676 CHAPTER 13 Nonparametric Tests 7.Clancy, Rowling, and Tolstoy Ease of Reading Pages were randomly selected from three books: The Bear and the Dragon by Tom Clancy, Harry Potter and the Sorcerer’s Stone by J. K. Rowling, and War and Peace by Leo Tolstoy. Listed below are Flesch Reading Ease Scores for those pages. Higher scores correspond to pages that are easier to read. Use a 0.01 significance level to test the claim that pages from books by those three authors have the same median Flesch Reading Ease score. Clancy 58.2 73.4 73.1 64.4 72.7 89.2 43.9 76.3 76.4 78.9 69.4 72.9 Rowling 85.3 84.3 79.5 82.5 80.2 84.6 79.2 70.9 78.6 86.2 74.0 83.7 Tolstoy 69.4 64.2 71.4 71.6 68.5 51.9 72.2 74.4 52.8 58.4 65.4 73.6 8.Clancy, Rowling, and Tolstoy Characters Per Word Numbers of characters per word were found from the same three books used in the preceding exercise. These data are shown below. Use a 0.05 significance level to test the claim that the three books have the same median number of characters per word. Does it appear that any of the authors use longer words? Clancy 4.8 4.5 4.6 4.5 4.0 4.0 4.6 4.5 4.4 4.4 4.3 4.3 Rowling 4.1 4.2 4.2 4.4 4.3 4.2 4.5 4.5 4.3 4.0 4.4 4.3 Tolstoy 4.3 4.5 4.5 4.5 4.5 4.8 4.3 4.2 4.7 4.3 4.4 4.5 Appendix B Data Sets. In Exercises 9–12, use the Kruskal-Wallis test with the data set in Appendix B. 9. M&M Candies Refer to Data Set 38 “Candies” in Appendix B and use the weights of the M&M candies categorized according to color. Use a 0.05 significance level to test the claim that the six different colors of M&M candies have the same median weight. Is the result as expected? 10. Passive and Active Smoke Data Set 15 “Passive and Active Smoke” in Appendix B lists measured cotinine levels from a sample of subjects who smoke, another sample of subjects who do not smoke but are exposed to environmental tobacco smoke, and a third sample of subjects who do not smoke and are not exposed to environmental tobacco smoke. Cotinine is produced when the body absorbs nicotine. Use a 0.01 significance level to test the claim that the three samples are from populations with the same median. What do the results suggest about a smoker who argues that he absorbs as much nicotine as people who don’t smoke? 11.Birth Weights Data Set 6 “Births” in Appendix B lists birth weights from babies born at Albany Medical Center, Bellevue Hospital in New York City, Olean General Hospital, and Strong Memorial Hospital in Rochester, New York. Use a 0.05 significance level to test the claim that the four different hospitals have different birth weights with different medians. 12.Disney World Wait Times Refer to Data Set 33 “Disney World Wait Times” in Appendix B and use the 10 AM wait times for Space Mountain, Rock ‘n’ Roller Coaster, Tower of Terror, and Flight of Passage. Use a 0.05 significance level to test the claim that the four rides have the same median wait time at 10 AM. 13.Correcting the H Test Statistic for Ties In using the Kruskal-Wallis test, there is a correction factor that should be applied whenever there are many ties: Divide H by 1 - ΣT N3 - N First combine all of the sample data into one list, and then, in that combined list, identify the different groups of sample values that are tied. For each individual group of tied observations, identify the number of sample values that are tied and designate that number as t; then calculate T = t3-t. Next, add the T values to get ΣT. The value of N is the total number of observations in all samples combined. 13-5 Beyond the Basics
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