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fundamentals of statistics

Questions and Answers of Fundamentals Of Statistics

47 Defects in nuclear missile housing parts. The technique of multivariable testing was discussed in The Journal of the Reliability Analysis Center (First Quarter, 2004).Multivariable testing was
45 Whales entangled in fishing gear. Refer to the Marine Mammal Science (April 2010) study of whales entangled in fishing gear, Exercise 15 . Recall that the length ( y ) of an entangled whale (in
41 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
40 If two variables x1 and x2 do not interact, how would you describe their effect on the mean response E ( y )?
39 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
37 Study of contaminated fish. Refer to Exercise 22 and the U.S.Army Corps of Engineers data on contaminated fish. You fit the first-order model E(y) = b0 + b1 x1 + b2 x2 + b3 x3 to the data saved in
32 Predicting runs scored in baseball. Refer to the Chance(Fall 2000) study of runs scored in Major League Baseball games, Exercise 17 . Multiple regression was used to model total number of runs
31 Characteristics of lead users. Refer to the Creativity and Innovation Management (Feb. 2008) study of lead users of children’s computer games, Exercise 13 . Recall that the researchers modeled
30 Which interval will be narrower, a 95% confidence interval for E ( y ) or a 95% prediction interval for y ? (Assume that the values of the x ’s are the same for both intervals.)
29 Explain why we use yn as an estimate of E ( y ) and to predict y .
Refer to Examples 1–4 and the first-order model E(y) = b0 + b1 x1 + b2 x2, where y = auction price of a grandfather clock, x1 = age of the clock, and x2 = number of bidders.a. Estimate the average
19 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 (
16 Estimation of urban population by means of satellite images.Can the population of an urban area be estimated without taking a census? In Geographical Analysis (Jan. 2007)geography professors at
15 Whales entangled in fishing gear. Marine Mammal Science(April 2010) conducted a study of whales entangled in fishing gear. Data collected for a sample of 207 entanglements in the East Sea of Korea
14 Dating and disclosure. The Journal of Adolescence (April 2010) conducted a study of adolescents’ disclosure of their dating and romantic relationships. Data collected for a sample of 222 high
13 Characteristics of lead users. During new product development, companies often involve “lead users,” i.e., creative individuals who are on the leading edge of an important market trend.
12 If the analysis-of-variance F -test leads to the conclusion that at least one of the model parameters is nonzero, can you conclude that the model is the best predictor for the dependent variable y
11 Suppose you fit the first-order model y = b0 + b1 x1 + b2 x2 + b3 x3 + b4 x4 + b5 x5 + e to n = 30 data points and obtain SSE = .33 R2 = .92a. Do the values of SSE and R2 suggest that the model
10 Consider the following first-order model equation in three quantitative independent variables:E(y) = 1 + 2x1 + x2 - 3x3a. Graph the relationship between y and x1 for x2 = 1 and x3 = 3.b. Repeat
9 How is the number of degrees of freedom available for estimating s2 (the variance of e ) related to the number of independent variables in a regression model?
8 Suppose you fit the first-order multiple-regression model y = b0 + b1 x1 + b2 x2 + e to n = 25 data points and obtain the prediction equation yn = 6.4 + 3.1x1 + .92x2 The estimated standard
7 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 = 3.4 - 4.6x1 + 2.7x2 + .93x3 The estimated standard errors of b n2 and b n3
5 How should you test the overall adequacy of a multipleregression model?
4 What are the caveats to conducting t -tests on all of the individual b parameters in a multiple-regression model?
3 Outline the six steps in a multiple-regression analysis.
2 List the four assumptions about the random error e required for a multiple-regression analysis.
1 Write a first-order model relating E ( y ) toa. two quantitative independent variablesb. four quantitative independent variablesc. five quantitative independent variables
Refer to Examples 1 and 2. The collector of antique grandfather clocks knows that the price ( y ) received for the clocks increases linearly with the age (x1) of the clocks.Moreover, the collector
Refer to the first-order model for auction price y considered in Example 1 .Interpret the estimates of the b parameters in the model.
Consider the problem of determining the highest level of education attained by each of a sample of n = 40 National Hockey League (NHL) players. Suppose we categorize level of education into one of
Many dependent variables in all areas of research serve as the subjects of regression-modeling efforts. We list five such variables here:1. Crime rate in various communities 2. Daily maximum
130 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
123 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
114 In fitting a least squares line to n = 15 data points, the following quantities were computed: SSxx = 55, SSyy = 198, SSxy = -88, x = 1.3, and y = 35.a. Find the least squares line.b. Graph the
113 True or False . In simple linear regression, about 95%of the y -values in the sample will fall within 2 s of their respective predicted values.
112 Outline the five steps in a simple linear regression analysis.
111 Give the general form of a straight-line model for E ( y ).
110 Explain the difference between a probabilistic model and a deterministic model.
107 Life tests of cutting tools. Refer to the data saved in the CUTTOOL file of Exercise 46 .a. Use a 90% confidence interval to estimate the mean useful life of a brand-A cutting tool when the
106 Feeding habits of snow geese. Refer to the Journal of Applied Ecology feeding study of the relationship between the weight change y of baby snow geese and their digestion efficiency x , presented
105 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
104 The “name game.” Refer to the Journal of Experimental Psychology—Applied (June 2000) name-retrieval study, presented in Exercise 30 . The data for the study are saved in the NAMEGAME2
103 Ideal height of your mate. Refer to the Chance (Summer 2008) study of the height of the ideal mate, Exercise 29 . The data in the IDHEIGHT file was used to fit the simple linear regression model,
102 Sound waves from a basketball. Refer to the American Journal of Physics (June 2010) study of sound waves in a spherical cavity, Exercise 27 . The frequencies of sound waves resulting from the
98 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
97 Do nice guys finish first or last? Refer to the Nature(March 20, 2008) study of the use of punishment in cooperation games, Exercise 18 . Recall that simple linear regression was used to model a
96 Refer to Exercise 95.a. Using no information about x , estimate and calculate a 95% confidence interval for the mean value of y . [ Hint: Use one-sample t methodology .]b. Plot the estimated mean
93 In fitting a least squares line to n = 10 data points, the following quantities were computed:SSxx = 32, x = 3, SSyy = 26, y = 4, SSxy = 28a. Find the least squares line.b. Graph the least squares
92 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
91 True or False . The greater the deviation between x and x, the wider the prediction interval for y will be.
90 True or False . For a given x , a confidence interval for E ( y )will always be wider than a prediction interval for y .
89 Explain the difference between y and E ( y ) for a given x .
Refer again to the drug reaction regression. Predict the reaction time for the 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%.
88 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
87 Effect of massage on boxing. Refer to the British Journal of Sports Medicine (April 2000) study of the effect of massage on boxing performance, presented in Exercise 60 . The data for the study
86 The “name game.” Refer to the Journal of Experimental Psychology—Applied (June 2000) name-retrieval study, first presented in Exercise 30 . The data for the study are saved in the NAMEGAME2
85 Do nice guys finish first or last? Refer to the Nature (March 20, 2008) study of the use of punishment in cooperation games, Exercise 18 . Recall that college students repeatedly played a version
81 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
80 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 23 .Recall that simple
79 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
77 Physical activity of obese young adults. The International Journal of Obesity (Jan. 2007) conducted a study of the physical activity of obese young adults. For two groups of young adults—13
76 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 55 . Recall that
75 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
74 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.
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.
73 Calculate r2 for the least squares line in Exercise 17.
72 Calculate r2 for the least squares line in Exercise 14.
70 True or False . A value of the correlation coefficient near 1 or near -1 implies a causal relationship between x and y .
69 Explain what each of the following sample correlation coefficients tells you about the relationship between the x and y values in the sample:a. r = 1b. r = -1c. r = 0d. r = .90e. r = .10f. r = -.88
68 Describe the slope of the least squares line ifa. r = .7b. r = -.7c. r = 0d. r2 = .64
67 True or False . The correlation coefficient is a measure of the strength of the linear relationship between x and y .
66 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 31 . Recall
64 The “name game.” Refer to the Journal of Experimental Psychology—Applied (June 2000) name-retrieval study, presented in Exercise 30 . Recall that the goal of the study was to investigate the
63 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
59 Sweetness of orange juice. Refer to Exercise 28 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
58 Ideal height of your mate. Refer to the Chance (Summer 2008) study of the height of the ideal mate, Exercise 45 .You used the data in the IDHEIGHT file to fit the simple linear regression model
57 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
56 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
51 Construct both a 95% and a 90% confidence interval for b1 for each of the following cases:a. b n1 = 31, s = 3, SSxx = 35, n = 12b. b n1 = 64, SSE = 1,960, SSxx = 30, n = 18c. b n1 = -8.4, SSE =
50 For each of the following 95% confidence intervals for b1 in simple linear regression, decide whether there is evidence of a positive or negative linear relationship between y and x :a. (22, 58)b.
49 How do you adjust the p -value obtained from a computer printout when you perform a one-tailed test of b1 in simple linear regression?
48 What conditions are required for valid inferences about the b>s in simple linear regression?
47 In the equation E1y2 = b0 + b1 x, what is the value of b1 if x has no linear relationship to y ?
Refer to the simple linear regression analysis of the drug reaction data performed in Examples 1 and 2 . Conduct a test (at a = .05 ) to determine whether the reaction time ( y ) is linearly related
45 Ideal height of your mate. Refer to the Chance (Summer 2008) study of the height of the ideal mate, Exercise 29 . The data in the IDHEIGHT file were used to fit the simple linear regression model,
44 Sweetness of orange juice. Refer to the study of the quality of orange juice produced at a juice manufacturing plant, Exercise 28 . The data are saved in the OJUICE file.Recall that simple linear
43 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), presented in Exercise 26 .
42 Extending the life of an aluminum smelter pot. Refer to The American Ceramic Society Bulletin (Feb. 2005) study of bricks that line aluminum smelter pots, presented in Exercise 24 . You fit the
41 Mongolian desert ants. Refer to the Journal of Biogeography(Dec. 2003) study of ant sites in Mongolia, presented in Exercise 22 . The data in the GOBIANTS file was used to estimate the
40 Quantitative models of music. Refer to the Chance (Fall 2004) study on modeling a certain pitch of a musical composition, presented in Exercise 20 . Recall that the number of times ( y ) a certain
38 Do nice guys really finish last? Refer to the Nature (March 20, 2008) study of whether “nice guys finish last,” Exercise 18 . Recall that Boston-area college students repeatedly played a
37 Refer to Exercises 14 and 17 . Calculate SSE, s2, and s for the least squares lines obtained in those exercises.Interpret the standard errors of the regression model for each.
36 Suppose you fit a least squares line to 12 data points and the calculated value of SSE is .429.a. Find s2, the estimator of s2 (the variance of the random error term e ).b. Find s , the estimate
33 Illustrate the assumptions of Exercise 32 with a graph.
32 What are the four assumptions made about the probability distribution of e in regression?
Refer to Example 1 and the simple linear regression of the drug reaction data in Table 3 .a. Compute an estimate of s.b. Give a practical interpretation of the estimate.
23 Redshifts of quasi-stellar objects. Astronomers call a shift in the spectrum of galaxies a “redshift.” A correlation between redshift level and apparent magnitude(i.e., brightness on a
21 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.
Use the applet entitled Regression by Eye to explore the relationship between the pattern of data in a scatterplot and the corresponding least squares model.a. Run the applet several times. For each

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