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 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 =? , an? ?2 = ???3 Exercise 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??
Solution 2BSC Step 1 Here the reason for not using three different hypothesis is to minimise the chance of committing type 1 error. Then if we conduct three hypothesis tests we may accept a null hypothesis which in fact was to be rejected. Here we assume that we plan to use a 0.05 level of significance level . Then,from the three hypothesis the overall significance level will be very low and thus we conclude that there is difference of mean between two populations which is actually a matter of chance. so, we can avoid such mistakes if we confine the number of hypothesis to one instead of three.