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Statistics 13th Global Edition James T. McClave And Terry T Sincich - Solutions
Suppose you fit the interaction model y = b0 + b1 x1 + b2 x2 + b3 x1 x2 + e to n = 32 data points and obtain the results below:SSyy = 500 SSE = 21 b n 3 = 10 sbn 3 = 4a. Find R2 and interpret its value.b. Is the model adequate for predicting y? Test at a = .05.c. Use a graph to explain the
Suppose the true relationship between E(y) and the quantitative independent variables x1 and x2 is given by the model below.E1y2 = -5 + x1 + 3x2 - 3x1 x2a. Describe the corresponding three-dimensional response surface.b. Plot the linear relationship between y and x2 for x1 = 0, 1, 2, where 0 … x2
Write an interaction model relating the mean value of y, E(y), toa. two quantitative independent variablesb. three quantitative independent variables [Hint: Include all possible two-way cross-product terms.]
Arsenic in groundwater. Refer to the Environmental Science & Technology (Jan. 2005) study of the reliability of a commercial kit designed to test for arsenic in groundwater, presented in Exercise 12.23(p. 700). You fit a first-order model for arsenic level (y) as a function of latitude, longitude,
Usability Professionals, salary survey. The Usability Professionals’ Association (UPA) supports people who research, design, and evaluate the user experience of products and services. The UPA conducted a salary survey of its members (UPA Salary Survey, Aug. 18, 2009). One of the report’s
Predicting runs scored in baseball. Refer to the Chance(Fall 2000) study of runs scored in Major League Baseball games, Exercise 12.19(p. 698). Multiple regression was used to model total number of runs scored (y) of a team during the season as a function of number of walks (x1), number of singles
Characteristics of lead users. Refer to the Creativity and Innovation Management (Feb. 2008) study of lead users of children’s computer games, Exercise 12.15(p. 698). Recall that the researchers modeled lead-user rating (y, measured on a 5-point scale) as a function of gender (x1 = 1 if female, 0
Explain why we use yn as an estimate of E(y) and to predict y.
Study of adolescents with ADHD. Children with attentiondeficit/hyperactivity disorder (ADHD) were monitored to evaluate their risk for substance (e.g., alcohol, tobacco, illegal drug) use (Journal of Abnormal Psychology, Aug. 2003).The following data were collected on 142 adolescents diagnosed with
Forecasting movie revenues with Twitter. Refer to the IEEE International Conference on Web Intelligence and Intelligent Agent Technology (2010) study on using the volume of chatter on Twitter.com to forecast movie box office revenue, Exercise 11.36(p. 631). Recall that opening weekend box office
Estimation of urban population by means of satellite images. Can the population of an urban area be estimated without taking a census? Geographical Analysis(Jan. 2007) demonstrated the use of satellite image maps in estimating urban population. A portion of Columbus, Ohio, was partitioned into n =
Whales entangled in fishing gear. Refer to the Marine Mammal Science (April 2010) study of whales entangled in fishing gear, Exercise 10.32(p. 552). Data collected for a sample of 207 entanglements in the East Sea of Korea were used to model the length (y) of an entangled whale (in meters). Two
Dating and disclosure. Refer to the Journal of Adolescence(Apr. 2010) study of adolescents’ disclosure of their dating and romantic relationships, Exercise 8.43 (p. 419).Data collected for a sample of 222 high school students were used to determine the level of disclosure of the date’s identity
Characteristics of lead users. Creativity and Innovation Management (Feb. 2008) published an article on identifying the social network characteristics of lead users of children’s computer games. Data were collected for n = 326 children and the following variables measured: lead-user rating (y,
Suppose you fit the first-order model y = b0 + b1 x1 + b2 x2 + b3 x3 + b4 x4 + b5 x5 + e to n = 27 data points and obtain SSE = .33 R2= .92a. Do the values of SSE and R2 suggest that the model provides a good fit to the data? Explain.b. Is the model of any use in predicting y? Test the null
Consider the following first-order model equation in three quantitative independent variables:E1y2 = 2 + 4x1 - 2x2 - 5x3a. Graph the relationship between y and x1 for x2 = -2 and x3 = 2.b. Repeat part a for x2 = 3 and x3 = 3.c. How do the graphed lines in parts a and b relate to each other? What is
Suppose you fit the model y = b0 + b1 x1 + b2 x2 + b3 x3 + e to n = 30 data points and obtain the following result:yn = 2.2 - 2.8x1 + 1.9x2 + .97x3 The estimated standard errors of b n 2 and b n 3 are 1.06 and .27, respectively.a. Test the null hypothesis H0: b2 = 0 against the alternative
What are the caveats to conducting t-tests on all of the individual b parameters in a multiple-regression model?
List the four assumptions about the random error e required for a multiple-regression analysis.
Write a first-order model relating E(y) toa. two quantitative independent variablesb. four quantitative independent variablesc. five quantitative independent variables
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
Snow geese feeding trial. Botanists at the University of Toronto conducted a series of experiments to investigate the feeding habits of baby snow geese (Journal of Applied Ecology, Vol. 32, 1995). Goslings were deprived of food LO9 until their guts were empty and then were allowed to feed for 6
Performance in online courses. Florida State University information scientists assessed the impact of online courses on student performance (Educational Technology& Society, Jan. 2005). Each in a sample of 24 graduate students enrolled in an online advanced Web application course was asked, “How
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 -273°C2, 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
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 LO9 Technology designed an experiment to answer this question and reported their results in Nature (Aug. 1998). Adult male
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 LO9 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
Removing metal from water. In the Electronic Journal of Biotechnology (Apr. 15, 2004), Egyptian scientists studied a new method for removing heavy metals from water. Metal solutions were prepared in glass vessels, and then biosorption was used to remove the metal ions. Two variables were measured
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
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. 124).Recall that the zoologists recorded the number of aggressive strikes of two black-bream fish feeding at the bottom of an aquarium in
Sports news on local TV broadcasts. The Sports Journal LO9 (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
Wind turbine blade stress. Mechanical engineers at the University of Newcastle (Australia) investigated the use of timber in high-efficiency small wind turbine LO9 blades (Wind Engineering, Jan. 2004). The strengths of two types of timber—radiata pine and hoop pine—were compared. Twenty
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 2 LO9 a. 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.
Consider the following sample data:y 5 1 3 x 5 1 3a. Construct a scatterplot for the data. LO9 b. It is possible to find many lines for whichΣ1y - yn2 = 0. For this reason, the criterionΣ1y - yn2 = 0 is not used to identify the “best-fitting”straight line. Find two lines that have Σ1y - yn2
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. LO9 c. Calculate SSE.d. Calculate s2.e. Find a 90% confidence interval for b1.
True or False. In simple linear regression, about 95% of the y-values in the sample will fall within 2s of their respective LO9 predicted values.
Outline the five steps in a simple linear regression LO9 analysis.
Give the general form of a straight-line model for E(y). LO9
Explain the difference between a probabilistic model and a deterministic model. LO9
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, LO9 two variables were measured: y = coefficient of restitution, COR (measured
Life tests of cutting tools. Refer to the data on life tests of cutting tools, Exercise 11.52 (p. 636).a. Use a 90% confidence interval to estimate the mean useful life of a brand-A cutting tool when the cutting speed is 45 meters per minute. Repeat for brand B.Compare the widths of the two
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 11.36 (p. 631). 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 11.35 (p. 630). 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 11.34 (p. 630).a. Find a 99% confidence interval for the mean recall proportion for students in the fifth position during the “name game.” Interpret the result.
Ideal height of your mate. Refer to the Chance (Summer 2008) study of the height of the ideal mate, Exercise 11.33(p. 629). 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 11.31 (p. 629). You fit a straight-line model relating sound wave frequency (y) LO9 to number of resonances (x) for n = 24 echoes resulting from striking a
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 11.24 (p. 626). Recall that the in-game heart rate (y, expressed as a percentage of maximum heart LO9 rate) of a player was modeled
Do nice guys finish first or last? Refer to the Nature (Mar.20, 2008) study of the use of punishment in cooperation games, Exercise 11.22 (p. 625). 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 11.107.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. LO9 c.
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 LO9 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
Consider the following pairs of measurements.x 1 2 3 4 5 6 7 y 3 5 4 6 7 7 10 LO9 a. 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
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. LO9 c. Calculate SSE.d. Calculate s2.e. Find a 90% confidence interval for the mean value of y
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
True or False. The greater the deviation between x and x, the wider the prediction interval for y will be. LO9
True or False. For a given x, a confidence interval for E(y) will always be wider than a prediction interval LO9 for y.
Explain the difference between y and E(y) for a given x. LO9
Refer again to the drug reaction regression. Predict the reaction time for the LO9 next performance of the experiment for a subject with a drug concentration of 4%. Use a 95% prediction interval.
Refer to the simple linear regression on drug reaction. Find a 95% confidence interval for the mean reaction time when the concentration of the drug in the bloodstream is 4%. LO9
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 LO9 reported his/her severity of chronic pain on a seven-point scale
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. 125). 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 LO9 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 11.70 (p. 643).Find and interpret the values of r and r2 for the simple LO9 linear regression relating the blood lactate
The “name game.” Refer to the Journal of Experimental Psychology—Applied (June 2000) name-retrieval study, first presented in Exercise 11.34 (p. 630). Find and interpret the values of r and r2 for the simple linear regression LO9 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 11.22 (p. 625). 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 11.71(p. 643). 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 threedimensional 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
Redshifts of quasi-stellar objects. Refer to the Journal of Astrophysics & Astronomy (Mar./Jun. 2003) study of redshifts in quasi-stellar objects presented in Exercise 11.27 LO9 (p. 627). Recall that simple linear regression was used to model the magnitude (y) of a quasi-stellar object as a
Physical activity of obese young adults. Refer to the International Journal of Obesity (Jan. 2007) study of the physical activity of obese young adults, presented in Exercise 6.37 (p. 331). For two groups of young adults—13 obese and 15 of normal weight—researchers recorded the LO9 total
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 11.63 (p. 642). 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,
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 LO9 9.14 (p. 476). Recall that the researchers theorized that consumers with last names that begin with letters later in the
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
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. LO9 a. Run the applet several times. Each time, guess the value of the correlation coefficient. Then click Show r to see the actual
Calculate r2 for the least squares line in Exercise 11.21 LO9 (p. 625).
Calculate r2 for the least squares line in Exercise 11.18(p. 625). LO9
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 LO9 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 LO9 1 or near -1 implies a causal relationship between x and y.
Explain what each of the following sample correlation coefficients tells you about the relationship between the x and y LO9 values in the sample:a. r = 1b. r = -1c. r = 0d. r = .90e. r = .10f. r = -.88
Describe the slope of the least squares regression line for LO9 the given information.a. r = -.4b. r = .4c. r = 0d. r2= .81
True or False. The correlation coefficient is a measure of the LO9 strength of the linear relationship between x and y.
Calculate the coefficient of determination for the drug reaction example. The data are repeated in Table 11.4 for convenience. Interpret the result. LO9
Legalized gambling is available on several riverboat casinos operated by a city in Mississippi. The mayor of the city wants to know the correlation between the number of casino employees and the yearly crime rate. The records for the past 10 years are examined, and the results listed in Table 11.3
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 LO9 11.35 (p. 630). Is there sufficient evidence (at a = .05) to indicate that the mass of the spill tends to
The “name game.” Refer to the Journal of Experimental Psychology—Applied (June 2000) name-retrieval study, presented in Exercise 11.34 (p. 630). Recall that the goal of the study was to investigate the linear trend between proportion LO9 of names recalled (y) and position (order) of the
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 LO9 in a sample of 10
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. Refer to the British Journal of Sports Medicine (Apr. 2000) study of the effect of massage on boxing performance, presented in Exercise 10.82 LO9 (p. 580). Two other variables measured on the boxers were blood lactate concentration (in mM) and the boxer’s perceived
Forest fragmentation study. Refer to the Conservation Ecology (Dec. 2003) study on the causes of fragmentation LO9 of 54 South American forests, presented in Exercise 2.166(p. 125). 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 11.33(p. 629). You used the data to fit the simple linear regression LO9 model E1y2 = b0 + b1x, where y = ideal partner’s height (in inches) and x = student’s height (in inches), for
Sweetness of orange juice. Refer to Exercise 11.32(p. 629) 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 LO9 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 11.30 (p. 628).Consider the simple linear regression relating math score LO9 (y) to percentage (x)
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