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 x = 2.15 and s = 1.05. Let m represent the mean response for the population of all New York City public school children. Suppose you want to test H0: m = 3 against Ha: m  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 a = .05.

c. Conduct the test from part b at a significance level of a = .10.