Sleep apnea is a disorder characterized by pauses in breathing during sleep. Children who sufer from untreated sleep apnea often have behavior problems, induding hyperactivity, inattention, and aggression. A common treatment for pediatric sleep apnea is the surgical 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 nine children without sleep apnea, nine children with untreated sleep apnea, and nine 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. Group Sample Mean Sum of Squares No Sleep Apnea 0.27 0.1568 Untreated Sleep Apnea 0.54 0.2592 Treated Sleep Apnea 0.32 0.1800 The researchers perform an analysis of variance (ANOVA) at a = 0.01 to test the hypothesis that the treatment means are equal. The results are presented in the following ANOVA table. ANOVA Table Source of Variation Sum of Squares Degrees of Freedom Mean Square Between Treatments 0.3714 2 0.1857 7.49 WIRhin Treatments 0.5960 24 0.0248 Total 0.9674 26 The ANOVA yielded a significant F statistic, so the nul hypothesis is rejected. Since there are more than two groups, the researchers are interested in determining which groups are different. The Tukey's Honestly Significant Difference (HSD) test will be used to evaluate the pairs. First, use the table given below to determine the appropriate value of q at a = 0.01. The q value for this problem is The Studentized Range Statistic (q) df for Error Term 2