Sieep apnea is a disorder characterized by pauses in breathing during sieep. Children who suffer from untreated sleep apnea often have behavior problems, including hyperactivity, inattention, and aggression. A common treatment for pediatric sleep apnea is the surpical removal of enlarged tonsils and adenoids that are obstructing the airways. Suppose researchers at a sleep clinic are interested in the effect of surgical treatment for pediatric sleep apnea on hyperactive behavior. They study 21 children without sleep apnea, 21 children with untreated sleep apnea, and 21 children who have been surgically treated for sleep apnea. Hyperactivity is measured using the Conners Rating Scales. The sample means and sums of squares of the scores for each of the three groups are presented in the following table. The researchers perform an analysis of variance (ANOVA) at o =0.01 to test the hypothesis that the treatment means are equal. The results are presented in the following ANova table. The ANOVA yielded a significant r stativic, so the nuil hypothesis is rojected. Since there are more than two groups, the researchers are interested in determining which groups are diferent, The Tukers Honesty Signifant Oifference (HSO) test will be used to evaluate the pairs, First, use the table given below to determine the opproprite value of q at a=0.01. The q value for this problem is The Studentized Range Statistic (q) The top value is a=.05; the bottom (bola) value is a =.01. The number of treatments is listed across, The df for the error term is in the left column, where the "error term" is another name for the within-treatments variance. Now, use the 4 value to calculste Tukey's HSD (round to two decimal places), Tuker's HSD is Thus, the mean difference between any two samples must be at least to be significant. The revearchers conclude that the population means for children without sleep aphea and children with untreated sleep apnea differ They cinclud that the population means for children whout sleep apnea and chidren with treated sleep apnea differ. They concude that the population means for children with untreated sleep apnes and children with treated sleep apnea differ