Exam 15: B:nonparametric Statistics

TV Commercials Narrative It is important to sponsors of television shows that viewers remember as much as possible about the commercials. The advertising executive of a large company is trying to decide which of two commercials to use on a weekly half-hour comedy. To help make a decision, she decides to have 12 individuals watch both commercials. After each viewing, each respondent is given a quiz consisting of 10 questions. The number of correct responses was recorded and is listed below. Assume that the quiz results are not normally distributed. Quiz Scores -Refer to TV Commercials Narrative. Which test is appropriate for this situation?

Hamburger Ratings Narrative The restaurant critic at a newspaper claims that the hamburgers that 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) and 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. Hamburger Ratings -Refer to Hamburger Ratings Narrative. Using the appropriate statistical table, what statement can be made about the p-value for this test?

Hamburger Ratings Narrative The restaurant critic at a newspaper claims that the hamburgers that 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) and 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. Hamburger Ratings -Refer to Hamburger Ratings Narrative. Which statistical technique is appropriate if you want to compare the quality of hamburger of the three chain restaurants?

Gourmet Meals Narrative Two gourmets, A and B, rated 22 meals on a scale of 1 to 10. The data are shown in the table. Do the data provide sufficient evidence to indicate that one of the gourmets tends to give higher ratings than the other? -Refer to Gourmet Meals Narrative. . Compare the results of the previous two questions.

Attitude Test Narrative Twenty students are given an attitude test before and after viewing a motion picture designed to change their attitudes favourably toward a new curriculum. A high score indicates a favourable attitude and a low score indicates an unfavourable attitude, with the scores ranging from 1 to 30. This will use the sign test on the data given below to see if we can conclude the motion picture was successful in improving attitudes. -Refer to Attitude Test Narrative. Determine the rejection region for the Wilcoxon signed-rank test at the 5% significance level.

Advertisement Narrative In a Kruskal-Wallis test to determine whether differences exist among three different advertisements, the following statistics were obtained: , , , , and . -Refer to Advertisement Narrative. Conduct the test at the 5% significance level.

Attitude Test Narrative Twenty students are given an attitude test before and after viewing a motion picture designed to change their attitudes favourably toward a new curriculum. A high score indicates a favourable attitude and a low score indicates an unfavourable attitude, with the scores ranging from 1 to 30. This will use the sign test on the data given below to see if we can conclude the motion picture was successful in improving attitudes. -Refer to Attitude Test Narrative. Is this a one-tailed test or a two-tailed test? Find the rejection region for = 0.10.

Books Manuscripts Narrative In general, before an academic publisher agrees to publish a book, each manuscript is thoroughly reviewed by university professors. Suppose that the Duxbury Publishing Company has recently received two manuscripts for statistics books. To help them decide which one to publish, both are sent to 30 professors of statistics who rate the manuscripts to judge which one is better. Suppose that 10 professors rate manuscript 1 better and 20 rate manuscript 2 better. -Refer to Books Manuscripts Narrative. Can Duxbury conclude at the 5% significance level that manuscript 2 is more highly rated than manuscript 1?

Typing Speed Narrative Ten secretaries were selected at random from among the secretaries of a large university. The typing speed (number of words per minute) was recorded for each secretary on two different brands of computer keyboards. Assume that the typing speeds are not normally distributed. The following results were obtained. -Refer to Typing Speed Narrative. Perform the test you suggested in the question above to determine if these data provide enough evidence at the 5% significance level to infer that the brands differ with respect to typing speed.

Two aptitude tests are currently being used to screen applicants for a certain position within a company. The question arose as to whether the two tests are comparable, i.e., whether they yield the same results. Six applicants were selected at random to take both tests (in a random order). The following scores were recorded: Use the Wilcoxon signed-rank test to determine whether there is a difference in scores between the two tests. Use = 0.10.

Frozen TV Dinner Narrative 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 -Refer to Frozen TV Dinner Narrative. Using the appropriate statistical table, what statement can be made about the p-value for this test?

Movie Ratings Narrative A movie critic wanted to determine whether or not moviegoers of different age groups evaluated a movie differently. With this objective, he commissioned a survey that asked people their ratings of the most recently watched movies. The rating categories were 1 = terrible, 2 = fair, 3 = good, and 4 = excellent. Each respondent was also asked to categorize his or her age as either 1 = teenager, 2 = young adult (20-34), 3 = middle age (35-50), and 4 = senior (over 50). The results are shown below. -Refer to Movie Ratings Narrative. What statement can be made about the p-value for this test?

A matched pairs experiment yielded the following results: Number of positive differences = 20 Number of negative differences = 8 Number of 0 differences = 2 Can we infer at the 5% significance level that the location of population 1 is to the right of the location of population 2? Justify your response.

Advertisement Narrative In a Kruskal-Wallis test to determine whether differences exist among three different advertisements, the following statistics were obtained: , , , , and . -Apply the Kruskal-Wallis test to determine if there is enough evidence at the 5% significance level to infer that at least two populations differ. Sample

In testing the hypotheses, The two population locations are the same, and The two population locations are different, the statistics , , , and are calculated with data drawn from two independent samples. a. Which test is used for testing the hypotheses above? b. What is the value of the test statistic? c. What is the rejection region for this test at = 0.05? d. What is your conclusion at = 0.05?