corporate sustainability (measured on a quantitative scale ranging from 0 to 160 points) was
Music performance anxiety. Refer to the British Journal of Music Education (Mar. 2014) study of music performance anxiety, Exercise 2.39 (p. 74). Scores on the Performance Anxiety Inventory (PAI) scale for participants in eight different studies are reproduced in the table.54 42 51 39 41 43 55 40
Characteristics of a rock fall. 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
Shaft graves in ancient Greece. Refer to the American Journal of Archaeology (Jan. 2014) study of sword shaft graves in ancient Greece, Exercise 2.37 (p. 74). The number of sword shafts buried at each of 13 recently discovered grave sites is reproduced in the following table.1 2 3 1 5 6 2 4 1 2 4 2
2.3 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 10a. Describe the shape of the
2.2 Use the applet Mean versus Median to illustrate your descriptions in Exercise 2.54. For each parta, b, andc, 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.
2.1 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.
Calculate the mean, median, and mode for each of the following samples:a. 7, -2, 3, 3, 0, 4b. 2, 3, 5, 3, 2, 3, 4, 3, 5, 1, 2, 3, 4c. 51, 50, 47, 50, 48, 41, 59, 68, 45, 37
Construct one data set consisting of five measurements, and another consisting of six measurements, for which the medians are equal.
Mineral flotation in water study. 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
Phishing attacks to e-mail accounts. Phishing is the term used to describe an attempt to extract personal/financial information (e.g., PIN numbers, credit card information, bank account numbers) from unsuspecting people through fraudulent e-mail. An article in Chance (Summer 2007)demonstrates how
Crab spiders hiding on flowers. Crab spiders use camouflage to hide on flowers while lying in wait to prey on other insects. Ecologists theorize that this natural camouflage also enables the spiders to hide from their own predators, such as birds and lizards. Researchers at the French Museum of
Sanitation inspection of cruise ships. To minimize the potential for gastrointestinal disease outbreaks, all passenger cruise ships arriving at U.S. ports are subject to unannounced sanitation inspections. Ships are rated on a 100-point scale by the Centers for Disease Control and Prevention. A
Is honey a cough remedy? Does a teaspoon of honey before bed really calm a child’s cough? To test the folk remedy, pediatric researchers at Pennsylvania State University carried out a designed study involving a sample of 105 children who were ill with an upper respiratory tract infection
Music performance anxiety. The nature of performance anxiety by music students was investigated in the British Journal of Music Education (Mar. 2014). Symptoms of music performance anxiety include increased heart rate, shallow breathing, anxious thoughts, and the avoidance of practice.A Performance
Cheek teeth of extinct primates. 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 2.9 (p. 62). In addition to degree of wear, the researchers recorded the dentary depth of
Shaft graves in ancient Greece. Archeologists have discovered a rise in shaft graves during the Middle Helladic period in ancient Greece (i.e., around 2000 BC). Shaft graves are named for the beautifully decorated sword shafts that are buried along with the bodies. An analysis of shaft graves was
Corporate sustainability of CPA firms. Refer to the Business and Society (Mar. 2011) study on the sustainability behaviors of CPA corporations, Exercise 1.26(p. 46). Recall that corporate sustainability refers to business practices designed around social and environmental considerations. Data on
Stability of compounds in new drugs. Testing the metabolic stability of compounds used in drugs is the cornerstone of new drug discovery. Two important values computed from the testing phase are the fraction of compound unbound to plasma (fup) and the fraction of compound unbound to microsomes
Irrelevant speech effects. In a psychological study of shortterm memory, irrelevant speech effects refer to the degree to which the memorization process is impaired by irrelevant background speech (for example, trying to memorize a list of numbers while listening to a speech in an unfamiliar
Refer to Exercise 2.32. Calculate the number of the 500 measurements falling into each of the measurement classes. Then graph a frequency histogram of these data.Applying the Concepts—Basic
How many classes are recommended in a histogram of a data set with less than 25 observations?Learning the Mechanics
Extinct New Zealand birds. Refer to the Evolutionary Ecology Research (July 2003) study of the patterns of extinction in the New Zealand bird population, Exercise 1.20(p. 45). Data on flight capability (volant or flightless), habitat (aquatic, ground terrestrial, or aerial terrestrial), nesting
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