Researchers wanted to determine if the psychological profile of healthy children was different than for children suffering from recurrent abdominal pain (RAP) or recurring headaches. A total of 210 children and adolescents were studied and their psychological profiles were graded according to the Child Behavior Checklist 4-18 (CBCL). Children were stratified in two age groups: 4 to 11 years and 12 to 18 years. The results of the study are summarized in the following table:

(a) Compute the sample standard deviations for each group.
(b) What sampling method was used for each treatment group? Why?
(c) Use a two sample t-test for independent samples to determine if there is a significant difference in mean CBCL scores between the control group and the RAP group (assume that both samples are simple random samples).
(d) Is it necessary to check the normality assumption to answer part (c)? Explain.
(e) Use the one-way ANOVA procedure with a = 0.05 to determine if the mean CBCL scores are different for the three treatment groups.
(f) Based on your results from parts (c) and (e), can you determine if there is a significant difference between the mean scores of the RAP group and the headache group? Explain.