Refer to the Development Psychology (Mar. 2003) study of the behavior of elementary school children, presented in Exercise. The researchers used a quadratic equation to model the level (y) of aggressive fantasies experienced by a child as a function of the child’s age (x). [Level y was measured as an average of responses to six questions (e.g., “Do you sometimes have daydreams about hitting or hurting someone you don’t like?”). Responses were measured on a scale ranging from 1 (never) to 5 (always).]

a. Write the equation of the hypothesized model for E (y).

b. Research psychologists theorized that a child’s aggressive fantasies increase with age, but at a slower rate of acceleration in older children. Sketch the curve hypothesized by the researchers.

c. Set up H0 and Ha for testing the researchers’ theory.

d. The model was fitted to data collected for over 11,000 elementary school children, with the following results: y = 1.926 + .097x – .003x2, standard error of β2 = .001. Compute the test statistic for the test you set up in part c.

e. Use the result you found in part d to make the appropriate conclusion. Take α = .05.