Exam 21: Nonparametric Techniques

Which of the following is the correct sample size requirement for the Wilcoxon signed rank sum test statistic to be approximately normally distributed? A. Sample sizes less than 10 . B. Sample sizes greater than 30 . C. Sample sizes greater than 5 . D. Sample sizes greater than 100 .

The non-parametric counterpart of the parametric one-way analysis of variance F-test is the: A Kruskal-Wallis test. B Friedman test. C Wilcoxon rank sum test. D Wilcoxon signed rank sum test.

In a diet test, each of four diet programs is applies to a sample of people. At the end of three weeks, the amount of pounds people lost is shown below. Diet Program 1 2 3 4 12 19 16 28 6 10 20 17 18 13 26 22 23 20 19 16 25 20 Test to determine whether there is enough evidence at the 5% significance level to infer that at least two population locations differ.

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. Can Cengage Australia conclude at the 5% significance level that manuscript B is more highly rated than manuscript A?

The Kruskal-Wallis test is applied to compare two or more populations when the samples are independent and the data are ordinal or numerical and non-normal.

The Wilcoxon signed rank sum test is applied to compare two populations when the samples are matched pairs and the data are interval but not normally distributed.

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. What is the p-value of this test?

In testing the hypotheses: $H _ { 0 } :$ The two population locations are the same $H _ { 1 } :$ The location of population A is to the right of the location of population B, with data drawn from a matched pairs experiment, the following statistics are calculated: $n = 27$ , $T ^ { + } = 271$ , $T ^ { - } = 107$ . a. Which test is used in testing the hypotheses above? b. What is the p-value of this test?

The critical value is taken from the t-distribution whenever the test is a Kruskal-Wallis test.

The marketing manager of a pizza chain is in the process of examining some of the demographic characteristics of her customers. In particular, she would like to investigate the belief that the ages of the customers of pizza parlours, hamburger emporiums and fast-food chicken restaurants are different. As an experiment, the ages of eight customers of each of the restaurants are recorded and listed below. From previous analysis we know that the ages are not normally distributed. Custoner Age Pizza Hamburger Chicken 23 26 25 19 20 28 25 18 36 17 35 23 36 33 39 25 25 27 28 19 38 31 17 31 Use Excel to find the exact p-value for this test of whether there are differences in age among the customers of the three restaurants.

In a Kruskal-Wallis test, the following statistics were obtained: T₁ = 55, n₁ = 5, T₂ = 54, n₂ = 5, T₃ = 54, n₃ = 5, T₄ = 47, n₄ = 5. Use Excel to find the exact p-value for this test.

The Friedman test statistic is approximately chi-squared distributed with (k - 1) degrees of freedom, provided that either the number of blocks b or the number of treatments k is greater than or equal to 5.

The general manager of a frozen TV dinner maker must decide which one of four new dinners to introduce to the market. He decides to perform an experiment to help make a decision. Each dinner is sampled by ten people who then rate the product on a 7-point scale, where 1 = poor, and 7 = excellent. The results are shown below. Taste Ratings Respondent Dinner 1 Dinner 2 Dinner 3 Dinner 4 1 6 6 4 5 2 5 5 2 4 3 7 7 3 4 4 6 6 5 4 5 7 6 4 3 6 7 5 3 5 7 6 4 3 4 8 5 6 4 6 9 4 4 3 5 10 7 5 6 4 Which test can the general manager use to help him make a decision?

Radio advertising is big business, second only to television advertising. The objective for radio advertisements is to get listeners to remember as much as possible about the product/service being advertised. The advertising executive of a large company must decide between two pitched radio advertisements for their company. In order to ascertain the general public's perception, 12 randomly chosen people are selected to listen to both potential advertisements and are then asked a series of 5 questions regarding the radio advertisement's content. The number of correct responses are recorded and listed below. Assume that responses are non-normal. $\text { Number of correct responses from } 10 \text { questions }$ Respondent Radio advertisement 1 Radio advertisement 2 1 3 1 2 5 5 3 5 4 4 4 3 5 3 2 6 2 1 7 1 3 8 4 2 9 5 1 10 3 4 11 4 3 12 3 1 a. Which test is appropriate for this situation? b. Do these data provide enough evidence at the 5% significance level to conclude that the two radio advertisements differ?

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 Use Excel to find the exact p-value for this test.

Which of the following best describes the hypotheses in the Kruskal-Wallis test and Friedman test? A Two-tailed. B One-tailed. C Based on one sample. D None of these choices are correct.

In a Kruskal-Wallis test, the following statistics were obtained: T₁ = 55, n₁ = 5, T₂ = 54, n₂ = 5, T₃ = 54, n₃ = 5, T₄ = 47, n₄ = 5. Conduct the test at the 5% significance level.

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 Use Excel to find the exact p-value for this test.

The general manager of a frozen TV dinner maker must decide which one of four new dinners to introduce to the market. He decides to perform an experiment to help make a decision. Each dinner is sampled by ten people who then rate the product on a 7-point scale, where 1 = poor, and 7 = excellent. The results are shown below. Taste Ratings Respondent Dinner 1 Dinner 2 Dinner 3 Dinner 4 1 6 6 4 5 2 5 5 2 4 3 7 7 3 4 4 6 6 5 4 5 7 6 4 3 6 7 5 3 5 7 6 4 3 4 8 5 6 4 6 9 4 4 3 5 10 7 5 6 4 Use Excel to find the exact p-value for this test.

In a Friedman test for comparing four populations, provided that there are eight blocks, the test statistic is calculated as F = 10.98. If the test is conducted at the 5% significance level, the conclusion and p-value will be: A reject the null hypothesis, and 0.010.025 C do not reject the null hypothesis, and p-value<0.05 D do not reject the null hypothesis, and p -value >0.05