“Sun safety” study. Excessive exposure to solar radiation is known to increase the risk of developing skin cancer, yet many people do not practice “sun safety.” A group of University of Arizona researchers examined the feasibility of educating preschool (four- to five-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 seven 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 you wrote in 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 of part

c, show that the slope of the line relating posttest score to pretest score differs for the two groups of children.

e. Assuming that interaction exists, give the reduced model for testing whether the mean posttest scores differ for the intervention and control groups.

f. With sun safety knowledge as the dependent variable, the test presented in part e was carried out and resulted in a p-value of .03. Interpret this result.

g. With sun safety comprehension as the dependent variable, the test presented in part e was carried out and resulted in a p-value of .033. Interpret this result.

h. With sun safety application as the dependent variable, the test presented in part e was carried out and resulted in a p-value of .322. Interpret this result.