F I L E Numerous studies have shown that watching too much television hurts school grades. Others have argued that television is not necessarily a bad thing for children (Mail Online, July 18, 2009). Like books and stories, television not only entertains, it also exposes a child to new information about the world. While watching too much TV is harmful, a little bit may actually help. Researcher Matt Castle gathers information on the grade point average (GPA) o f 28 middle school children and the number o f hours o f TV they watched per week. A portion o f the data is shown in the accompanying table; the complete data, labeled Television, is found on the text website.

GPA Hours TV 3.24 19 3.10 21 3.31 4

a. Estimate a quadratic regression m odel where the GPA of m iddle school children is regressed on hours and hourssquared.

b. Is the quadratic term in this m odel justified? Explain.

c. Find the optim al num ber o f weekly hours o f TV for m iddle school children.