Exam 21: Nonparametric Techniques

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. $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$$\text { 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.

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. $\quad$ $\quad$ $\quad$$\text { Assessments of Television 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?

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?

In a Kruskal-Wallis test for comparing five populations, the test statistic is calculated as H = 10.20. If the test is conducted at the 1% significance level, then:

Which of the following statements is correct regarding the Kruskal-Wallis test?

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. $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$$\text { 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.

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. $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$$\text { 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?

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

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. $\quad$ $\quad$ $\quad$ $\quad$$\text { Computer Keyboard }$ Stafmen 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?

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?

The non-parametric counterpart of the randomised block model of the analysis of variance is the:

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:

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

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?

In a Kruskal-Wallis test there are five samples and the value of the test statistic is calculated as H = 11.15. The most accurate statement that can be made about the p-value is that:

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.

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

One of the required conditions of the sign test is that the number of nonzero differences n must be smaller than or equal to 10.

Which of the following tests would be an example of a non-parametric method?