In Exercise? ?use analysis of variance for the indicated test. Head Injury Crash Test Data? Exercise 1-4 use chest deceleration data for three different size categories (small, midsize, large). The data are from a standard crash test and they are listed in Data Set 13 in Appendix B. If we use the head injury measurements (in HIC, which is a standard head injury criterion) with the same three size categories, we get the SPSS results shown here. Using a 0.05 significance level, test the claim that the three size categories have the same mean head injury measurement. Does the size of a car appear to affect head injuries? Exercise 1 In Exercise?, ?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.) Also shown (on the next page) are the SPSS results for analysis of variance. Assume that we plan to use a 0.05 significance level to test the claim that the different size categories have the same mean chest deceleration in the standard crash test. Chest Deceleration Measurements ?(g)? from a Standard Crash Test S m a l l M i d s i z e L a r g e 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 three size categories have the same mean? chest deceleration, why is the method referred to as analysis of ?variance?? Exercise 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 three means, why don’t we use three separate hypothesis tests for ??? = ??? , ???1 =? , and? ?2 = ???3 Exercise 3 Test Statistic? What is the value of the test statistic? What distribution is used with the test statistic? Exercise 4 P-?Value? If we use a 0.05 significance level in analysis of variance with the sample data given in Exercise, what is the ?P-?value? What should we conclude?
Solution 9BSC Step 1 The given problem explain about head injury crash test data. From the given problem we know that chest deceleration data for three different size categories is small, midsize and large.Then If we use the head injury measurements with the same three size categories. So,The three car categories of null hypothesis have same mean head injuries or = = . 1 2 3 Here, e know that the significance level of . Therefore level of significance =0.05 Then we have to calculate the P-value. From the given SPSS output labels P -value as significance value. From the SPSS table ,significance value is 0.852 Hence, the P -value =0.852 Now, We are comparing P-value and the significance level of . Hence the P-value > the significance level of =0.05 Therefore 0.852 > 0.05 So,we cannot reject the null hypothesis of (equal means) = 1= 2 3 Hence we can accept the null hypothesis of (equal means) = 1 . 2 3 From the given information we can accept the null hypothesis of equal means the claim that the three size categories have the same mean. Therefore we do not have sufficient evidence to say that car size has an effect on head injuries.Then the three categories of the means may be different but that difference may be simply due to random sampling error. Hence, we accept that small, medium and high sized cars have same number of head injuries.