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statistics for engineers and scientists

Questions and Answers of Statistics For Engineers And Scientists

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
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
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.
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
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
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
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
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
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
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
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
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
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
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
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
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
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).
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
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
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
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.
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
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
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).
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
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
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
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
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
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
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
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
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 =
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 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
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
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
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
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
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
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
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 +
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
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
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
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
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
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
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
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
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
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
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.
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
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
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
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
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
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 “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
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
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
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
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),
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
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
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?
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
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
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
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
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
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
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.
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
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
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
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
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
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
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,
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
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
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
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).
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
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
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
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
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.
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
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,

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