Determine if the following statements are true or false, and explain your reasoning for statements you identify as false. If the null hypothesis that the means of four groups are all the same is rejected using ANOVA at a 5% significance level, then ...

(a) We can then conclude that all the means are different from one another.

(b) The standardized variability between groups is higher than the standardized variability within groups.

(c) The pairwise analysis will identify at least one pair of means that are significantly different.

(d) The appropriate α to be used in pairwise comparisons is 0.05 / 4 = 0.0125 since there are four groups.