Nonparametric Statistical Inference 4th Edition Gibbons, Jean Dickinson, Chakraborti, Subhabrata - Solutions

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*9. Indicate the probable shape of each of the following distributions:(a) heights of a large sample of 25-year-olds(b) scores on the same math test taken by 30 fifth graders and 30 ninth graders(combined into a single frequency distribution)(c) verbal aptitude of high school students(d) SAT scores
(c) The graph that you construct to impartially portray these data.
(b) A graph to give the impression that faculty salary increases have been quite impressive(constructed by, say, a representative of the university administration).
(a) A graph to give the impression that faculty salary increases have been inadequate(constructed by, say, the president of the faculty union).
*8. Suppose these are the median salaries, over a 10-year period, for tenure-track faculty at a local university:Using these data, create a \trend graph" from each of three perspectives:
7. Construct a graph of the race/ethnicity breakdown from Problem 9 in Chapter 2.
6. Construct a histogram based on the GPA data in Table 2.5.
5. Suppose that in Problem 4 you had used percentages along the vertical axis instead of frequencies. What would be different about the new graph, and what would be the same?
*4. Following the guidelines presented in this chapter, construct a histogram (using frequencies)to exhibit the distribution of test scores obtained in Problem 7 of Chapter 2.(Be sure to provide clear labels for the two axes and a title.)
3. Give the midpoints of each of the following intervals (assume the scores are rounded to the nearest whole number or decimal place indicated unless otherwise specified):(a) 10–14(b) 200–399(c) 2.50–2.74(d) 3.00–3.19(e) 30–40 (accurate to the nearest 10)
2. Generate side-by-side box plots to compare the CGPA distributions of students who enrolled in algebra in the eighth grade and those who did not. Comment on which group maintained higher CGPAs.
(b) Assume that a symmetric distribution of CPGA is indicative of \grading on the curve." Does this distribution suggest to you that teachers at this school subscribe to such a philosophy? Do you find any evidence to support claims of \grade inflation"at this school?
(a) Describe the distribution of scores in terms of central tendency, variability, and shape.
1. Generate a histogram for CGPA, and then address the following:
13 using an interval width of 5 and 15–19 as the lowest interval. Compare the result with the distribution obtained in Problem 13. From this example, what would you say are the advantages of sometimes using a larger interval size and thus fewer intervals?
*14. Construct a relative frequency distribution (use proportions) from the scores in Problem
13. The following scores were obtained by middle-level students on an \educational aspirations" assessment:41 33 18 41 36 50 27 34 36 36 36 36 39 33 40 48 29 41 28 39 30 44 41 39 45 30 36 27 21 46 40 47 46 47 35 24 32 46 33 39 33 45 39 31 37 46 34 18 30 35 27 42 27 31 33 44 39 36 24 27 30 24 22 33
*12. Imagine the data below are the GPAs for a sample of 60 sophomores at your university.Prepare a relative frequency distribution (use proportions), using an interval width of .30 and .90–1.19 as the score limits for the lowest interval.3.08 1.81 3.63 2.52 2.97 3.48 1.00 2.70 2.95 3.29 1.40
11. Provide the exact limits for the data we presented earlier in Table 2.5:GPA f Exact Limits 3.80–3.99 2 3.60–3.79 3 3.40–3.59 4 3.20–3.39 6 3.00–3.19 5 2.80–2.99 9 2.60–2.79 7 2.40–2.59 2 2.20–2.39 3 2.00–2.19 3 1.80–1.99 1 1.60–1.79 1
Why? Provide an illustration to support your reasoning.34 Chapter 2 Frequency Distributions
Which would you concentrate on—the original frequencies or the relative frequencies?
*10. Imagine that you want to compare the frequency distributions for males and females separately (on some variable), and there are considerably more females than males.
9. Suppose that the racial/ethnic breakdown of participants in your investigation is as follows:African American, n ¼ 25; White, n ¼ 90; Asian, n ¼ 42; Hispanic, n ¼ 15;\other," n ¼ 10. Construct a frequency distribution for these data.
(e) Between which two scores is the \middle" of this distribution?
(d) One-fifth of the cases fall at or below which score?
(c) Roughly two-thirds of the cases fall at or below which score?
(b) Find the cumulative percentage and percentile ranks for each of the following scores: 67, 57, and 49.
(a) Fill in the three blank columns (round the cumulative percentages to the nearest whole number).
8. The following is the cumulative frequency distribution for 30 scores on a \test anxiety"survey.Test Anxiety f Cum. f Cum. % Percentile Rank 79 1 73 1 70 1 67 1 66 1 64 1 63 2 62 2 61 3 60 4 59 2 58 2 57 2 56 1 55 1 53 1 52 1 49 1 45 1 39 1
(c) Construct a frequency distribution with i ¼ 2 and 64–65 as the lowest interval; include percentages, cumulative frequencies, and cumulative percentages.(d) Which frequency distribution do you prefer—one based on i ¼ 2 or i ¼ 3? Why?Exercises 33
(b) Construct a frequency distribution with i ¼ 3 and 63–65 as the lowest interval; include score limits and exact limits, frequencies, percentages, cumulative frequencies, and cumulative percentages.
(a) How did we get these two values of i?
*7. Thirty prospective teachers take a standards-based teacher competency test. The results are as follows (each score reflects the percentage of standards for which the prospective teacher demonstrates proficiency):81 91 89 81 79 82 70 92 80 64 73 86 87 72 74 75 90 85 83 82 79 82 78 96 77 85 83 87
6. Convert the following percents to proportions (again, to the same degree of accuracy):(a) 42%(b) 6.6%(c) 43.7%(d) 78%(e) .8%
*5. Convert the following proportions to percents (to the same degree of accuracy):(a) .26(b) .05(c) .004(d) .555(e) .79
4. For each of the following intervals, give (1) the interval width, (2) the exact limits of the interval, and (3) the score limits and exact limits of the next higher interval(assume the scores are rounded to the nearest whole number or decimal place indicated unless otherwise specified):(a)
2. Determine the proportion of females in the sophomore class.
(d) What score, roughly speaking, separates the top half from the bottom half of students?
(c) Approximately one-tenth of the cases fall at or below which score?
(b) Find the cumulative percentage for each of the following scores: 226, 262, and 280.
(a) Generate a frequency distribution for READING.
1. The test scores represented by the READING variable are on a scale ranging from 200 to 300 points.
Step 5 List all class intervals, placing the interval containing the highest score at the top. We make sure that our intervals are continuous and of the same width: 50–54, 55–59, . . . , 95–99.
Step 4 Determine the lowest class interval. Our lowest score is 51, so we select 50 for the beginning point of the lowest interval (it is a multiple of our interval width). Because i ¼ 5, we add 4 (i.e., 5 1) to this point to obtain our lowest class interval: 50–54. (If we had added 5, we
a frequency distribution based on both values of i. In practice, of course, one frequency distribution will do!)
Step 3 Divide the range by 10 and by 20 to see what interval widths are acceptable;choose a convenient width. Dividing by 10 gives us 4.8, which we round to 5, and dividing by 20 gives us 2.4, which we round to 3. We decide to go with i ¼ 5. (In Table 2.3, for illustrative purposes we present
Step 2 Find the ange" of scores by subtracting the lowest score from the highest.Simple: 99 51 ¼ 48.
Find the value of the lowest score and the highest score. For our data, the values are 51 and 99, respectively.
=+14.17. Verify the equivalence of the expressions in (3.1), (3.2), and (3.3)
=+14.15. Derive the maximum likelihood estimators for the parameters in the likelihood function of (2.1)
=+dents who had completed their first year of college calculus were classified according to their high school calculus experience as Zero (None), Brief (One semester), Year (Two semesters), and AP (Advanced Placement); these same students were then classified according to their grade in first year
=+14.13. A study was conducted to investigate whether high school experience with calculus has an effect on performance in first-year college calculus. A total of 686 stuJob satisfaction (1 ¼ least satisfied)Age 1 2 3 Total Under 25 8 7 5 20 25–39 12 8 20 40 40 and over 20 15 5 40 Total 40 30
=+such as relative cost and distance so that their preference would reflect only their expected pleasure from each type of vacation. The husband voted for the beach 7 times and his wife agreed 4 times. The husband voted for the mountains 13 times and his wife agreed 5 times. Determine whether
=+14.12. Twenty married couples were selected at random from a large population and each person was asked privately whether the family would prefer to spend a week’s summer vacation at the beach or at the mountains. The subjects were told to ignore factors
=+favor both before and after receiving the newsletter, and 6 were opposed both times. Is there evidence that the letter is effective in persuading people to favor a flat tax?
=+14.11. A small random sample was used in an experiment to see how effective an informative newsletter was in persuading people to favor a flat income tax bill. Thirty persons were asked their opinion before receiving the letter and these same persons were then asked again after receiving the
=+Find the P value for the alternative that the probability of a change from negative to positive is greater than the corresponding probability of a change in the opposite direction.
=+14.10. A random sample of 135 U.S. citizens were asked their opinion about the current U.S. foreign policy in Afghanistan. Forty-three reported a negative opinion and the others were positive. These 135 persons were then put on a mailing list to receive an informative newsletter about U.S.
=+ðaÞ Test whether there is any association between age and job satisfaction using the chi-square test.ðbÞ Calculate the contingency coefficient and the phi coefficient.ðcÞ Calculate Kendall’s tau with correction for ties and test for association.ðdÞ Calculate the Goodman-Kruskal
=+14.9. In a study designed to investigate the relationship between age and degree of job satisfaction among clerical workers, a random sample of 100 clerical workers were interviewed and classified according to these characteristics as shown in the table below.
=+14.8. A financial consultant is interested in testing whether the proportion of debt that exceeds equity is the same irrespective of the magnitude of the firm’s assets. Sixty-two firms are classified into three groups according to asset size and data in Table 2 are obtained on the numbers with
=+Table 1 Data for Problem 14.3 Rating after film Rating before film Acceptable Not acceptable Total Acceptable 5 4 9 Nonacceptable 13 6 19 Total 18 10 28 Table 2 Data for Problem 14.8 Firm asset size ($1000)Less than 500 500–2000 Over 2000 Total Debt less than equity 7 10 8 25 Debt greater than
=+There were 69 pairs in which the case pair member was in the specified occupation while the control member was not. There were 30 pairs in which the control member was in the occupation and the case pair member was not. In all of the remaining 1400 pairs, neither the case nor the control member
=+death, and stating any cause of death other than the neoplastic disease. The occupation of each decedent was determined. Only one matched pair had both the case and control members in the specified occupation.
=+14.7. A retrospective study of death certificates was aimed at determining whether an association exists between a particular occupation and a certain neoplastic disease. In a certain geographical area over a period of time, some 1500 certificates listed the neoplastic disease as primary cause
=+Believe work load is heavier than it should be 25 17 9 Day Evening Night Defects 70 60 80 Sample total 400 300 300 548 CHAPTER 14 same 100 employees were then placed on the prepaid policy and after one year, it was found that among the 20, 5 had been rehospitalized, and among the 80, 10 had been
=+ During the previous year under the current policy, 20 of them had been hospitalized and 80 had not been hospitalized. These Sophomore Junior Senior Believe work load is lighter than it should be 5 8 11 Believe work load is at the appropriate level 30 35 40
=+14.4. An employer wanted to find out if changing from his current health benefit policy to a prepaid policy would change hospitalization rates among his employees. A random sample of 100 employees was selected for the study.
=+For the data in Table 1 determine whether the training film has a positive effect on the ratings.
=+14.3. A group of 28 salespersons were rated on their sales presentations and then asked to view a training film on improving selling techniques. Each person was then rated a second time.
=+14.2. A manufacturer produces units of a product in three 8-hour shifts: Day, Evening, and Night. Quality control teams check production lots for defects at the end of each shift by taking random samples. For the data below, do the three shifts have the same proportion of defects?
=+(a) Test the null hypothesis that there is no association between the stage of a student’s program and his attitude with respect to the appropriateness of the academic work load in his courses.ðbÞ Measure the degree of association.
=+it should be, at the appropriate level, or heavier than it should be. A stratified random sample yielded the following results:
=+14.1. An ongoing problem on college campuses is the instructor evaluation form. To aid in the interpretation of the results of such evaluations, a study was made to determine whether any relationship exists between the stage of a student’s academic career and his attitude with respect to
=+of tests, say T1 and T3, when the relevant AREs exist, AREðT1;T3Þ ¼ AREðT1;T2ÞAREðT2;T3Þ¼½AREðT3;T1Þ1 where we take 1=1 to be 0 and 1/0 to be 1.
=+13.9. Suppose there are three test statistics, T1;T2, and T3, each of which can be used to test a null hypothesis Ho against an alternative hypothesis H1. Show that for any pair
=+13.6. Evaluate the efficacies of the MN and AN test statistics and compare their efficiency for the scale model where, as in Problem 13.1:(a) FX is uniform.(b) FX is double exponential.
=+13.4. Calculate the efficacy of the sign test and the Student’s t test for the location model FX ðxÞ ¼ Fðx yÞ where y is the median of FX and F is the cdf of the logistic distribution FðxÞ¼ð1 exÞ1
=+(c) FX is double exponential, with FX ðxÞ ¼ ð1=2Þelx x40 1 ð1=2Þelx x > 0
=+13.1 Use the results of Theorem 7.3.8 to evaluate the efficacy of the two-sample Wilcoxon rank-sum test statistic of (8.2.1) for the location model FYðxÞ ¼ FX ðx yÞwhere:(a) FX is NðmX ;s2Þ or FX ðxÞ ¼ F½ð x mX Þ=s(b) FX is uniform, with 518 CHAPTER 13 FX ðxÞ ¼0 x4 1=2 x þ
=+The experimenter comes to you and asks you to:(a) Comment about the design of the experiment, including any criticisms.(b) Help him get some useful information from his study. Do the best you can to help. You may want to use more than one kind of analysis.
=+The 100 students were assigned randomly into four groups and each student received a letter asking her to come for an interview as a prospective member of the club. At each interview, the goals and membership requirements were outlined and the student was asked to rank on a 10-point scale how
=+12.15. A study was made of a sample of 100 female students at a large college on the relative popularity of four experimental types of service clubs having essentially the Store no.Size of store(1000 ft2)Food sales($10,000)Nonfood sales($10,000)1 35 305 35 2 22 130 98 3 27 189 83 4 16 175 76 5 28
=+patient gave an estimate of the relative degree of pain suffered from migraines during that month on a scale from 0 to 10, with 10 being the most severe pain. Test the null hypothesis that the drugs are equally effective.
=+12.14. An experimenter is attempting to evaluate the relative effectiveness of four drugs in reducing the pain and trauma of persons suffering from migraine headaches.He gave seven patients each drug for a month at a time. At the end of each month, each
=+(b) Use all the data given to estimate the rank ordering of the products. In what sense is this estimate a good one?
=+(a) Is there agreement between the three sets of rankings? Give a descriptive measure of agreement and find a P value.
=+12.13. Suppose in Problem 11.15 that an independent group of female consumers also ranked the products as follows:
=+12.12. A town has 10 different supermarkets. For each market, data are available on the following three variables: X1¼ food sales, X2 ¼ nonfood sales, and X3 ¼ size of store in thousands of square feet. Calculate the partial tau coefficient for X1 and X2, when the effects of X3 are eliminated.
=+12.11. Show that if m ¼ n and l ¼ k in (5.3) so that the design is complete, then (5.3) is equivalent to Q ¼ 12S=kn(n þ 1), as it should be.Taster Varieties presented 1 ABD 2 BCE 3 CDF 4 DEG 5 EFA 6 FGB 7 GAC Taster Ranks Taster Ranks Taster Ranks 1 2 1 3 8 2 1 3 15 2 1 3 2 1 2 3 9 2 1 3 16 1
=+(c) Will it be difficult to decide which students should be given a passing grade?
=+(b) Give an overall estimate of the relative performance of each student.
=+12.10. Ten graduate students take identical comprehensive examinations in their major field. The grading procedure is that each professor ranks each student’s paper in relation to all others taking the examination. Suppose that four professors give the following ranks, where 1 indicates the
=+The ranks resulting from the three repetitions are shown below with each rank corresponding to the variety shown above. For example, the rank 3 by taster 12 is for variety E. Determine whether there is a positive association between the rankings.
=+presented together three times, to a group of seven of the tasters, with the design shown below used each of the three times.Student Score 1 2 3 4 5 6 7 8 Verbal 90 60 45 48 58 72 25 85 Quantitative 62 81 92 76 70 75 95 72 Logic 60 91 85 81 90 76 93 80 Model Factor Nissan Maxima SE Acura Legend
=+12.9. A manufacturer of ice cream carried out a taste preference test on seven varieties of ice cream, denoted by A, B, C, D, E, F, G. The subjects were a random sample of 21 tasters and each taster had to compare only three varieties. Each pair of varieties is
=+comfort, and performance. The scores of the six best models are shown below. Determine whether the median scores are the same. Which model(s) would you buy, on the basis of this report?
=+12.8. Automobile Magazine (July 1989) published results of a comparison test of 15 brand models of $20,000 sedans. Each car was given a subjective score out of a possible 60 points (60 ¼ best) on each of 10 characteristics that include factors of appearance,
=+12.7. Eight students are given examinations on each of verbal reasoning, quantitative reasoning, and logic. The scores range from 0 to 100, with 100 a perfect score. Use the data below to find the Kendall partial tau coefficient between quantitative and logic when the effect of verbal is removed.
=+Table 2 Data for Problem 12.6 Group Mean age Optimism index Cynicism index Owners=managers 60 þ 55 1.1 Corporate executives 44 59 1.4 Middle managers 34 41 1.4 MBA students 25 30 1.8 Undergraduates 20 23 2.2 MEASURES OF ASSOCIATION IN MULTIPLE CLASSIFICATIONS 489

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Nonparametric Statistical Inference 4th Edition Gibbons, Jean Dickinson, Chakraborti, Subhabrata - Solutions

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