A First Course In Statistics 12th Edition James T McClave, Terry T Sincich - Solutions

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Spall damage in bricks. A recent civil suit revolved around a five-building brick apartment complex located in the Bronx, New York, which began to suffer spalling damage (i.e., a separation of some portion of the face of a brick from its body). The owner of the complex alleged that the bricks were
Long-jump “takeoff error.” The long jump is a trackand-field event in which a competitor attempts to jump a maximum distance into a sandpit after a running start. At the edge of the pit is a takeoff board. Jumpers usually try to plant their toes at the front edge of this board to maximize their
Regression through the origin. Sometimes it is known from theoretical considerations that the straight-line relationship between two variables x and y passes through the origin of the xy-plane. Consider the relationship between the total weight y of a shipment of 50-pound bags of flour and the
Dance/movement therapy. In cotherapy, two or more therapists lead a group. An article in the American Journal of Dance Therapy (Spring/Summer 1995) examined the use of cotherapy in dance/movement therapy.Two of several variables measured on each of a sample of 136 professional dance/movement
Quantum tunneling. At temperatures approaching absolute zero 1 -273C2, helium exhibits traits that seem to defy many laws of Newtonian physics. An experiment has been conducted with helium in solid form at various temperatures near absolute zero. The solid helium is placed in a dilution
Winning marathon times. In Chance (Winter 2000), statistician Howard Wainer and two students compared men’s and women’s winning times in the Boston Marathon. One of the graphs used to illustrate gender differences is reproduced below. The scatterplot graphs the winning times (in minutes)
Mortality of predatory birds. Two species of predatory birds—collard flycatchers and tits—compete for nest holes during breeding season on the island of Gotland, Sweden. Frequently, dead flycatchers are found in nest boxes occupied by tits. A field study examined whether the risk of mortality
Relation of eye and head movements. How do eye and head movements relate to body movements when a person reacts to a visual stimulus? Scientists at the California Institute of Technology designed an experiment to answer this question and reported their results in Nature (Aug. 1998). Adult male
Extending the life of an aluminum smelter pot. An investigation of the properties of bricks used to line aluminum smelter pots was published in The American Ceramic Society Bulletin (Feb. 2005). Six different commercial bricks were evaluated. The life span of a smelter pot depends on the porosity
New method of estimating rainfall. Accurate measurements of rainfall are critical for many hydrological and meteorological projects. Two standard methods of monitoring rainfall use rain gauges and weather radar. Both, however, can be contaminated by human and environmental interference. In the
Feeding habits of fish. Refer to the Brain and Behavior Evolution (Apr. 2000) study of the feeding behavior of black-bream fish, presented in Exercise 2.162(p. 120). Recall that the zoologists recorded the number of aggressive strikes of two black-bream fish feeding at the bottom of an aquarium in
English as a second language reading ability. What are the factors that allow a native Spanish-speaking person to understand and read English? A study published in the Bilingual Research Journal (Summer 2006) investigated the relationship of Spanish (first-language) grammatical knowledge to English
Baseball batting averages versus wins. Is the number of games won by a major league baseball team in a season related to the team’s batting average? Consider data from the Baseball Almanac on the number of games won and the batting averages for the 14 teams in the American League for the 2013
College protests of labor exploitation. Refer to the Journal of World-Systems Research (Winter 2004) study of student “sit-ins” for a “sweat-free campus” (p. 133).Data on the duration (in days) of each sit-in as well as the number of student arrests were measured. The data for 5 sit-ins in
Sports news on local TV broadcasts. The Sports Journal(Winter 2004) published the results of a study conducted to assess the factors that affect the time allotted to sports news on local television news broadcasts. Information on total time (in minutes) allotted to sports and on audience ratings of
Predicting sale prices of homes. Real-estate investors, home buyers, and homeowners often use the appraised value of property as a basis for predicting the sale of that property. Data on sale prices and total appraised value of 78 residential properties sold recently in an upscale Tampa, Florida,
Wind turbine blade stress. Mechanical engineers at the University of Newcastle (Australia) investigated the use of timber in high-efficiency small wind turbine blades (Wind Engineering, Jan. 2004). The strengths of two types of timber—radiata pine and hoop pine—were compared. Twenty specimens
Consider the following 10 data points.x 3 5 6 4 3 7 6 5 4 7 y 4 3 2 1 2 3 3 5 4 2a. Plot the data on a scatterplot.b. Calculate the values of r and r2.c. Is there sufficient evidence to indicate that x and y are linearly correlated? Test at the a = .10 level of significance.Applying the
Consider the following sample data:y 5 1 3 x 5 1 3a. Construct a scatterplot for the data.b. It is possible to find many lines for which1y - yn2 = 0. For this reason, the criterion1y - yn2 = 0 is not used to identify the “best-fitting”straight line. Find two lines that have 1y - yn2 = 0.c.
In fitting a least squares line to n = 20 data points, the following quantities were computed: SSxx = 60, SSyy = 225, SSxy = -75, x = 2.4, and y = 45.a. Find the least squares line.b. Graph the least squares line.c. Calculate SSE.d. Calculate s2.e. Find a 90% confidence interval for b1. Interpret
True or False. In simple linear regression, about 95% of the y-values in the sample will fall within 2s of their respective predicted values.
Outline the five steps in a simple linear regression analysis.
Give the general form of a straight-line model for E(y).
Explain the difference between a probabilistic model and a deterministic model.
Food availability at middle schools. Refer to the Journal of School Health (Dec. 2009) study of identifying and quantifying food items in the a la carte line at a middle school, Exercise 7.99 (p. 446). Recall that two methods were compared—a detailed inventory approach and a checklist
Pain empathy and brain activity. Refer to the Science (Feb.20, 2004) study on the relationship between brain activity EmPAtHY and pain-related empathy in persons who watch others Couple Brain Activity ( y) Empathic Concern (x)1 .05 12 2 -.03 13 3 .12 14 4 .20 16 5 .35 16 6 0 17 7 .26 17 8 .50 18 9
Taste-testing scales. Refer to the Journal of Food Science(Feb. 2014) taste-testing study, Exercise 9.86 (p. 563).Recall that a sample of 200 subjects used the perceived hedonic intensity (PHI) scale to rate their most favorite and least favorite food. In addition, each rated the sensory intensity
Do nice guys finish first or last? Refer to the Nature(Mar. 20, 2008) study of whether the saying “nice guys finish last” applies to the competitive corporate world, Exercise 9.22 (p. 536). Recall that college students repeatedly played a version of the game “prisoner’s dilemma,”where
Groundwater contamination of wells. Environmental Science & Technology (Jan. 2005) published an investigation of MTBE contamination in 70 New Hampshire groundwater wells. The researchers wanted an estimate of the correlation between the MTBE level of a groundwater well and the depth (in feet) of a
The “name game.” Refer to the Journal of Experimental Psychology—Applied (June 2000) study in which the“name game” was used to help groups of students learn the names of other students in the group, presented in Exercise 9.34 (p. 541). Recall that one goal of the study was to investigate
Effect of massage on boxers. Refer to the British Journal of Sports Medicine (Apr. 2000) study of the effect of massaging boxers between rounds, presented in Exercise 9.70(p. 554). Two variables measured on the boxers were blood lactate level (y) and the boxer’s perceived recovery (x). The data
Lobster fishing study. Refer to the Bulletin of Marine Science (Apr. 2010) study of teams of fishermen fishing for the red spiny lobster in Baja California Sur, Mexico, Exercise 9.63 (p. 553). Recall that two variables measured for each of 8 teams from the Punta Abreojos (PA) fishing cooperative
Game performance of water polo players. Refer to the Biology of Sport (Vol. 31, 2014) study of the physiological performance of top-level water polo players, Exercise 9.24 (p. 537). Two variables were measured for each of eight Olympic male water polo players during competition: mean heart rate
Mongolian desert ants. Refer to the Journal of Biogeography (Dec. 2003) study of ants in Mongolia, presented in Exercise 9.26 (p. 538). Data on annual rainfall, maximum daily temperature, and number of ant species recorded at each of 11 study sites are reproduced in the table below.Site Region
Measuring the moon’s orbit. Refer to the American Journal of Physics (Apr. 2014) study of the moon’s orbit, Exercise 9.23 (p. 537). Recall that photographs were used to measure the angular size (in pixels) of the moon at various distances (heights) above the horizon (measured in degrees). The
The following sample data were collected on variables x and y:x 0 3 0 -4 3 0 4 y 0 2 2 0 3 1 2a. Specify the null and alternative hypotheses that should be used in conducting a hypothesis test to determine whether the variables x and y are correlated.b. Conduct the test of parta, using a = .05.c.
Specify the rejection region for Spearman’s nonparametric test for rank correlation in each of the following situations:a. H0: r = 0, Ha: r 0, n = 10, a = .05b. H0: r = 0, Ha: r 7 0, n = 20, a = .025c. H0: r = 0, Ha: r 6 0, n = 30, a = .01 9.127 Compute Spearman’s rank correlation coefficient
What is the value of rs when there is perfect negative rank correlation between two variables? Perfect positive rank correlation?Learning the Mechanics
What conditions are required for a valid Spearman’s test?
Legal advertising—does it pay? To gain a competitive edge, lawyers aggressively advertise their services. Does legal advertising really pay? To partially answer this question, consider the case of an actual law firm that specializes in personal injury (PI) cases. The firm spends thousands of
An MBA’s work-life balance. Many business schools offer courses that assist MBA students with developing good work-life balance habits and most large companies have developed work-life balance programs for their employees. The Graduate Management Admission Council (GMAC) conducted a survey of
Thickness of dust on solar cells. The performance of a solar cell can deteriorate when atmospheric dust accumulates on the solar panel surface. In the International Journal of Energy and Environmental Engineering (Dec.2012), researchers at the Renewable Energy Research Laboratory, University of
Impact of dropping ping-pong balls. The impact of dropping hollow balls was investigated in the American Journal of Physics (Mar. 2014). Standard ping-pong balls were dropped vertically onto a force plate. Upon impact, two variables were measured: y = coefficient of restitution, COR (measured as a
Life tests of cutting tools. Refer to the data on life tests of cutting tools, Exercise 9.52 (p. 547).a. Use a 90% confidence interval to estimate the mean useful life of a brand-A cutting tool when the cutting Tweet Rate Revenue (millions)1365.8 142 1212.8 77 581.5 61 310.1 32 455 31 290 30 250 21
Forecasting movie revenues with Twitter. Refer to the IEEE International Conference on Web Intelligence and Intelligent Agent Technology (2010) study of how social media (e.g., Twitter.com) may influence the products consumers buy, Exercise 9.36 (p. 542). Recall that opening weekend box office
Spreading rate of spilled liquid. Refer to the Chemicial Engineering Progress (Jan. 2005) study of the rate at which a spilled volatile liquid will spread across a surface, presented in Exercise 9.35 (p. 541). Recall that simple linear regression was used to model y = mass of the spill as a
The “name game.” Refer to the Journal of Experimental Psychology—Applied (June 2000) name-retrieval study, presented in Exercise 9.34 (p. 541).a. Find a 99% confidence interval for the mean recall proportion for students in the fifth position during the “name game.” Interpret the
Ideal height of your mate. Refer to the Chance (Summer 2008) study of the height of the ideal mate, Exercise 9.33(p. 540). The data were used to fit the simple linear regression model, E1y2 = b0 + b1x, where y = ideal partner’s height (in inches) and x = student’s height (in inches). One model
Sound waves from a basketball. Refer to the American Journal of Physics (June 2010) study of sound waves in a spherical cavity, Exercise 9.31 (p. 540). You fit a straightline model relating sound wave frequency (y) to number of resonances (x) for n = 24 echoes resulting from striking a basketball
Game performance of water polo players. Refer to the Biology of Sport (Vol. 31, 2014) study of the physiological performance of top-level water polo players, Exercise 9.24 (p. 537). Recall that the in-game heart rate (y, expressed as a percentage of maximum heart rate) of a player was modeled as a
Removing nitrogen from toxic wastewater. Highly toxic wastewater is produced during the manufacturing of dry-spun acrylic fiber. One way to lessen toxicity is to remove the nitrogen from the wastewater. A group of environmental engineers investigated a promising method—called anaerobic ammonium
Sweetness of orange juice. Refer to the simple linear regression of sweetness index y and amount of pectin, x, for n = 24 orange juice samples, presented in Exercise 9.32(p. 540). A 90% confidence interval for the mean sweetness index E(y) for each value of x is shown on the SPSS spreadsheet on the
Ranking driving performance of professional golfers.Refer to The Sport Journal (Winter 2007) study of a new method for ranking the total driving performance of golfers on the Professional Golf Association (PGA) tour, presented in Exercise 9.29 (p. 539). You fit a straight-line model relating
Mongolian desert ants. Refer to the Journal of Biogeography(Dec. 2003) study of ant sites in Mongolia, presented in Exercise 9.26 (p. 538). You applied the method of least squares to estimate the straight-line model relating annual rainfall (y) and maximum daily temperature (x).A SAS printout
Measuring the moon’s orbit. Refer to the American Journal of Physics (Apr. 2014) study of the moon’s orbit, Exercise 9.23 (p. 537). Recall that the angular size (y) of the moon was modeled as a straight-line function of height above horizon (x). A MINITAB printout showing both a 95% prediction
Do nice guys finish first or last? Refer to the Nature (Mar.20, 2008) study of the use of punishment in cooperation games, Exercise 9.22 (p. 536). Recall that simple linear regression was used to model a player’s average payoff(y) as a straight-line function of the number of times punishment was
Refer to Exercise 9.105.a. Using no information about x, estimate and calculate a 95% confidence interval for the mean value of y. [Hint: Use the one-sample t methodology of Section 7.3.]b. Plot the estimated mean value and the confidence interval as horizontal lines on your scatterplot.c. Compare
Consider the following pairs of measurements.x 4 6 0 5 2 3 2 6 2 1 y 3 5 -1 4 3 2 0 4 1 1 For these data, SSxx = 38.900, SSyy = 33.600, SSxy = 32.8, and yn = -.414 + .843x.a. Construct a scatterplot of the data.b. Plot the least squares line on your scatterplot.c. Use a 95% confidence interval to
Consider the following pairs of measurements.x 1 2 3 4 5 6 7 y 3 5 4 6 7 7 10a. Construct a scatterplot of these data.b. Find the least squares line, and plot it on your scatterplot.c. Find s2.d. Find a 90% confidence interval for the mean value of y when x = 4. Plot the upper and lower bounds of
In fitting a least squares line to n = 5 data points, the following quantities were computed:SSxx = 31, x = 2, SSyy = 24, y = 6, SSxy = 26a. Find the least squares line.b. Graph the least squares line.c. Calculate SSE.d. Calculate s2.e. Find a 90% confidence interval for the mean value of y when xp
For each of the following, decide whether the proper inference is a prediction interval for y or a confidence interval for E(y):a. A jeweler wants to predict the selling price of a diamond stone on the basis of its size (number of carats).b. A psychologist wants to estimate the average IQ of all
Pain tolerance study. A study published in Psychosomatic Medicine (Mar./Apr. 2001) explored the relationship between reported severity of pain and actual pain tolerance in 337 patients who suffer from chronic pain. Each patient reported his/her severity of chronic pain on a seven-point scale 11 =
Plants that grow on Swiss cliffs. Refer to the Alpine Botany(Nov. 2012) study of rare plants that grow on the limestone cliffs of the Northern Swiss Jura mountains, Exercise 2.165(p. 121). Data on altitude above sea level (meters), plant population size (number of plants growing), and molecular
Child labor in diamond mines. The role of child laborers in Africa’s colonial-era diamond mines was the subject of research published in the Journal of Family History (Vol.35, 2010). One particular mining company lured children to the mines by offering incentives for adult male laborers to
Effect of massage on boxing. Refer to the British Journal of Sports Medicine (Apr. 2000) study of the effect of massage on boxing performance, presented in Exercise 9.70 (p. 530).Find and interpret the values of r and r2 for the simple linear regression relating the blood lactate concentration and
The “name game.” Refer to the Journal of Experimental Psychology—Applied (June 2000) name-retrieval study, first presented in Exercise 9.34 (p. 531). Find and interpret the values of r and r2 for the simple linear regression relating the proportion of names recalled (y) and the position
Do nice guys finish first or last? Refer to the Nature (Mar.20, 2008) study of the use of punishment in cooperation games, Exercise 9.22 (p. 536). Recall that college students repeatedly played a version of the game “prisoner’s dilemma”and the researchers recorded the average payoff(y) and
Eye anatomy of giraffes. Refer to the African Zoology(Oct. 2013) study of giraffe eye characteristics, Exercise 9.71(p. 530). Recall that the researchers fit a simple linear regression equation of the form ln 1y2 = b0 + b1 ln 1x2 + e, where y represents an eye characteristic and x represents body
View of rotated objects. Perception & Psychophysics(July 1998) reported on a study of how people view three- dimensional objects projected onto a rotating two- dimensional image. Each in a sample of 25 university students viewed various depth-rotated objects (e.g., a hairbrush, a duck, and a shoe)
Salary linked to height. Are short people shortchanged when it comes to salary? According to business professors T. A. Judge (University of Florida) and D. M. Cable(University of North Carolina), tall people tend to earn more money over their career than short people earn(Journal of Applied
Physical activity of obese young adults. The International Journal of Obesity (Jan. 2007) published a study of the physical activity of obese young adults. For two groups of young adults—13 obese and 15 of normal weight—researchers recorded the total number of registered movements (counts) of
Lobster fishing study. Refer to the Bulletin of Marine Science (Apr. 2010) study of teams of fishermen fishing for the red spiny lobster in Baja California Sur, Mexico, Exercise 9.63 (p. 553). Recall that simple linear regression was used to model y = total catch of lobsters (in kilograms)during
Going for it on fourth down in the NFL. Each week coaches in the National Football League (NFL) face a decision during the game. On fourth down, should the team punt the ball or go for a first down? To aid in the decision-making process, statisticians at California State University, Northridge,
Taste-testing scales. The Journal of Food Science (Feb.2014) published the results of a taste-testing study. The researchers evaluated the general Labeled Magnitude Scale (gLMS), used to rate the palatability of food items on a scale ranging from -100 (for strongest imaginable dislike) to + 100
Last name and acquisition timing. Refer to the Journal of Consumer Research (Aug. 2011) study of the speed with which consumers decide to purchase a product, Exercise 7.12 (p. 406). Recall that the researchers theorized that consumers with last names that begin with letters later in the alphabet
RateMyProfessors.com. A popular Web site among college students is RateMyProfessors.com (RMP).Established over 10 years ago, RMP allows students to post quantitative ratings of their instructors. In Practical Assessment, Research & Evaluation (May 2007), University of Maine researchers investigated
Calculate r2 for the least squares line in Exercise 9.21(p. 536).Applet Exercise 9.2 Use the applet entitled Correlation by the Eye to explore the relationship between the pattern of data in a scatterplot and the corresponding correlation coefficient.a. Run the applet several times. Each time,
Calculate r2 for the least squares line in Exercise 9.18(p. 536).
Construct a scatterplot for each data set. Then calculate r and r2 for each data set. Interpret their values.a. x -2 -1 0 1 2 y -1 2 3 6 9b. x -2 -1 0 1 2 y 9 6 4 3 1c. x 2 3 3 4 4 4 5 y 3 2 4 2 3 4 3d. x -2 -1 1 3 4 y 0 1 2 1 0
True or False. A value of the correlation coefficient near 1 or near -1 implies a causal relationship between x and y.Learning the Mechanics
Spreading rate of spilled liquid. Refer to the Chemical Engineering Progress (Jan. 2005) study of the rate at which a spilled volatile liquid will spread across a surface, Exercise 9.35 (p. 541). Is there sufficient evidence (at a = .05) to indicate that the mass of the spill tends to diminish
Does elevation affect hitting performance in baseball?Refer to the Chance (Winter 2006) investigation of the effects of elevation on slugging percentage in Major League Baseball, Exercise 2.160 (p. 120). Data were compiled on players’ composite slugging percentages at each of 29 cities for the
The “name game.” Refer to the Journal of Experimental Psychology—Applied (June 2000) name-retrieval study, presented in Exercise 9.34 (p. 541). Recall that the goal of the study was to investigate the linear trend between proportion of names recalled (y) and position (order) of the student(x)
Characterizing bone with fractal geometry. In Medical Engineering & Physics (May 2013), researchers used fractal geometry to characterize human cortical bone.A measure of the variation in the volume of cortical bone tissue—called fractal dimension—was determined for each in a sample of 10 human
Pain empathy and brain activity. Empathy refers to being able to understand and vicariously feel what others actually feel. Neuroscientists at University College of London investigated the relationship between brain activity and pain-related empathy in persons who watch others in pain (Science,
Eye anatomy of giraffes. Giraffes are believed to have excellent vision. The journal African Zoology (Oct.2013) published a study of giraffe eye characteristics.Data were collected for a sample of 27 giraffes inhabiting southeastern Zimbabwe. Of interest to the researchers was how these eye
Effect of massage on boxers. The British Journal of Sports Medicine (Apr. 2000) conducted a study of the effect of massage on boxing performance. Two variables measured on the boxers were blood lactate concentration (in mM)and the boxer’s perceived recovery (on a 28-point scale).On the basis of
Forest fragmentation study. Refer to the Conservation Ecology (Dec. 2003) study on the causes of fragmentation of 54 South American forests, presented in Exercise 2.166(p. 121). Recall that researchers developed two fragmentation indexes for each forest—one index for anthropogenic(human
Ideal height of your mate. Refer to the Chance (Summer 2008) study of the height of the ideal mate, Exercise 9.33(p. 540). You used the data to fit the simple linear regression model E1y2 = b0 + b1x, where y = ideal partner’s height (in inches) and x = student’s height (in inches), for both
Sweetness of orange juice. Refer to Exercise 9.32 (p. 516)and the simple linear regression relating the sweetness index (y) of an orange juice sample to the amount of water-soluble pectin (x) in the juice. Find a 95% confidence interval for the true slope of the line. Interpret the result.
FCAT scores and poverty. Refer to the Journal of Educational and Behavioral Statistics (Spring 2004) study of scores on the Florida Comprehensive Assessment Test(FCAT), first presented in Exercise 9.30 (p. 539). Consider the simple linear regression relating math score (y) to percentage(x) of
Ranking driving performance of professional golfers.Refer to The Sport Journal (Winter 2007) study of a new method for ranking the total driving performance of golfers on the Professional Golf Association (PGA) tour, presented in Exercise 9.29 (p. 539). You fit a straight-line model relating
Beauty and electoral success. Are good looks an advantage when running for political office? This was the question of interest in an article published in the Journal of Public Economics (Feb. 2010). The researchers focused on a sample of 641 non-incumbent candidates for political office in Finland.
Lobster fishing study. Refer to the Bulletin of Marine Science (April 2010) study of teams of fishermen fishing for the red spiny lobster in Baja California Sur, Mexico, Exercise 7.18 (p. 407). Two variables measured for each of 8 teams from the Punta Abreojos (PA) fishing cooperative were y =
Generation Y’s entitlement mentality. The current workforce is dominated by “Generation Y”—people born between 1982 and 1999. These workers have a reputation as having an entitlement mentality (e.g., they believe they have a right to a high-paying job without the work ethic). The reasons
Estimating repair and replacement costs of water pipes.Refer to the IHS Journal of Hydraulic Engineering(Sept. 2012) study of water pipes susceptible to breakage, Exercise 9.28 (p. 541). Recall that civil engineers used simple linear regression to model y = the ratio of repair to replacement cost
Congress voting on women’s issues. The American Economic Review (Mar. 2008) published research on how the gender mix of a U.S. legislator’s children can L09058 L09059 Exercises 9.53–9.76 influence the legislator’s votes in Congress. Specifically, the researcher investigated how having
Consider the following pairs of observations:y 4 2 5 3 2 4 x 1 4 5 3 2 4a. Construct a scatterplot of the data.b. Use the method of least squares to fit a straight line to the six data points.c. Graph the least squares line on the scatterplot of part a.d. Compute the test statistic for determining
Consider the following pairs of observations:x 1 5 3 2 6 6 0 y 1 3 3 1 4 5 1a. Construct a scatterplot of the data.b. Use the method of least squares to fit a straight line to the seven data points in the table.c. Plot the least squares line on your scatterplot of part a.d. Specify the null and
Construct both a 95% and a 90% confidence interval for b1 for each of the following cases.a. b n1 = 32, s = 4, SSxx = 32, n = 10b. b n1 = 65, SSE = 1,860, SSxx = 20, n = 14c. b n1 = -8.4, SSE = 143, SSxx = 49, n = 18

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A First Course In Statistics 12th Edition James T McClave, Terry T Sincich - Solutions

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