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fundamentals of statistics

Questions and Answers of Fundamentals Of Statistics

Discuss the statement that stem-and-leaf displays are quick and easy to construct.How can we use a stem-and-leaf display to make the construction of a frequency table easier? How does a stem-and-leaf
What do we mean when we say a histogram is skewed to the left? to the right?What is a bimodal histogram? Discuss the following statement: “A bimodal histogram usually results if we draw a sample
In your own words, explain the differences among histograms, relative-frequency histograms, bar graphs, circle graphs, time-series graphs, Pareto charts, and stem-and-leaf displays. If you have
Focus Problem: Fuel Economy Solve the focus problem at the beginning of this chapter. LO.1
Expand Your Knowledge How are dotplots and stem-and-leaf displays similar?How are they different? LO.1
Critical Thinking Describe how data outliers might be revealed in histograms and stem-and-leaf plots. LO.1
Critical Thinking A consumer interest group is tracking the percentage of household income spent on gasoline over the past 30 years. Which graphical display would be more useful, a histogram or a
Critical Thinking Consider these types of graphs: histogram, bar graph, Pareto chart, pie chart, stem-and-leaf display.(a) Which are suitable for qualitative data?(b) Which are suitable for
You have selected three independent variables as predictors of a dependent variable of your choice and obtained at least 10 data values. Now, by means of an available software package, fit the
185 FLAG study of bid collusion. Road construction contracts in the state of Florida are awarded on the basis of competitive, sealed bids; the contractor who bids the lowest price wins the contract.
184 IQ and The Bell Curve. The Bell Curve (New York: Free Press, 1994) by Richard Herrnstein and Charles Murray(H&M), is a controversial book about race, genes, IQ, and economic mobility. The book
183 Abundance of bird species. Multiple-regression analysis was used to model the abundance y of an individual bird species in transects in the United Kingdom ( Journal of Applied Ecology , Vol. 32,
182 Characteristics of sea-ice melt ponds. Surface albedo is defined as the ratio of solar energy directed upward from a surface over energy incident upon the surface.Surface albedo is a critical
176 “Sun safety” study. Excessive exposure to solar radiation is known to increase the risk of developing skin cancer, yet many people do not practice “sun safety.” A group of University of
169 Occupational safety study. An important goal in occupational safety is “active caring.” Employees demonstrate active caring about the safety of their coworkers when they identify
167 Density of mosquito larvae. A field experiment was conducted to assess the effect of organic enrichment on the mean density of mosquito larvae ( Journal of the American Mosquito Control
166 Frequency of drinking alcohol. To what degree do the attitudes of your peers influence your behavior? A study presented in Social Psychology Quarterly (Vol.50, 1987) included a sample of n = 143
164 Listen-and-look study. Where do you look when you are listening to someone speak? Researchers have discovered that listeners tend to gaze at the eyes or mouth of the speaker. In a study published
163 Distress in EMS workers. The Journal of Consulting and Clinical Psychology (June 1995) reported on a study of emergency service (EMS) rescue workers who responded to the I-880 freeway collapse
162 Students’ ability in science. An article published in the American Educational Research Journal (Fall 1998) used multiple regression to model the students’ perceptions of their ability in
160 Suppose you fit the regression model E(y) = b0 + b1 x1 + b2 x2 + b3 x2 2 + b4 x1 x2 + b5 x1 x2 2 to n = 35 data points and wish to test the null hypothesis H0: b4 = b5 = 0.a. State the
159 To model the relationship between y (a dependent variable)and x (an independent variable), a researcher has taken one measurement of y at each of three different x values. Drawing on his
157 Suppose you have developed a regression model to explain the relationship between y and x1, x2, and x3.The ranges of the variables you observed were as follows: 10 … y … 100, 5 … x1 … 55,
155 Suppose you fit the model y = b0 + b1 x1 + b2 x21+ b3 x2 + b4 x1 x2 + e to n = 25 data points and find that bn 0 = 1.26 b n1 = -2.43 b n2 = .05 b n3 = .62 b n4 = 1.81 sb n1 = 1.21 sb n2 = .16 sb
154a. Write a first-order model relating E ( y ) to two quantitative independent variables x1 and x2.b. Write a complete second-order model.
153 It is desired to relate E ( y ) to a quantitative variable x1 and a qualitative variable at three levels.a. Write a first-order model.b. Write a model that will graph as three different
152 Explain why stepwise regression is used. What is its value in the model-building process?
151 Write a model relating E ( y ) to one qualitative independent variable that is at four levels. Define all the terms in your model.
150 Cooling method for gas turbines. Refer to the Journal of Engineering for Gas Turbines and Power (Jan. 2005)study of a high-pressure inlet fogging method for a gas turbine engine, presented in
149 Reality TV and cosmetic surgery. Refer to the Body Image: An International Journal of Research (March 2010) study of the influence of reality TV shows on one’s desire to undergo cosmetic
148 Contamination of fish in the Tennessee River. 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
147 Arsenic in groundwater. Refer to the Environmental Science & Technology (Jan. 2005) study of the reliability of a commercial kit to test for arsenic in groundwater, Exercise 21 . Recall that you
145 Accuracy of software effort estimates. Refer to the Journal of Empirical Software Engineering (Vol. 9, 2004)study of the accuracy of new software effort estimates, Exercise 124 . Recall that
142 Yield strength of steel alloy. Refer to Exercise 126 and the Modelling and Simulation in Materials Science and Engineering (Vol. 13, 2005) study in which engineers built a regression model for
140 Women in top management. The Journal of Organizational Culture, Communications and Conflict (July 2007) published a study on women in upper management positions at U.S. firms. Monthly data ( n =
139 Dating and disclosure. Refer to the Journal of Adolescence(April 2010) study of adolescents’ disclosure of their dating and romantic relationships, Exercise 14 . Recall that multiple regression
136 Define extrapolation.
135 Give three indicators of a multicollinearity problem.
134 Define multicollinearity in regression.
133 True or False . Regression models fit to time-series data typically result in uncorrelated errors.
132 Give two properties of the regression residuals from a model.
131 Define an outlier.
130 Define a regression residual.
Refer to Example 16 . Analyze the distribution of the residuals in the grandfather clock example, both before and after the outlier residual is removed. Determine whether the assumption of a normally
The data in Table 8 are the salaries, y , and years of experience, x , for a sample of 50 social workers. The first-order model E(y) = b0 + b1 x was fitted to the data using by SPSS. The SPSS
Refer to the problem of modeling the relationship between home size ( x ) and electrical usage ( y ) in Example 7 . The data for n = 15 homes are repeated in Table 7 .MINITAB printouts for a
127 Bus rapid-transit study. Bus rapid transit (BRT) is a rapidly growing trend in the provision of public transportation in America. The Center for Urban Transportation Research (CUTR) at the
122 Give two caveats associated with using the stepwise regression results as the final model for predicting y .
121 Explain the difference between a stepwise model and a standard regression model.
An international management consulting company develops multiple-regression models for executive salaries of its client firms. The consulting company has found that models which use the natural
120 Emotional distress in firefighters. The Journal of Human Stress (Summer 1987) reported on a study of the “psychological response of firefighters to chemical fire.” It is thought that the
119 Whales entangled in fishing gear. Refer to the Marine Mammal Science (April 2010) study of whales entangled in fishing gear, Exercise 101 . A first-order model for the length ( y ) of an
118 Glass as a waste encapsulant. Since glass is not subject to radiation damage, the encapsulation of waste in glass is considered to be one of the most promising solutions to the problem of
117 Improving SAT scores. Refer to the Chance (Winter 2001)study of students who paid a private tutor (or coach) to help them improve their SAT scores, presented in Exercise 84 .Recall that the
116 Reality TV and cosmetic surgery. Refer to the Body Image: An International Journal of Research (March 2010) study of the influence of reality TV shows on one’s desire to undergo cosmetic
113 Workplace bullying and intention to leave. Refer to the Human Resource Management Journal (Oct. 2008) study of workplace bullying, Exercise 103 . Recall that multiple regression was used to model
112 Mental health of a community. An article in the Community Mental Health Journal (Aug. 2000) used multiple-regression analysis to model the level of community adjustment of clients of the
109 What is a parsimonious model?
108 Explain why the F -test used to compare complete and reduced models is a one-tailed, upper-tailed test.
106 Iron supplement for anemia. Many women suffer from anemia. A female physician who is also an avid jogger wanted to know if women who exercise regularly have a different mean red blood cell count
105 Chemical composition of rainwater. Refer to the Journal of Agricultural, Biological, and Environmental Statistics(March 2005) study of the chemical composition of rainwater, presented in Exercise
103 Workplace bullying and intention to leave. Workplace bullying (e.g., work-related harassment, persistent criticism, withholding of key information, spreading of rumors, intimidation) has been
101 Whales entangled in fishing gear. Refer to the Marine Mammal Science (April 2010) study of whales entangled in fishing gear, Exercises 15 and 79 . Now consider a model for the length ( y ) of an
100 Winning marathon times. Chance (Winter 2000) conducted a study of men’s and women’s winning times in the Boston Marathon. Suppose the researchers want to build a model for predicting winning
94 Write a model that relates E ( y ) to two independent variables, one quantitative and one qualitative (at four levels). Construct a model that allows the associated response curves to be second
93 Refer to Exercise 92.a. Write a complete second-order model that relates E ( y )to the quantitative variable.b. Add the main-effect terms for the qualitative variable(at three levels) to the model
92 Consider a multiple-regression model for a response y with one quantitative independent variable x1 and one qualitative variable at three levels.a. Write a first-order model that relates the mean
Substitute the appropriate values of the dummy variables in Model 3 to obtain the equations of the three response lines in Figure 23 .
91 Community responses to a violent crime. How communities respond to a disaster or a violent crime was the subject of research published in the American Journal of Community Psychology (Vol. 44,
89 Extinct New Zealand birds. Evolutionary Ecology Research(July 2003) conducted a study of the patterns of extinction in the New Zealand bird population. The NZBIRDS file contains qualitative data
88 Homework assistance for college students. Do college professors who provide their students with assistance on homework help improve student grades? This was the research question of interest in
87 Expert testimony in homicide trials of battered women.For over 20 years, courts have accepted evidence of “battered woman syndrome” as a defense in homicide cases.An article published in the
86 Study of recall of TV commercials. The Journal of Applied Psychology (June 2002) conducted a study of recall of television commercials. Participants were assigned to watch one of three types of TV
85 Major depression and personality disorders. When psychiatric patients have an episode of depression, they are often diagnosed with several personality disorders. A team of physicians,
84 Improving SAT scores. Chance (Winter 2001) did a study of students who paid a private tutor (or coach) to help them improve their SAT scores. Multiple regression was used to estimate the effect of
83 Detecting quantitative traits in genes. In gene therapy, it is important to know the location of a gene for a disease on the genome (genetic map). Although many genes yield a specific trait (e.g.,
82 Chemical composition of rainwater. Researchers at the University of Aberdeen (Scotland) developed a statistical model for estimating the chemical composition of water( Journal of Agricultural,
81 Impact of race on football card values. University of Colorado sociologists investigated the impact of race on the value of professional football players’ “rookie” cards( Electronic Journal
80 Production technologies, terroir, and quality of Bordeaux wine . In addition to state-of-the-art technologies, the production of quality wine is strongly influenced by the natural endowments of
79 Whales entangled in fishing gear. Refer to the Marine Mammal Science (April 2010) study of whales entangled in fishing gear, Exercise 15 . These entanglements involved one of three types of
76 Write a regression model relating E ( y ) to a qualitative independent variable that can assume three levels.Interpret all the terms in the model.
75 Write a regression model relating the mean value of y to a qualitative independent variable that can assume two levels. Interpret all the terms in the model.
69 Estimating change-point dosage. A standard method for studying toxic substances and their effects on humans is to observe the responses of rodents exposed to various doses of the substance over
68 Violent behavior in children. Development Psychology(Mar. 2003) performed a study of the behavior of elementary school children. The researchers used a quadratic equation to model the level ( y )
67 Estimation of urban population by means of satellite images. Refer to the Geographical Analysis (Jan. 2007)study that demonstrated the use of satellite image maps for estimating urban population,
66 Goal congruence in top management teams. Do chief executive officers (CEOs) and their top managers always agree on the goals of the company? Goal importance congruence between CEOs and vice
63 Going for it on fourth down in the NFL. Chance (Winter 2009) performed a study of fourth-down decisions by coaches in the National Football League (NFL). Statisticians at California State
61 Consider the following quadratic models:(1) y = 1 - 2x + x2(2) y = 1 + 2x + x2(3) y = 1 + x2(4) y = 1 - x2(5) y = 1 + 3x2a. Graph each of these quadratic models, side by side, on the same sheet of
59 Suppose you fit the second-order model y = b0 + b1 x + b2 x2 + e to n = 25 data points. Your estimate of b2 is b n2 = .47, and the estimated standard error of the estimate is .15.a. Test H0: b2 =
58 Suppose you fit the quadratic model E(y) = b0 + b1 x + b2 x2 to a set of n = 20 data points and find that R2 = .91, SSyy = 29.94, and SSE = 2.63.a. Is there sufficient evidence to indicate that
57 Write a second-order model relating the mean of y , E ( y ), toa. one quantitative independent variableb. two quantitative independent variablesc. three quantitative independent variables [ Hint:
56 In the model E(y) = b0 + b1 x + b2 x2,a. Which b represents the y -intercept?b. Which b represents the shift?c. Which b represents the rate of curvature?
A social scientist would like to relate the number of hours worked per week (outside the home) by a married woman to the number of years of formal education she has completed and the number of
In all-electric homes, the amount of electricity expended is of interest to consumers, builders, and groups involved with energy conservation. Suppose we wish to investigate the monthly electrical
55 Cooling method for gas turbines. Refer to the Journal of Engineering for Gas Turbines and Power (Jan. 2005) study of a high-pressure inlet fogging method for a gas turbine engine, presented in
54 Arsenic in groundwater. Refer to the Environmental Science & Technology (Jan. 2005) study of the reliability of a commercial kit to test for arsenic in groundwater, presented in Exercise 21 .
52 Unconscious self-esteem study. Psychologists define implicit self-esteem as unconscious evaluations of one’s worth or value. In contrast, explicit self-esteem refers to the extent to which a
51 Child abuse report. Licensed therapists are mandated by law to report child abuse by their clients. This law requires the therapist to breach confidentiality and possibly lose the client’s
50 Reality TV and cosmetic surgery. Refer to the Body Image:An International Journal of Research (March 2010) study of the influence of reality TV shows on one’s desire to undergo cosmetic surgery,
48 Psychology of waiting in line. While waiting in a long line for service (e.g., to use an ATM or at the post office), at some point you may decide to leave the line. The Journal of Consumer

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