Exam 21: Nonparametric Techniques

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 two-tailed and the level of significance is 0.05, then the null hypothesis will be rejected.

In testing the hypotheses H₀: The two population locations are the same H₁: The location of population A is to the left of the location of population B, with data drawn from two independent samples, the following statistics are calculated: $n _ { A } = 6$ , $T _ { A } = \mathbf { 3 2 }$ , $n _ { B } = 8$ , $T _ { B } = 73$ . a. Which test is used for testing the hypotheses above? b. What is the p-value of this test?

Ten administration staff members were selected at random from among the secretaries of a large university. The typing speed (number of words per minute) was recorded for each administration staff member on two different brands of computer keyboards. The following results were obtained. Computer Keyboard Stafimem ber Brand A Brand B Amy 75 74 Betty 85 86 Jack 73 72 Donna 79 70 Ellen 91 85 John 80 73 Gwen 83 72 Wejing 74 65 Ingrid 81 79 Peter 70 64 Assume that the typing speeds are not normally distributed. Perform the Wilcoxon signed rank sum test at the 5% significance level.

Which of the following will never be a required condition of a non-parametric test? A The data are ordinal. B The samples are drawn from unimodal and symmetrically distributed populations. C The data are interval. D The populations being compared are identical in spread and shape.

In a Wilcoxon signed rank sum test, the test statistic is calculated as T = 45. The alternative hypothesis is stated as: The location of population 1 is different from the location of population 2. If there are n = 15 observations for which $D \neq 0$ , and the 5% significance level is used, then: A. he null hypothesis will be rejected. B. the null hypothesis will not be rejected. C. the test results are inconclusive. D. the normal approximation must be used.

We can use the Friedman test to determine whether two populations differ. The conclusion will be the same as that produced by the sign test.

Because of the cost of producing television shows and the profits associated with successful shows, television network executives are keenly interested in public opinion. A network has recently developed three comedy series. The pilot of each series is shown to 10 randomly selected people, who evaluate each show on a 9-point scale where 1 = terrible and 9 = excellent. The results are shown below. Assessments of Televion Shows Person Show 1 Show 2 Show 3 1 6 4 7 2 5 4 5 3 7 6 8 4 7 7 8 5 9 9 9 6 5 7 6 7 4 4 5 8 6 3 7 9 5 6 6 10 7 7 8 Using the appropriate statistical table, what statement can be made about the p-value for this test?

Which of the following distributions approximates the Kruskal-Wallis test statistic H when the problem objective is to compare k distributions and the sample sizes are greater than or equal to 5? A. Normal. B. Chi-squared distribution with k-1 degrees of freedom. C. Student t -distribution with k-2 degrees of freedom. D. Either chi-squared distribution with k-5 degrees of freedom or Student t -distribution with k+5 degrees of freedom.

A Wilcoxon rank sum test for comparing two independent samples involves two samples of sizes 5 and 8. The alternative hypothesis is that the location of population 1 is different from the location of population 2. Using the 0.10 significance level, the appropriate critical values are 21 and 49.

Which of the following statements is correct regarding the Kruskal-Wallis test? A The Kruskal-Wallis test uses data that are ordinal or numerical and normal. B The Knuskal-Wallis test uses data that is numerical and normal. C The Knuskal-Wallis test uses data that are ordinal or numerical and non-normal. D None of these choices are correct.

Use the Wilcoxon rank sum test on the data below to determine at the 10% significance level whether the two population locations differ. Sample 1: 15 14 15 16 16 17 13 15 16 14 Sample 2: 17 15 15 16 18 15 17 17 15 18

Because of the rising costs of industrial accidents many chemical, mining and manufacturing firms have instituted safety courses. Employees are encouraged to take these courses, which are designed to heighten safety awareness. A company is trying to decide which one of two courses to institute. To help make a decision, eight employees take course 1 and another eight take course 2. Each employee writes a test, which is marked out of a possible 25. The results are shown below. Do these data provide sufficient evidence at the 5% level of significance to conclude that the marks from course 2 are higher than those of course 1? Assume that the scores are not normally distributed. Safety Test Scores Course 1 Course 2 14 20 21 18 17 22 14 15 17 23 19 21 20 19 16 15

Which of the following best describes when the Wilcoxon rank sum test statistic T is approximately normally distributed? A For sample sizes larger than 30 . B For sample sizes larger than 15 . C For sample sizes larger than 20 . D For sample sizes larger than 10 .

Apply the Friedman test to the following table of ordinal data to determine whether we can infer at the 5% significance level that at least two population locations differ. Treatment Block A B C D i 2 5 3 1 iii 1 4 5 4 iii 3 4 2 2 iv 2 5 4 1 1 5 3 5

Ten business people who fly frequently from Melbourne to Sydney were asked to rank four airlines in terms of the quality of service. The people assigned scores using a 5-point Likert scale where: 1 = bad, 2 = poor, 3 = average, 4 = good, and 5 = excellent. The results are shown below. Airline Person A B C D 1 5 5 2 1 2 3 3 4 2 3 2 3 4 3 4 1 1 4 3 5 4 1 5 3 6 2 3 4 2 7 1 3 5 2 8 3 3 5 1 9 1 3 5 2 10 2 4 3 1 Which test is appropriate if you want to compare the quality of service of the four airlines?

The Kruskal-Wallis test can be used to determine whether a difference exists between two populations. However, to determine whether one population location is larger than another, we must apply the Wilcoxon rank sum test.

The Friedman test is the non-parametric counterpart of the randomised block experimental design of the analysis of variance.

Which of the following best describes when to apply the Friedman test to determine whether the locations of two or more populations are the same? A The populations must be normally distributed. B The sample sizes must be at least 30 . C The data must be generated from a randomised block experiment. D All of these choices are correct.

The significance level for a Wilcoxon signed rank sum test is 0.05. The alternative hypothesis is stated as: the location of population 1 is to the right of the location of population 2. The appropriate critical value for a sample of size 20 (that is, the number of nonzero differences is 20) is: A. 158. B. 150. C. 60 D. 52

In a sign test, the following information is given: number of zero differences = 3, number of positive differences = 20, and number of negative differences = 5. The value of the standardised test statistic z is: A. 5. B. 4. C. 3. D. 2.