Exam 21: Nonparametric Techniques

In testing the hypotheses: $H _ { 0 } :$ The two population locations are the same $H _ { 1 } :$ The two population locations are different, with data drawn from a matched pairs experiment, the following statistics are calculated: $n = 40$ , $T ^ { + } = 238$ , $T ^ { - } = 582$ . a. Which test is used for testing the hypotheses above? b. What is the p-value of this test?

Use the Wilcoxon rank sum test on the data below to determine at the 5% significance level whether the location of population A is to the left of the location of population B. Sample A: 75 60 67 54 69 Sample B: 80 84 100 74 90

In a Wilcoxon signed rank sum test for matched pairs with n = 35, the rank sums of the positive and negative differences are 380 and 225, respectively. The value of the standardised test statistic z is: A. 1.689. B. 1.065. C. 1.206. D. 1.400.

A two-independent-sample t-test corresponds to a Wilcoxon signed rank sum test for paired samples.

Which of the following are statistical methods that require few assumptions, if any, about the distribution of the population? A Parametric techniques. B Inferential statistics C Non-parametric techniques. D All of these choices are correct.

The z-test approximation to the Wilcoxon rank sum test for two independent samples requires that at least one of the two sample sizes exceed 10.

The F-test of the randomised block design of the analysis of variance requires that the random variable of interest must be normally distributed and the population variances must be equal. When the random variable is not normally distributed, we can use: A one-way ANOVA. B two-way ANOVA. C the chi-squared test. D the Friedman test.

The Wilcoxon signed rank sum test is the nonparametric counterpart of the t-test of µ_D.

The restaurant critic on a newspaper claims that the hamburgers one gets at the hamburger chain restaurants are all equally bad, and that people who claim to like one hamburger over others are victims of advertising. In fact, he claims that if there were no differences in appearance, then all hamburgers would be rated equally. To test the critic's assertion, ten teenagers are asked to taste hamburgers from three different fast-food chains. Each hamburger is dressed in the same way (mustard, relish, tomato and pickle) with the same type of bun. The teenagers taste each hamburger and rate it on a 9-point scale with 1 = bad and 9 = excellent. The data are listed below. Ham burger Ratings Teenager Chain 1 Chain 2 Chain 3 1 7 5 6 2 5 3 4 3 6 4 5 4 9 8 8 5 4 3 2 6 4 5 4 7 6 5 5 8 5 4 5 9 8 7 9 10 9 8 7 Can we infer at the 1% significance level that the critic is wrong?

The sign test and the Wilcoxon signed rank sum test require matched pairs.

In general, before an academic publisher agrees to publish a book, each manuscript is thoroughly reviewed by university lecturers. Suppose that Cengage Australia publishing company has recently received two manuscripts for statistics books. To help them decide which one to publish, both are sent to 50 professors of statistics who rate the manuscripts to judge which one is better. Suppose that 20 lecturers rate manuscript A as better and 30 rate manuscript B as better. Which test is appropriate for this situation?

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 Use Excel to find the exact p-value for this 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 Can we infer at the 5% significance level that differences exist among the show's evaluations?

A supermarket chain has its own house brand of ice cream. The general manager claims that her ice cream is better than the ice cream sold by a well-known ice cream parlour chain. To test the claim, 40 individuals are randomly selected to participate in the following experiment. Each respondent is given the two brands of ice cream to taste (without any identification) and asked to judge which one is better. Suppose that 25 people judge the ice cream parlour brand better, four say that the brands taste the same, and the rest claim that the supermarket brand is better. Can we conclude at the 1% significance level that the general managers' claim is false?

In a Wilcoxon signed rank sum test, the test statistic is calculated as T = 75. If there are n = 15 observations for which $D \neq 0$ , and a two-tail test is performed at the 5% significance level, then: A. we reject the null hypothesis. B. we don't reject the null hypothesis. C. the test results are inconclusive. D. we perform a parametric test.

In a normal approximation to the sign test, the standardised test statistic is calculated as z = -1.58. To test the alternative hypothesis that the location of population 1 is to left of the location of population 2, the p-value is: A. 0.1142. B. 0.2215. C. 0.0571 D. 0.2284

A non-parametric method to compare two populations, when the samples consist of matched pairs of observations and the data are either ordinal or interval, and where the normality requirement necessary to perform the parametric test is not satisfied, is the: A Wil coxon rank sum test B Chi-squared test. C Wil coxon signed rank sum test. D Kruskal-Wallis test.

Consider the following data set: 1.2 1.3 1.3 1.3 1.6 1.7 1.8 1.8 1.8 1.9 2.1 2.2 2.5 The rank assigned to the three observations of value 1.3 is: A. 2.5. B. 3. C. 2. D. 1.

Use the 5% significance level to test the hypotheses. $H _ { 0 } :$ The two population locations are the same $H _ { 1 } :$ The two population locations are different, given that the data below are drawn from a matched pair experiment. Matched Pair 1 2 3 4 5 6 7 8 9 10 A 32 15 19 25 39 18 26 41 33 23 B 28 14 20 20 27 23 25 31 25 23

Consider the following data set: 11 11 12 13 15 16 16 17 18 19 20 22 22 22 22 25 The rank assigned to the four observations of value 22 is: A. 12. B. 12.5 C. 13. D. 13.5