The 95% confidence interval for m derived from a sample of n observations from a normal population gets smaller as the sample size increases because the standard error of the mean s / √n decreases. Adding more groups to an ANOVA also increases n.
(a) Does adding more groups improve the accuracy of the estimated mean of the first group?
(b) Tukey and Bonferroni intervals for the difference between means get longer if more groups are added, even though n increases. Why?