Informal and subjective comparisons show that the “small” cars have a mean that is somewhat higher than the means of the “midsize,” “large,” and “SUV” vehicles. The boxplots overlap, so differences do not appear to be dramatic. But we need more formal methods that allow us to recognize any significant differences. We could use the methods of Section 9-2 “Two Means: Independent Samples” to compare means from samples collected from two different populations, but here we need to compare means from samples collected from four different populations. When we have samples from three or more populations, we can test for equality of the population means by using the method of analysis of variance, to be introduced in Section 12-1. In Section 12-1, we will use analysis of variance to test the claim that the four samples are from populations with the same mean. Chapter Problem 611 TABLE 12-1 Measurements of Head Injuries (HIC) in Car Crash Tests Small Midsize Large SUV 253 117 249 121 143 121 90 112 124 204 178 261 301 195 114 145 422 186 183 198 324 178 87 193 258 157 180 193 271 203 103 111 467 132 154 276 298 212 129 156 315 229 266 213 304 235 338 143 Small Midsize Large SUV n 12 12 12 12 x 290.0 180.8 172.6 176.8 s 96.7 40.6 77.9 55.1 Distribution Normal Normal Normal Normal Outliers Low outliers of 124 and 143 and high outlier of 467 0 0 0
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