525 Where You’re Going In this chapter, you will learn how to test a hypothesis that compares three or more populations. For instance, in addition to the crash tests for large pickups and midsize SUVs, a third group of vehicles was also tested. The table shows the results for all three types of vehicles. Vehicle Number Mean chest injury Standard deviation Large Pickups n1 = 12 x1 = 23.0 s1 = 2.09 Midsize SUVs n2 = 19 x2 = 22.4 s2 = 4.26 Large Cars n3 = 10 x3 = 27.2 s3 = 6.65 From these three samples, is there evidence of a difference in chest injury potential among large pickups, midsize SUVs, and large cars in a frontal offset crash at 40 miles per hour? You can answer this question by testing the hypothesis that the three means are equal. For the means of chest injury, the P@value for the hypothesis that m1 = m2 = m3 is about 0.0283. At a = 0.01, you fail to reject the null hypothesis. So, there is not enough evidence at the 1% level of significance to conclude that at least one of the means is different from the others. Where You’ve Been In Chapter 8, you learned how to test a hypothesis that compares two populations by basing your decisions on sample statistics and their distributions. For instance, the Insurance Institute for Highway Safety buys new vehicles each year and crashes them into a barrier at 40 miles per hour to compare how different vehicles protect drivers in a frontal offset crash. In this test, 40% of the total width of the vehicle strikes the barrier on the driver side. The forces and impacts that occur during a crash test are measured by equipping dummies with special instruments and placing them in the car.The crash test results include data on head, chest, and leg injuries. For a low crash test number, the injury potential is low. If the crash test number is high, then the injury potential is high. Using the techniques of Chapter 8, you can determine whether the mean chest injury potential is the same for midsize SUVs and large pickups. (Assume the populations are normally distributed and the population variances are equal.) The table shows the sample statistics. (Adapted from Insurance Institute for Highway Safety) Vehicle Number Mean chest injury Standard deviation Large Pickups n1 = 12 x1 = 23.0 s1 = 2.09 Midsize SUVs n2 = 19 x2 = 22.4 s2 = 4.26 For the means of chest injury, the P@value for the hypothesis that m1 = m2 is about 0.6655. At a = 0.01, you fail to reject the null hypothesis. So, you do not have enough evidence to conclude that there is a significant difference in the means of the chest injury potential in a frontal offset crash at 40 miles per hour for large pickups and midsize SUVs.
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