statistics21 by keller.docx

1、statistics21 by kellerCHAPTER 21NONPARAMETRIC STATISTICSSECTIONS 1 MULTIPLE CHOICE QUESTIONSIn the following multiple-choice questions, please circle the correct answer.1. Consider the following data set: 14, 14, 15, 16, 18, 19, 19, 20, 21, 22, 23, 25, 25, 25, 25, and 28. The rank assigned to the fo

2、ur observations of value 25 is:a. 12b. 12.5 c. 13d. 13.5ANSWER: d2. To apply the Wilcoxon rank sum test to determine whether the location of population 1 is different from the location of population 2, the samples must be:a. drawn from normal populationsb. drawn from matched pairs experimentc. indep

3、endentd. larger than 30ANSWER: c3. The Wilcoxon rank sum test statistic T is approximately normally distributed whenever the sample sizes are larger than:a. 10b. 15c. 20d. 25ANSWER: a4. A Wilcoxon rank sum test for comparing two populations involves two independent samples of sizes 5 and 7. The alte

4、rnative hypothesis is stated as: The location of population 1 is different from the location of population 2. The appropriate critical values at the 5% significance level are:a. 20 and 45b. 22 and 43c. 33 and 58d. 35 and 56ANSWER: a5. Consider the following two independent samples: Sample A: 16 17 1

5、9 22 47 Sample B: 27 31 34 37 40 The value of the test statistic for a left-tail Wilcoxon rank sum test is:a. 6b. 20c. 35d. 55ANSWER: b6. A nonparametric method to compare two populations, when the samples are independent and the data are either ordinal or interval, and where the normality requireme

6、nt necessary to perform the parametric test is not satisfied, is the:a. Wilcoxon rank sum testb. sign testc. Wilcoxon signed rank sum testd. equal-variance t-test of ANSWER: a7. Statistical methods that require few assumptions, if any, about the population distribution are known as:a. parametric tec

7、hniquesb. nonparametric techniquesc. free agent techniquesd. All of the above ANSWER: b8. Which of the following statements about nonparametric tests is false?a. We can safely employ nonparametric tests even when we know nothing at all about the populations from which sample data are being drawnb. W

8、e can conduct nonparametric tests with nominal datac. We can conduct nonparametric tests with ordinal datad. We can only conduct nonparametric tests with data of a higher order than nominal or ordinalANSWER: d9. Which of the following statements is false?a. We can conduct nonparametric tests even wi

9、th nominal and ordinal datab. When parametric assumptions are valid and, therefore, either type of test could be used, nonparametric tests are less powerful than parametric testsc. Given sample size and specified significance level, the probability of a Type II error is larger for a nonparametric te

10、std. Using a nonparametric test when we could employ a parametric test can be less efficient: A nonparametric test often tends to ignore available sample information-for example, by focusing only on the directions rather than the sizes of observed differences.ANSWER: c10. Consider the following two

11、independent samples: Sample A: 15 17 18 Sample B: 14 16 19 19 20 22 23 The value of the test statistic for a right-tail Wilcoxon rank sum test is:a. 3b. 7c. 11d. 44ANSWER: c11. The nonparametric tests discussed in your book (Wilcoxon rank sum test, sign test, Wilcoxon signed rank sum test, Kruskal-W

12、allis test and Friedman test) all require that the probability distributions be:a. identical except with respect to locationb. identical except with respect to spread (variance)c. identical except with respect to shape (distribution)d. different with respect to location, spread, and shapeANSWER: a12

13、. Statistical methods that require, among other assumptions, that the populations be normally distributed are known as:a. distribution-free techniquesb. nonparametric techniquesc. parametric techniquesd. both (a) and (b) are correctANSWER: c13. In a Wilcoxon rank sum test, the two sample sizes are 4

14、 and 6, and the value of the Wilcoxon test statistic is T = 20. If the test is a two-tail and the level of significance is, then:a. the null hypothesis will be rejectedb. the null hypothesis will not be rejectedc. the alternative hypothesis will not be rejectedd. not enough information has been give

15、n to answer this questionANSWER: b14. Comparing the output of strawberries grown on plots using fertilizer A with that grown on otherwise identical plots using fertilizer B, in order to make a general assessment of relative fertilizer effectiveness, may well call for aa. Friedman testb. Kruskal-Wall

16、is testc. Wilcoxon rank-sum testd. Spearman rank correlation testANSWER: c15. A Wilcoxon rank sum test for comparing two populations involves two independent samples of sizes 15 and 20. The un-standardized test statistic (that is the rank sum) is T = 210. The value of the standardized test statistic

17、 z is:a. 14.0b. 10.5c. 6.0d. 2.0ANSWER: d16. The appropriate measure of central location of ordinal data is the:a. meanb. medianc. moded. All of the above ANSWER: b17. You are performing the Wilcoxon rank-sum test. The 13th through 15th values in an ordered array of pooled sample data all equal $180

18、 (while the 12th value is less and the 16th value is more). The appropriate ranks for the three $180 values area. 13, 14, 15b. 14, 14, 14c. 12.5, 13, 14.5d. 12.5, 13, 15ANSWER: b18. In a normal approximation to the Wilcoxon rank sum test, the standardized test statistic is calculated as z = 1.80. Fo

19、r a two- tail test, the p-value is:a. 0.0359b. 0.4641c. 0.2321d. 0.0718 ANSWER: d19. Which of the following will never be a required condition of a nonparametric test?a. Data are ordinalb. Data are intervalc. The samples are drawn from normally distributed populations d. The populations being compar

20、ed are identical in spread and shapeANSWER: c20. A nonparametric method that is equivalent to the Wilcoxon rank sum test is the:a. Wilcoxon signed rank sum testb. Friedman testc. Kruskal-Wallis testd. Mann-Whitney testANSWER: d21. Consider the following data set: 2.2, 2.3, 2.3, 2.5, 2.6, 2.7, 2.8, 2

21、.8, 2.8, 2.9, 3.1, 3.2, and 3.5. The rank assigned to the three observations of value 2.8 is:a. 6b. 7c. 8d. 9ANSWER: c22. The Wilcoxon rank sum test (like most of the nonparametric tests presented in your book) actually tests to determine whether the population distributions have identical:a. locati

22、onsb. spreads (variances)c. shapes d. All of the above ANSWER: d23. Inferential procedures that are free from restrictive assumptions about the sampled populations are known asa. Distribution-free tests(because no assumption about the nature of the population distribution is being made).b. Distribut

23、ion-free tests (because no assumption about the nature of the sampling distributions of test statistics is being made).c. Parametric testsd. All of the aboveANSWER: a24. To use the Wilcoxon Rank Sum Test as a test for location, we must assume that a. the obtained data are either ordinal or interval

24、where the normality requirement necessary to perform the equal-variances t test of is unsatisfiedb. both samples are randomly and independently drawn from their respective populationsc. both underlying populations from which the samples were drawn are equivalent in shape and dispersiond. All of the

25、aboveANSWER: d25. Which of the following correctly describes the Wilcoxon rank-sum test?a. It is a nonparametric test based on two independent simple random samplesb. It is designed to determine whether the relative frequency distributions of two statistical populations of continuous values are iden

26、tical to or different from one anotherc. It is equivalent to a parametric t - test of the difference between two means.d. All of the above. ANSWER: d26. The first step in a Wilcoxon rank sum test is to combine the data values in the two samples and assign a rank of 1 to the:a. smallest observationb.

27、 middle observationc. largest observationd. observation that occurs most frequentlyANSWER: aTRUE / FALSE QUESTIONS27. A parametric test is a hypothesis test that depends on certain specific assumptions about the probability distribution of population values or the sizes of population parameters. ANS

28、WER: T28. Nonparametric tests are methods of inference that make no assumptions whatsoever about the nature of underlying population distributions or their parameters. ANSWER: T29. A nonparametric test is one that makes no assumptions about the specific shape of the population from which a sample is

29、 drawn. ANSWER: T30. Nonparametric procedures are often, and perhaps more accurately, called free-agent statistics. ANSWER: F31. A Wilcoxon rank sum test for comparing two independent samples involves two samples of sizes 6 and 9. The alternative hypothesis is that the location of population 1 is to

30、 the left of the location of population 2. Using a 0.05 significance level, the appropriate critical values are 31 and 65. ANSWER: F 32. In a Wilcoxon rank sum test for independent samples, the two sample sizes are 4 and 6, and the value of the Wilcoxon test statistic is T = 25. If the test is a two

31、-tail and the level of significance is 0.05, then the null hypothesis will be rejected. ANSWER: F33. A Wilcoxon rank sum test for comparing two populations involves two independent samples of sizes 15 and 20. If the value of un-standardized test statistic is T = 225, then the value of the standardized test statistic is z = 1.50. ANSWER: T34. Statistical tests that are not very sensitive to errors in assumptions are called parametric tests. ANSWER: F35. Nonparametric tests are often more efficient than parametric tests. ANSWER: F36. The statistical methods discus