Numerous "sun safety"' products exist on the market to prevent excessive exposure to solar radiation. But many people do not practice "sun safety" or recognize the effectiveness of these products. A group of University of Arizona researchers examined the feasibility of educating preschool (4- to 5-year-old) children about sun safety (American Journal of Public Health, July 1995). A sample of 122 preschool children was divided into two groups, the control group and the intervention group. Children in the intervention group received a Be Sun Safe curriculum in preschool, while the control group did not. All children were tested for their knowledge, comprehension, and application of sun safety at two points in time: prior to the sun safety curriculum (pretest, x1) and 7 weeks following the curriculum (posttest, y).
a. Write a first-order model for mean posttest score, E(y), as a function of pretest score, x1 and group. Assume that no interaction exists between pretest score and group.
b. For the model, part a, show that the slope of the line relating posttest score to pretest score is the same for both groups of children.
c. Repeat part a but assume that pretest score and group interact.
d. For the model, part c, show that the slope of the line relating posttest score to pretest score differs for the two groups of children.