Nonparametric Statistical Inference 5th Edition Jean Dickinson Gibbons, Subhabrata Chakraborti - Solutions

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2.23. Repeat the previous exercise for the data file created in Exercise 1.12 (page 9).
2.22. Refer to the Student survey data file introduced in Exercise 1.11 (page 8). For each variable in the data set, indicate whether it is:(a) Categorical or quantitative(b) Nominal, ordinal, or interval
2.21. Clusters versus strata:(a) With a cluster random sample, do you take a sample of (i) the clusters? (ii) the subjects within every cluster?(b) With a stratified random sample, do you take a sample of (i) the strata? (ii) the subjects within every stratum?(c) Summarize the main differences
2.20. You plan to sample from the 3500 undergraduate students enrolled at the University of Rochester, to compare the proportions of female and male students who would like to sec the U.S. have a female President.(a) Suppose that you use random numbers to select students, but you stop selecting
2.19. You plan to sample from the 5000 students at a college, to compare the proportions of men and women who believe that the legal age for alcohol should be changed to 18. Explain how you would proceed if you want a systematic random sample of 100 students.
2.18. Refer to Exercise 2.12 about selecting 5 of 52,000 names on 400 pages of a directory.(a) Select five numbers to identify subjects for a systematic random sample of five names from the directory.(b) Is clustersampling applicable? How could it be carried out, and what would be the advantages
2.17. A Roper Poll was designed to determine the percentage of Americans who express some doubt that the Nazi Holocaust occurred. In response to the question, "Does it seem possible or does it seem impossible to you that the Nazi extermination of the Jews never happened?" 22% said it was possible
2.16. The BBC in Britain requested viewers to call the network and indicate their favorite poem. Of more than 7500 callers, more than twice as many voted for Rudyard Kipling's If than for any other poem.The BBC reported that this was the clear favorite.(a) Explain what it means to call this a
2.15. Table 2.2 shows the result of the 2000 Presidential election and the predictions of several organizations in the days before the election. The sample sizes were typically about 2000. The percentages for each poll do not sum to 100 because of voters reporting as undecided or favoring another
2.14. A study is planned to study whether passive smoking (being exposed to secondhand cigarette smoke on a regular basis) leads to higher rates of lung cancer.(a) One possible study is to take a sample of children, randomly select half of them for placement in an environment where they are passive
2.13. Explain whether an experiment or an observational study would be more appropriate to investigate the following:(a) Whether or not cities with higher unemployment rates tend to have higher crime rates(b) Whether a Honda Accord or a Toyota Camry gets better gas mileage(c) Whether or not higher
2.12. A local telephone directory has 400 pages with 130 names per page, a total of 52,000 names. Explain how you could choose a simple random sample of 5 names. Using the second column of Table 2.1 or software or a calculator, select 5 random numbers to identify subjects for the sample.
2.11. A class has 50 students. Use the column ofthe first two digits in the random number table (Table 2.1)to select a simple random sample ofthree students.If the students are numbered 01 to 50, what are the numbers of the three students selected?
2.10. Which of the following variables are continuous when the measurements are as fine as possible?(a) Age of mother, (b) number of children in family, (c) income of spouse, (d) population of cities,(e) latitude and longitude of cities, (f) distance of home from place of cmploj'mcnt, (g) number of
2.9. Which of the following variables could theoretically be measured on a continuous scale? (a)Method of contraception used, (b) length oftime of residence in a state, (c) task completion time, (d)intelligence, (e) authoritarianism, (f) alienation,(g) county of residence.
2.8. A survey asks subjects to rate five issues according to their importance in determining voting intention for U.S. senator, using the scale (very important, somewhat important, unimportant). The issues are foreign policy, unemployment, inflation, the arms race, and civil rights. The evaluations
2.7. A poll conducted by YouGov for the British newspaper The Daily Telegraph in June 2006 asked a random sample of 1962 British adults several questions about their image of the U.S. One question asked, "How would you rate George W. Bush as a world leader?" The possible choices were (great leader,
2.6. Give an example of a variable that is (a) categorical, (b) quantitative, (c) ordinal scale, (d) nominal scale, (e) discrete, (f) continuous, (g) quantitative and discrete.
2.5. Which scale of measurement is most appropriate for "attained education" measured as(a) Number of years (0,1,2, 3,...)(b) Grade level (elementary school, middle school, high school, college, graduate school)(c) School type (public school, private school)
2.4. Which scale of measurement is most appropriate for(a) Occupation (plumber, teacher, secretary,...)(b) Occupational status (blue collar, white collar)(c) Social status (lower, middle, upper class)(d) Statewide murder rate (number of murders per 1000 population)(e) County population size (number
2.3. Which scale of measurement (nominal, ordinal, or interval) is most appropriate for(a) Attitude toward legalization of marijuana(favor, neutral, oppose)(b) Gender (male, female)(c) Number of children in family (0,1,2,...)(d) Political party affiliation (Democrat, Republican, Independent)(e)
2.2. Identify each variable as categorical or quantitative:(a) Number of pets in family(b) County of residence(c) Choice of auto (domestic or import)(d) Distance (in miles) commute to work(e) Choice of diet (vegetarian, nonvegetarian)(f) Time spent in previous month browsing the World Wide Web(g)
2.1. Explain the difference between(a) Discrete and continuous variables(b) Categorical and quantitative variables(c) Nominal and ordinal variables Why do these distinctions matter for statistical analysis?
1.19. Check whether you have accessto JSTOR (Journal Storage) at yourschool by visiting www.jstor.org. If so, click on Browse and then Sociology or another discipline of interest to you. Select a journal and a particular issue, and browse through some of the articles. Find an article that uses
1.18. Go to the Web site for the Gallup poll, www.galluppoll.com. From information listed on or linked from the homepage, give an example of a (a) descriptive statistical analysis, (b) inferential statistical analysis.
1.17. In a recent survey by Eurobarometer ofEuropeans about energy issues and global warming,1 one question asked, "Would you be willing to pay more for energy produced from renewable sources than for energy produced from other sources?" The percentage of yes responses varied among countries
1.15. You have data for a population, from a census.Explain why descriptive statistics are helpful but inferential statistics are not needed.
1.14. Illustrating with an example, explain the difference between(a) a statistic and a parameter.(b) description and inference as two purposes for using statistical methods.
1.13. For the statistical software your instructor has chosen for your course, find out how to access the software, enter data, and print any data files that you create. Create a data file using the data in Figure 1.1 in Section 1.3, and print it.
1.12. Using a spreadsheet program (such as Microsoft Office Excel) orstatistical software, yourinstructor will help the class create a data file consisting of the values for class members of characteristics such as those in the previous exercise. One exercise in each chapter will use this data
1.11. The "Student survey" data file at definitely yes, probably yes, probably not, and www.siat.ufl.edu/~aa/social/data.hlml showsresponses of a class ofsocialscience graduate students at the University of Florida to a questionnaire that asked about GE = gender, AG - age in years, H! — high
1.10. Construct a data file describing the criminal behavior offive inmates in a local prison. The characteristics measured were race (with observations for the five subjects: white, black, white, Hispanic, white), age (19, 23, 38, 20, 41), length ofsentence in years(2, 1, 10, 2, 5), whether
1.9. A BBC story (September 9, 2004) about a poll in 35 countries concerning whether people favored George W. Bush or John Kerry in the 2004 U.S.Presidential election stated that Kerry was clearly preferred. Ofthe sample from Germany, 74% preferred Kerry, 10% preferred Bush, with the rest undecided
1.8. The Current Population Survey (CPS) is a monthly survey of households conducted by the U.S. Census Bureau. A CPS of 60,000 households indicated that of those households, 8.1% of the whites, 22.3% of the blacks, 20.9% of the Hispanics, and 10.2% of the Asians had annual income below the poverty
1.6. Go to the GSS Web site, sda.berkeley.edu/GSS/.By entering TVHOURS as the Row variable, find a summary ofresponses to the question, "On a typical day, about how many hours do you personally watch television?"(a) What was the most common response?(b) Is your answer in (a) a descriptive
1.5. A GSS asked subjects whether astrology—the study ofstar signs—has some scientific truth (GSS question SC1TEST3). Of 1245 sampled subjects, 651 responded definitely or probably true, and 594 responded definitely orprobably nottrue. The proportion responding definitely or probably true was
1.4. The Institute for Public Opinion Research at Florida International University has conducted the FIU/Florida Poll (www.fiu.edu/orgs/ipor/ffp)of about 1200 Floridians annually since 1988 to track opinions on a wide variety of issues. The poll reported in 2006 that 67% ofFloridians believe that
1.3. The student government at the University of Wisconsin conducts a study about alcohol abuse among students. One hundred of the 40,858 members of the student body arc sampled and asked to complete a questionnaire. One question asked is, "On how many days in the past week did you consume at least
1.2. In the 2006 gubernatorial election in California, an exit poll sampled 2705 of the 7 million people who voted. The poll stated that 56.5% reported voting for the Republican candidate, Arnold Schwarzenegger. Of all 7 million voters, 55.9% voted for Schwarzenegger.(a) For this exit poll, what
1.1. The Environmental Protection Agency (EPA)uses a few new automobiles of each brand every year to collect data on pollution emission and gasoline mileage performance. For the Toyota Prius brand, identify the (a) subject, (b) sample,(c) population.
8.1 Given independent samples ofmX and n Y variables, define the following random variables for i¼1, 2, . . . , m:Ki¼rank of Xi among X1, X2, . . . , Xm Ri¼rank of Xi among X1, X2, . . . , Xm, Y1, Y2, . . . , Yn Use Ki and Ri to prove the linear relationship between the Mann–Whitney and
8.2 A single random sample D1, D2, . . . , DN of size N is drawn from a population which is continuous and symmetric. Assume there are m positive values, n negative values, and no zero values. Define the mþ n¼N random variables Xi ¼ Di if Di > 0 Yi ¼ jDij if Di < 0 Then the X1, X2, . . . , Xm
8.3 Generate by enumeration the exact null probability distribution of TsBr as defined in (8.3.5) for m¼n¼3, all S¼R
8.4 Verify the results given in (8.3.6) for the mean and variance of TsBr when S¼R and N is even and derive a similar result for S¼R when N is odd.
8.5 Show that the median test of Section 6.4 is a linear rank test.
8.6 Giambra and Quilter (1989) performed a study to investigate gender and age difference in ability to sustain attention when given Mackworth’s clock-test. This clock is metal with a plain white face and a black pointer that moves around the face in 100 discrete steps of 368 each. During the
8.7 Elam (1988) conducted a double-blind study of 18 adult males to investigate the effects of physical resistance exercises and amino acid dietary supplements on body mass, body fat, and composite girth. Ten of the subjects received the diet supplement and eight received a placebo. All subjects
8.8 Howard et al. (1986) (see Problem 5.12) also investigated whether pretest anxiety scores differed for students enrolled in two different sections of the introduction to computer courses. Seven students were enrolled in each section, and the data are shown below. Is there a difference in median
8.9 A travel agency wanted to compare the noncorporate prices charged by two major motel chains for a standard-quality single room at major airport locations around the country. A random sample of five Best Eastern motels and an independent sample of six Travelers’ Inn motels, all located at
8.10 Smokers are commonly thought of as nervous people whose emotionality is at least partly caused by the stimulating effect tobacco has on the nervous system. Nesbitt (1972) conducted a study with 300 college students and concluded that smokers are less emotional than nonsmokers, that smokers are
8.11 A group of 20 mice are allocated to individual cages randomly. The cages are assigned in equal numbers, randomly, to two treatments, a control A and a certain drug B. All animals, in a random sequence, are infected with tuberculosis. The numbers of days until the mice die after infection are
8.12 The following data represent two independent random samples drawn from continuous populations that are thought to have the same form but possibly different locations.X: 79, 13, 138, 129, 59, 76, 75, 53 Y: 96, 141, 133, 107, 102, 129, 110, 104 Using a significance level not exceeding 0.10,
8.13 A problem of considerable import to the small-scale farmer who purchases young pigs to fatten and sell for slaughter is whether there is any difference in weight gain for male and female pigs when the two genders are subjected to identical feeding treatments. If there is a difference, the
8.14 How would you find the confidence-interval endpoints for the parameter of interest when the interval has confidence level nearest 0.90 and corresponds to(a) The sign test with n¼11(b) The Wilcoxon signed-rank test with n¼11(c) The Wilcoxon rank-sum test with m¼5, n¼6 In each case define
8.15 A self-concept test was given to a random sample consisting of six normal subjects and three subjects under psychiatric care. Higher scores indicate more self-esteem. The data are as follows:Normal: 62, 68, 78, 92, 53, 81 Psychiatric: 54, 70, 79(a) Find a P value relevant to the alternative
8.16 Verify the confidence interval estimate of mX mY with exact confidence coefficient at least 0.95 given in the MINITAB solution of Example 8.2.1.
9.1 Develop by enumeration for m ¼ n ¼ 3 the null probability distribution of Mood’s statistic MN of (9.2.1).
9.2 Develop by enumeration for m ¼ n ¼ 3 the null probability distribution of the Freund–Ansari–Bradley statistic of (9.3.3).
9.3 Verify the expression given in (9.2.3) for var(MN).
9.4 Apply Theorem 7.3.2 to derive the mean and variance of the statistic AN defined in (9.3.1).
9.5 Apply Theorem 7.3.2 to derive the mean and variance of the statistic BN defined in (9.3.5).
9.6 Verify the relationship between AN, BN and FN given in (9.4.3) for N even.
9.7 Use the relationship in (9.4.3) and the moments derived for FN for N even in (9.3.4) to verify your answers to Problems 9.4 and 9.5 for N even.
9.8 Use Theorem 7.3.2 to derive the mean and variance of Ts þ Br for N even, S 6¼ R, where S þ R N.
9.9 Verify the result given in (9.9.2) for the null probability distribution of Rosenbaum’s R statistic.
9.10 Olejnik (1988) suggested that research studies in education and the social sciences should be concerned with differences in group variability as well as differences in group means. For example, a teacher can reduce variability in student achievement scores by focusing attention and classroom
9.11 The psychology departments of public universities in each of two different states accepted seven and nine applicants, respectively, for graduate study next fall. Their respective scores on the Graduate Record Examination are:University X: 1200, 1220, 1300, 1170, 1080, 1110, 1130 University Y:
9.12 In industrial production processes, each measurable characteristic of any raw material must have some specified average value, but the variability should also be small to keep the characteristics of the end product within specifications. Samples of lead ingots to be used as raw material are
9.13 Data on weekly rate of item output from two different production lines for 7 weeks are as follows:Line I: 36, 36, 38, 40, 41, 41, 42 Line II: 29, 34, 37, 39, 40, 43, 44 We want to investigate the relative variability between the two lines.(a) Find a one-tailed P value using the Siegel–Tukey
10.1 Generate by enumeration the exact null distribution of the k-sample median test statistic for k ¼ 3, n1 ¼ 2, n2 ¼ 1, n3 ¼ 1. If the rejection region consists of those arrangements which are least likely under the null hypothesis, find this region R and the exacta. Compute the values of the
10.2 Generate the exact null distribution of the Kruskal–Wallis statistic H for the same k and ni as in Problem 10.1. Find the critical region which consists of those rank sums R1, R2,R3, which have the largest value of H and find exact a.
10.3 By enumeration, place the median test criterion (U1,U2,U3) and the H test criterion (R1, R2, R3) in one-to-one correspondence for the same k and ni as in Problems 10.1 and 10.2. If the two tests reject for the largest values of Q and H, respectively, which test seems to distinguish better
10.4 Verify that the form of H given in (10.4.4) is algebraically equivalent to(10.4.2).
10.5 Show that H with k ¼ 2 is exactly equivalent to the large-sample approximation to the two-sample Wilcoxon rank-sum test statistic of Section 8.2 with m ¼ n1, n ¼ n2.
10.6 Show that H is equivalent to the F test statistic in a one-way ANOVA problem if applied to the ranks of the observations rather than the actual numbers.Hint: Express the F ratio as a function of H in the form given in(10.4.4) or (10.4.2) to show that F ¼k 1 N k N 1 H 1 1 This is
10.7 Write the k-sample median test statistic given in (10.2.2) in the form of(10.5.1) (cf., Problem 7.2).
10.8 How could the subsampling procedure described in Section 9.9 be extended to test the equality of variances in k populations?
10.9 In the context of the k-sample control median test defined in Section 10.3, show that for any i( ¼ 2, 3, . . . , k) and j( ¼ 0, 1, . . . , q) the random variable Vij has a binomial distribution. What are the parameters of the distribution (1) in general and (2) under H0?
10.10 Show that under H0 : u1 ¼ u2 ¼ ¼ uk the distribution of V*, the sum test statistic for comparisons with a control when u1 is known in the case of unequal sample sizes defined in Section 10.7.1, is given by P[V* ¼ v] ¼ (0:5)N XYk i¼2 ni vi where N ¼Pki ¼2 ni, and the sum is
10.11 In the context of the Jonckheere–Terpstra test of Section 10.6, show that under H0 for i < j < r, cov(Uij,UirjH0) ¼ cov(Uji,UrijH0) ¼ninjnr 12 cov(Uij,UrijH0) ¼ cov(Uji,UirjH0) ¼ ninjnr 12 Hint: 2cov(Uij,Uir) ¼ var(Uij,Uir) var(Uij) var(Uir) ¼ var(Ui, jþr) var(Uij) var(Uir),
10.12 Many psychologists have developed theories about how different kinds of brain dominance may affect recall ability of information presented in various formats. Brown and Evans (1986) compare recall ability of subjects classified into three groups according to their approach to problem solving
10.13 Andrews (1989) examines attitudes toward advertising by undergraduate marketing students at universities in six different geographic regions. Attitudes were measured by answers to a questionnaire that allowed responses on a 7-point Likert scale (1¼strongly disagree and 7¼strongly agree).
10.14 Random samples of 100 insurance company executives, 100 transportation company executives, and 100 media company executives were classified according to highest level of formal education using the code 10¼ some college, 20¼bachelor’s degree, 30¼master’s degree, 40¼more than
10.15 Eighteen fish of a comparable size in a particular variety are divided randomly into three groups and each group is prepared by a different chef using the same recipe. Each prepared fish is then rated on each of the criteria of aroma, flavor, texture, and moisture by professional tasters. Use
10.16 An office has three computers, A, B, and C. In a study of computer usage, the firm has kept records on weekly use rates for 7 weeks, except that computer A was out for repairs for part of 2 weeks. The eventual goal is to decide which computers to put under a service contract because they have
10.17 Below are four sets of five measurements, each set an array of data on the smoothness of a certain type of paper, each set obtained from a different laboratory. Find an approximate P value to test whether the median smoothness can be regarded as the same for all laboratories.Laboratory Data A
10.18 Verify the value of the Kruskal–Wallis test statistic given in the SAS solution to Example 8.2.1.
10.19 A sample of 100 female students at a large university were questioned about four experimental types of service clubs that have essentially the same goals. The types differed only with respect to the difficulty of achieving membership, with Type I having no membership requirements, . . . , and
11.1 A beauty contest has eight contestants. Two judges are each asked to rank the contestants in a preferential order of pulchritude. Answer parts (a) and (b) using (1) the Kendall tau-coefficient procedures and(2) the Spearman rank-correlation-coefficient procedures.Contestant Judge A B C D E F G
11.2 Verify the result given in (11.4.9).
11.3 Two independent random samples of sizes m and n contain no ties.A set of m þ n paired observations can be derived from these data by arranging the combined samples in ascending order of magnitude and (a) assigning ranks, (b) assigning sample indicators. Show that Kendall’s tau, calculated
11.4 Show that for the standardized bivariate normal distribution F(0, 0) ¼1 4 þ1 2p arcsin r
11.5 The Census Bureau reported that Hispanics are expected to overtake blacks as the largest minority in the United States by the year 2030. Use two different tests to see whether there is a direct relationship between number of Hispanics and percent of state population for the nine states
11.6 Company-financed expenditures in manufacturing on research and development (R&D) are currently about 2.7% of sales in Japan and 2.8% of sales in the United States. However, when these figures are looked at separately according to industry, the following data from Mansfield (1989) show some
11.7 The World Almanac and Book of Facts published the following divorce rates per 1000 population in the United States. Determine whether these data show a positive trend using four different methods.Year Divorce Rate 1945 3.5 1950 2.6 1955 2.3 1960 2.2 1965 2.5 1970 3.5 1975 4.8 1980 5.2 1985 5.0
11.8 For the time series data in Example 3.4.1, use the Mann test based on Spearman’s rank correlation coefficient to see if the data show a positive trend.
11.9 Do Problem 11.8 using the Daniels’ test based on Kendall’s tau.
11.10 The rainfall measured by each of 12 gauges was recorded for 20 successive days. The average results for each day are as follows:Day Rainfall Day Rainfall April 1 0.00 April 11 2.10 April 2 0.03 April 12 2.25 April 3 0.05 April 13 2.50 April 4 1.11 April 14 2.50 April 5 0.00 April 15 2.51
11.11 A company has administered a screening aptitude test to 20 new employees over a 2 year period. The record of scores and data on which the person was hired are shown below.1=4=08 75 9=21=08 72 12=9=08 81 5=10=09 91 3=9=08 74 10=4=08 77 1=22=09 93 7=17=09 95 6=3=08 71 10=9=08 76 1=26=09 82
11.12 Ten randomly chosen male college students are used in an experiment to investigate the claim that physical strength decreases with fatigue.Describe the relationship for the data below, using several methods of analysis.Minutes between Rest Periods Pounds Lifted Per Minute 5.5 350 9.6 230 2.4

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Nonparametric Statistical Inference 5th Edition Jean Dickinson Gibbons, Subhabrata Chakraborti - Solutions

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