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fundamentals of statistics

Questions and Answers of Fundamentals Of Statistics

11 Excavating ancient pottery. In the Chance (Fall 2000) study of ancient Greek pottery, 837 pottery pieces were uncovered at the excavation site. The table describing the types of pottery found is
10 Beetles and slime molds. Myxomycetes are mushroomlike slime molds that are a food source for insects. The Journal of Natural History (May 2010) published the results of a study that investigated
8 A multinomial experiment with k = 4 cells and n = 400 produced the data shown in the accompanying table. Do these data provide sufficient evidence to contradict the null hypothesis that p1 = .2, p2
7 A multinomial experiment with k = 4 cells and n = 205 produced the data shown in the following table:a. Is there sufficient evidence to conclude that the multinomial probabilities differ? Test,
6 A multinomial experiment with k = 3 cells and n = 320 produced the data shown in the accompanying table. Do these data provide sufficient evidence to contradict the null hypothesis that p1 = .25,
Suppose an educational television station has broadcast a series of programs on the physiological and psychological effects of smoking marijuana. Now that the series is finished, the station wants to
181 Entry-level job preferences. Benefits Quarterly (First Quarter, 1995) published a study of entry-level job preferences.A number of independent variables were used to model the job preferences
179 Sale prices of apartments. A Minneapolis, Minnesota, real-estate appraiser used regression analysis to explore the relationship between the sale prices of apartment buildings sold in Minneapolis
178 Habitats of grizzly bears. Do grizzly bears segregate on the basis of sex? One hypothesis is that female grizzlies avoid male-occupied habitats because of competition for food and cannibalism. A
177 Soil loss during rainfall. Phosphorus used in soil fertilizers can contaminate freshwater sources during rainfall runoff. Consequently, it is important for water quality engineers to estimate the
175 Rating funny cartoons. Newspaper cartoons, although designed to be funny, often invoke hostility, pain, or aggression in readers, especially when those cartoons depict violence.A study was
174 Comparing mosquito repellents. Which insect repellents protect best against mosquitoes? Periodically, consumer groups conduct tests to compare insect repellents (e.g., Consumer Reports, June
173 Socialization of graduate students. Teaching Sociology(July 1995) developed a model for the professional socialization of graduate students working toward a Ph.D. in sociology. One of the
172 Optimizing semiconductor material processing. Fluorocarbon plasmas are used in the production of semiconductor materials. In the Journal of Applied Physics(Dec. 1, 2000), electrical engineers at
171 Snow geese feeding trial. The Journal of Applied Ecology(Vol. 32, 1995) performed a study of the feeding habits of baby snow geese. Data on gosling weight change, digestion efficiency,
170 Deferred tax allowance study. A study was conducted to identify accounting choice variables that influence a manager’s decision to change the level of the deferred tax asset allowance at a firm
165 Genetics of a brain disease. Spinocerebellar ataxia type 1 (SCA1) is an inherited neurodegenerative disorder characterized by dysfunction of the brain. From a deoxyribonucleic acid (DNA) analysis
161 Global warming and foreign investments. Scientists believe that a major cause of global warming is higher levels of carbon dioxide (CO2) in the atmosphere. In the Journal of World-Systems
158 The first-order model E(y) = b0 + b1 x1 was fit to n = 19 data points. A plot of the residuals of the model is shown.Is the need for a quadratic term in the model evident from the plot? Explain
156 Suppose you used MINITAB to fit the model y = b0 + b1 x1 + b2 x2 + e to n = 15 data points and you obtained the printout below.a. What is the least squares prediction equation?b. Find R2 and
146 Failure times of silicon wafer microchips. Refer to the National Semiconductor study of manufactured silicon wafer integrated circuit chips, Exercise 72. Recall that the failure times of the
144 Passive exposure to smoke (continued). Refer to Exercise 143 . Two MINITAB residual plots for the simple linear regression model are shown below.a. Which graph should be used to check for normal
143 Passive exposure to smoke. Passive exposure to environmental tobacco smoke has been associated with suppression of growth and an increased frequency of respiratory tract infections in normal
137 Consider fitting the multiple regression model E(y) = b0 + b1 x1 + b2 x2 + b3 x3 + b4 x4 + b5 x5 A matrix of correlations for all pairs of independent variables is shown. Do you detect a
129 Using corn in a duck diet. Corn is high in starch content;consequently, it is considered excellent feed for domestic chickens. Does corn possess the same potential in feeding ducks bred for
128 Modeling species abundance. A marine biologist was hired by the EPA to determine whether the hot-water runoff from a particular power plant located near a large gulf is having an adverse effect
124 Accuracy of software effort estimates. Periodically, software engineers must provide estimates of their effort in developing new software. In the Journal of Empirical Software Engineering (Vol.
123 Suppose there are six independent variables x1, x2, x3, x4, x5, and x6 that might be useful in predicting a response y . A total of n = 50 observations is available, and it is decided to employ
A botanist conducted an experiment to study the growth of carnations as a function of the temperature x1 (F) in a greenhouse and the amount of fertilizer x2 [kilograms (kg) per plot] applied to the
102 RNA analysis of wheat genes. Engineers from the Department of Crop and Soil Sciences at Washington State University used regression to estimate the number of copies of a gene transcript in an
99 Smoking and resting energy. The influence of cigarette smoking on resting energy expenditure (REE) in normalweight and obese smokers was investigated ( Health Psychology , Mar. 1995). The
98 Impact of race on football card values. Refer to the Electronic Journal of Sociology (2007) study of the impact of race on the value of professional football players’ “rookie”cards,
96 Consider the modelwhere x1 is a quantitative variable andThe resulting least squares prediction equation isa. What is the equation of the response curve for E ( y )when x2 = 0 and x3 = 0? When x2
Consider the modelwhere x1 is a quantitative variable and x2 and x3 are dummy variables describing a qualitative variable at three levels, using the coding schemeThe resulting least squares
77 The model E(y) = b0 + b1 x1 + b2 x2 + b3 x3, wherewas used to relate E ( y ) to a single qualitative variable with four levels. This model was fitted to n = 30 data points and the following result
74 Tree frog study. The optomotor responses of tree frogs were studied in the Journal of Experimental Zoology (Sept.1993). Microspectrophotometry was used to measure the threshold quantal flux (the
53 Factors that affect an auditor’s judgment. A study was conducted to determine the effects of linguistic delivery style and client credibility on auditors’ judgments ( Advances in Accounting
49 Eye movement and spatial distortion. A study of how eye movement behavior can distort one’s judgment of the location of an object was published in Advances in Cognitive Psychology (Vol. 6,
46 Role of retailer interest in shopping behavior. Retailinterest is defined by marketers as the level of interest a consumer has in a given retail store. Marketing professors at the University of
43 Suppose you fit the interaction modelto n = 32 data points and obtain the following results:SSyy = 479 SSE = 21 b n 3 = 10 sb n 3 = 4a. Find R2 and interpret its value.b. Is the model adequate for
Refer to Examples 1–4. Suppose the collector of grandfather clocks, having observed many auctions, believes that the rate of increase in the auction price with age will be driven upward by a large
36 California rain levels. An article published in Geography(July 1980) used multiple regression to predict annual rainfall levels in California. Data on the average annual precipitation ( y ),
23 Reality TV and cosmetic surgery. How much influence do the media, especially reality television programs, have on one’s decision to undergo cosmetic surgery? This was the question of interest to
22 Study of contaminated fish. Refer to the U.S. Army Corps of Engineers data on fish contaminated from the toxic discharges of a chemical plant located on the banks of the Tennessee River in
Refer to Example 3 , in which an antique collector modeled the auction price y of grandfather clocks as a function of the age x1 of the clock and the number x2 of bidders.Recall that the hypothesized
136 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
134 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
133 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.
132 Sports participation survey. The Sasakawa Sports Foundation conducted a national survey to assess the physical activity patterns of Japanese adults. The next table lists the frequency (average
131 Conversing with the hearing impaired. A study was conducted to investigate how people with a hearing impairment communicate with their conversational partners.( Journal of the Academy of
129 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
128 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
127 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
126 Organic chemistry experiment. Chemists at Kyushu University (Japan) examined the linear relationship between the maximum absorption rate y (in nanomoles)and the Hammett substituent constant x for
125 Are geography journals worth their cost? Geoforum(Vol. 37, 2006) conducted a study of whether the price of a geography journal is correlated with quality. Several quantitative variables were
124 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
122 English as a second language reading ability. Refer to the Bilingual Research Journal (Summer 2006) study of the relationship of Spanish (first-language) grammatical knowledge to English
121 Feeding habits of fish. Brain and Behavior Evolution(Apr. 2000) performed a study of the feeding behavior of black-bream fish. Z oologists recorded the number of aggressive strikes of two
120 College protests of labor exploitation. The Journal of World-Systems Research (Winter 2004) did a study of student “sit-ins” for a “sweat-free campus” at universities.The SITIN file
119 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
118 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
117 Arsenic in soil. In Denver, Colorado, environmentalists have discovered a link between high arsenic levels in soil and a crabgrass killer used in the 1950s and 1960s( Environmental Science &
116 Consider the following 10 data points saved in the LM11_116 file.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
109 Legal advertising—does it pay? According to the American Bar Association, there are over one million lawyers competing for your business. To gain a competitive edge, these lawyers are
108 An MBA’s work-life balance. The importance of having employees with a healthy work-life balance has been recognized by U.S. companies for decades. Many business schools offer courses that
101 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 28 .The SPSS printout of the
84 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,
78 Wind turbine blade stress. Refer to the Wind Engineering(Jan. 2004) study of two types of timber—radiata pine and hoop pine—used in high-efficiency small wind turbine blades, presented in
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
65 Does elevation affect hitting performance in baseball?Chance (Winter 2006) conducted an investigation of the effects of elevation on slugging percentage in Major League Baseball. Data were
62 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
61 Forest fragmentation study. In the Conservation Ecology(Dec. 2003) study on the causes of fragmentation of 54 South American forests, researchers developed two fragmentation indexes for each
60 Effect of massage on boxers. The British Journal of Sports Medicine (Apr. 2000) performed a study of the effect of massage on boxing performance. Two other variables measured on the boxers were
55 Lobster fishing study. The Bulletin of Marine Science (April 2010) performed a study of teams of fishermen fishing for the red spiny lobster in Baja California Sur, Mexico. Two variables measured
54 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
53 Consider the following pairs of observationsa. 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
52 Consider the following pairs of observationsa. 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
46 Life tests of cutting tools. To improve the quality of the output of any production process, it is necessary first to understand the capabilities of the process (For example, see Gitlow, H.,
39 New method for blood typing. Refer to the Analytical Chemistry (May 2010) study in which medical researchers tested a new method of typing blood using lost cost paper, Exercise 19 . The data in
28 Sweetness of orange juice The quality of the orange juice produced by a manufacturer is constantly monitored. There are numerous sensory and chemical components that combine to make the
27 Sound waves from a basketball. The American Journal ofPhysics (June 2010) did a study of sound waves in a spherical cavity. The frequencies of sound waves (estimated using a mathematical formula)
26 FCAT scores and poverty. In the state of Florida, elementary school performance is based on the average score obtained by students on a standardized exam, called the Florida Comprehensive
25 Ranking driving performance of professional golfers.The Sport Journal (Winter 2007) conducted a study of a new method for ranking the total driving performance of golfers on the Professional Golf
24 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).
22 Mongolian desert ants. The Journal of Biogeography (Dec.2003) did a study of ants in Mongolia. Data on annual rainfall, maximum daily temperature, and number of ant species recorded at each of 11
20 Quantitative models of music. Writing in Chance (Fall 2004), University of Konstanz (Germany) statistics professor Jan Beran demonstrated that certain aspects of music can be described by
17 Consider the following pairs of measurements, saved in the LM11_17 file:a. Construct a scatterplot of these data.b. What does the scatterplot suggest about the relationship between x and y ?c.
16 Construct a scatterplot of the following data.a. Plot the following two lines on your scatterplot:y = 3 - x and y = 1 + xb. Which of these lines would you choose to characterize the relationship
15 Refer to Exercise 14. After the least squares line has been obtained, the following table (which is similar to Table 4 )can be used (1) to compare the observed and the predicted values of y and
14 The accompanying table is similar to Table 3 . It is used to make the preliminary computations for finding the least squares line for the given pairs of x and y values.a. Complete the table.b.
Due to ever-increasing food costs, consumers are becoming more discerning in their choice of supermarkets. It is usually more convenient to shop at just one market, as opposed to buying different
127 Anticorrosive behavior of steel coated with epoxy.Organic coatings that use epoxy resins are widely used to protect steel and metal against weathering and corrosion.Researchers at National
126 Therapy for binge eaters. Do you experience episodes of excessive eating accompanied by being overweight? If so, you may suffer from binge eating disorder. Cognitivebehavioral therapy (CBT), in
116 Exposure to low-frequency sound. Infrasound refers to sound frequencies below the audibility range of the human ear. A study of the physiological effects of infrasound was published in the
114 Income and road rage. The phenomenon of road rage has received much media attention in recent years. Is a driver’s propensity to engage in road rage related to his or her income? Researchers at
112 Contaminated fish in the Tennessee River. Refer to the U.S.Army Corps of Engineers data on contaminated fish, saved in the FISHDDT file. The results of an ANOVA and Tukey multiple-comparison
111 Heights of grade school repeaters. The Archives of Disease in Childhood (Apr. 2000) conducted a study conducted a of whether height influences a child’s progression through elementary school.
105 An experiment utilizing a randomized block design was conducted to compare the mean responses for four treatments, A, B, C, and D. The treatments were randomly assigned to the four experimental
104 A completely randomized design is utilized to compare four treatment means. The data are shown in the accompanying table and saved in the LM10_104 file.a. Given that SST = 36.95 and SS(Total) =
93 The thrill of a close game. Do women enjoy the thrill of a close basketball game as much as men do? To answer this question, male and female undergraduate students were recruited to participate in

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