Answer: Appendix B Data Sets. In Exercises 912, use the KruskalWallis test with the data

Effect of Lead on IQ Score Listed below are full IQ scores from simple random samples of subjects with low lead exposure, medium lead exposure, and high lead exposure (from Data Set 5 in Appendix B). In using the KruskalWallis test, we must rank all of the data combined, then we must find the sum of the ranks for each sample. Find the sum of the ranks for each of the three samples. Low Lead Level Medium Lead Level High Lead Level 70 72 82 85 90 93 86 92 85 76 71 75 84 86 85 79

. Requirements Assume that we want to use the data from Exercise 1 with the KruskalWallis test. Are the requirements satisfied? Explain.

Notation For the data given in Exercise 1, identify the values of n 1 , n 2 , n 3 , and N.

Efficiency Refer to Table 132 in Section 131 and identify the efficiency of the KruskalWallis test. What does that value tell us about the test? Using the KruskalWallis Test. In Exercises 58, use the KruskalWallis test.

Triathlon Times Jeff Parent is a statistics instructor who participates in triathlons. Listed below are times (in minutes and seconds) he recorded while riding a bicycle for five laps through each mile of a 3mile loop. Use a 0.05 significance level to test the claim that the samples are from populations with the same median. What do the data suggest? Mile 1 3:15 3:24 3:23 3:22 3:21 Mile 2 3:19 3:22 3:21 3:17 3:19 Mile 3 3:34 3:31 3:29 3:31 3:29

Clancy, Rowling, Tolstoy Readability Pages were randomly selected by the author from 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. The Flesch Reading Ease scores are listed on the next page. Use a 0.05 significance level to test the claim that the three samples are from populations with the same median. Do the books appear to have different reading levels of difficulty?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

Car Crash Measurements Use the following listed chest deceleration measurements (in g, where g is the force of gravity) from samples of small, midsize, and large cars. (These values are from Data Set 13 in Appendix B.) Use a 0.05 significance level to test the claim that the different size categories have the same median chest deceleration in the standard crash test. Do the data suggest that larger cars are safer? Small 44 39 37 54 39 44 42 Midsize 36 53 43 42 52 49 41 Large 32 45 41 38 37 38 33

Highway Fuel Consumption Listed below are highway fuel consumption amounts (mi/gal) for cars categorized by the sizes of small, midsize, and large (from Data Set 14 in Appendix B). Using a 0.05 significance level, test the claim that the three size categories have the same median highway fuel consumption. Does the size of a car appear to affect highway fuel consumption? Small 28 26 23 24 26 24 25 Midsize 28 31 26 30 28 29 31 Large 34 36 28 40 33 35 26

Appendix B Data Sets. In Exercises 912, use the KruskalWallis test with the data set from Appendix B.. IQ and Lead Exposure Data Set 5 in Appendix B lists performance IQ scores for random samples of subjects with blood lead levels categorized as low, medium, and high. Use a 0.01 significance level to test the claim that subjects in those categories have the same median performance IQ score. Does lead exposure appear to have an adverse effect?

Appendix B Data Sets. In Exercises 912, use the KruskalWallis test with the data set from Appendix B. Passive and Active Smoke Data Set 9 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?

Appendix B Data Sets. In Exercises 912, use the KruskalWallis test with the data set from Appendix B.Nicotine in Cigarettes Refer to Data Set 10 in Appendix B and use the amounts of nicotine (mg per cigarette) in the kingsize cigarettes, the 100 mm menthol cigarettes, and the 100mm nonmenthol cigarettes. The kingsize cigarettes are nonfiltered, nonmenthol, and nonlight. The 100mm menthol cigarettes are filtered and nonlight. The 100mm nonmenthol cigarettes are filtered and nonlight. Use a 0.05 significance level to test the claim that the three categories of cigarettes yield the same median amount of nicotine. Given that only the kingsize cigarettes are not filtered, do the filters appear to make a difference?

Appendix B Data Sets. In Exercises 912, use the KruskalWallis test with the data set from Appendix B.Car Crash Measurements Refer to Data Set 13 in Appendix B and use the pelvis deceleration measurements for small cars, midsize cars, and large cars. Use a 0.05 significance level to test the claim that the different size categories have the same median pelvis deceleration in the standard crash test. Do the data suggest that larger cars are safer?

Correcting the H Test Statistic for Ties In using the KruskalWallis test, there is a correction factor that should be applied whenever there are many ties: Divide H by 1 T N 3 N For each individual group of tied observations in the combined set of all sample data, calculate T = t 3 t , where t is the number of observations that are tied within the individual group. Find t for each group of tied values, then compute the value of T for each group, then add the T values to get T . The value of N is the total number of observations in all samples combined. Use this procedure to find the corrected value of H for Exercise 11. Does the corrected value of H differ substantially from the value found in Exercise 11?