12-1 One-Way ANOVA 623 Statistical Literacy and Critical Thinking In Exercises 1–4, use the following listed measured amounts of chest compression (mm) from car crash tests (from Data Set 35 “Car Data” in Appendix B). Also shown are the SPSS results from analysis of variance. Assume that we plan to use a 0.05 significance level to test the claim that the different car sizes have the same mean amount of chest compression. Small 29 31 35 33 26 32 21 26 25 34 26 34 Midsize 32 28 26 23 25 26 19 29 26 20 22 22 Large 27 32 39 27 31 26 34 30 34 26 24 31 SUV 24 31 31 25 30 39 22 33 34 35 29 26 12-1 Basic Skills and Concepts SPSS 1. ANOVA a. What characteristic of the data above indicates that we should use one-way analysis of variance? b. If the objective is to test the claim that the four car sizes have the same mean chest compression, why is the method referred to as analysis of variance? 2.Why Not Test Two at a Time? Refer to the sample data given in Exercise 1. If we want to test for equality of the four means, why don’t we use the methods of Section 9-2 “Two Means: Independent Samples” for the following six separate hypothesis tests? H0: m1 = m2 H0: m1 = m3 H0: m1 = m4 H0: m2 = m3 H0: m2 = m4 H0: m3 = m4 3. Test Statistic What is the value of the test statistic? What distribution is used with the test statistic? 4. P-Value If we use a 0.05 significance level in analysis of variance with the sample data given in Exercise 1, what is the P-value? What should we conclude? If the four populations have means that do not appear to be the same, does the analysis of variance test enable us to identify which populations have means that are significantly different? In Exercises 5–16, use analysis of variance for the indicated test. 5.Car Size and Left Femur in Crash Tests Example 1 used measured amounts of chest compression from car crash tests for four different vehicle size categories. If we use the same four categories of vehicle size with measured amounts of left leg femur force (kN), we get the following Minitab display. (The data are listed in Data Set 35 “Car Data” in Appendix B.) Using a 0.05 significance level, test the claim that the four vehicle size categories have the same mean force on the femur of the left leg. Does size of the car appear to have an effect on the force on the left femur in crash tests?
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