The Child Behavior Checklist (CBCL) is one of the most widely used tools to identify problem behaviors in children. Schools often use the CBCL to help identify specific target behaviors as a part of Response to Intervention (RTI) programs. A certain school wants to use CBCL pre- and post-ratings to test the effectiveness of a yearlong RTI program targeting aggressive behavior. The RTI interventionists would like to see at least a 1.75-point decrease in the CBCL ratings at the end of the yearlong treatment. (a) Define the parameter of interest. ?d is the mean difference in pre-ratings minus post-ratings for aggression on the CBCL ?d is the post-rating for aggression on the CBCL ?d is the mean rating for boys ratings on the CBCL ?d is the pre-rating for aggression on the CBCL (b) State the appropriate null and alternative hypotheses. H0: ?d ? 1.75 Ha: ?d ? 1.75
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Teacher perceptions of child behavior. Developmental Psychology (Mar. 2003) published a study on teacher perceptions of the behavior of elementary school children. Teachers rated the aggressive behavior of a sample of 11,160 New York City public school children by responding to the statement "This child threatens or bullies others in order to get his/her own way." Responses were measured on a scale ranging from 1 (never) to 5 (always). Summary statistics for the sample of 11,160 children were reported as $\bar{x}=2.15$ and $s=1.05 .$ Let $\mu$ represent the mean response for the population of all New York City public school children. Suppose you want to test $H_{0}: \mu=3$ against $H_{\mathrm{a}}: \mu \neq 3$ a. In the words of the problem, define a Type I error and a Type II error. b. Use the sample information to conduct the test at a significance level of $\alpha=.05$ c. Conduct the test from part $\mathbf{b}$ at a significance level of $\alpha=10$.
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