19. For the preceding prohlem you should find that there are significant differences among the three trealmcnts. One reason for the significance is that the sample variances are relatively small. To create the following data, we kept the same sample means that appeared in problem 8 but increased the 33 values within each sample. Treatment | II III 4 4 (J N = 12 2 0 3 G = 48 6 3 6 2X2 = 260 4 l 6 c. Use an ANOVA with a = .05 to determine whether there are any significant differencesamong the three treatment means. (Does your answer agree with your prediction in part b?) STEP1 STEP 2 Often it is easier to post- pone nding the critical region until after Step 3, where you compute the df values as part of the calculations for the F-ratio. State the hypotheses and select an alpha level. H0: \"'1 = pt2 = p.) [There is no treatment effect.} HI: At least one of the treatment means is different. We will use at : .05. Locate the critical region. We rst must determine degrees of freedom for MS between treatments and MS (the numerator and denominator of the Fralio), so we begin by analyz w'tlhin treatments mg the degrees of freedom. For these data, the total degrees of freedom are dim-.1: N] 218] = 17 Analyzing this total into two components, we obtain dfaltt..en=k1=31 =2 dt'tlhm : Edfhldc eat'ltlrcatment : 5 + 5 + 5 Z 15 The Fratio for these data has df = 2, 15. The distribution of all the possible F-ratios with df= 2, 15 is presented in Figure 12.8. Note that Fratios larger than 3.68 are extremely rare (p