614 CHAPTER 12 Analysis of Variance Because the calculations required for one-way analysis of variance are messy, we recommend using technology with this study strategy: 1. Understand that a small P-value (such as 0.05 or less) leads to rejection of the null hypothesis of equal means. (“If the P is low, the null must go.”) With a large P-value (such as greater than 0.05), fail to reject the null hypothesis of equal means. 2. Develop an understanding of the underlying rationale by studying the examples in this section. Use the head injury criterion (HIC) measurements listed in Table 12-1 and use a significance level of a = 0.5 to test the claim that the four samples come from populations with means that are all equal. CP EXAMPLE 1 Size of Vehicle and Head Injury Measurements Statdisk Minitab Excel SOLUTION REQUIREMENT CHECK (1) Based on the four samples listed in Table 12-1, the four populations appear to have distributions that are approximately normal, as indicated by normal quantile plots that are not shown here. (2) The four samples in Table 12-1 have standard deviations that differ by considerable amounts, but those differences are not substantial, so we can consider the four population variances to be about the same. (3) On the basis of the study design, we can treat the samples as simple random samples. (4) The samples are independent of each other; the HIC measurements are not matched in any way. (5) The four samples are from populations categorized according to the single factor of vehicle size (small, midsize, large, SUV). The requirements are satisfied. The null hypothesis and the alternative hypothesis are as follows: H0: m1 = m2 = m3 = m4 H1: At least one of the means is different from the others The significance level is a = 0.05. Step 1: Use technology to obtain ANOVA results, such as one of those shown in the accompanying displays.
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