Consider hypothetical data based on a study concerning the effects of rapid cultural change on blood pressure levels for native citizens of an island in Micronesia. Blood pressures were taken on a random sample of 30 males over age 40 from a certain province. These persons, who commuted to work in the nearby westernized capital city, were also given a sociological questionnaire from which their social rankings in both their traditional and their modern (i.e., westernized) cultures were determined. The results are summarized in the following table.

a. Discuss the table of sample means for this data set.
b. Give an appropriate regression model for this data set, treating the two factors as nominal avariables.
c. Using the regression ANOVA tables that follow (where Appertains to factor A and
Z pertains to factor B), carry out two different main-effect tests for each factor, and also rest for interaction. Compare the results of the two main-effect tests for each factor.

d. How might you modify the regression model given in part (b) so that any trends in blood pressure levels could be quantified in terms of increasing social rankings for the two factors? (This requires assigning numerical values to the categories of each factor.) What difficulty do you encounter in defining such a model?

Traditional Rank (Factor B) Modern Rank (Factor A) HI MED LO HI MED LO 130, 140. 135 145, 140, 150 180, 160, 145 150, 145 150, 160, 155 155, 140. 135 175, 160, 170,165, 155 165, 155, 165, 170, 160 125, 130, 110 Source d.f. MS Xi 469.17985 08.52217 187.97673 7.54570 ,925.29395 9.70621 633.17613 2.67593 x,z1x," ,, z," z,.xz,.xz,.x,zi Residual 21 75.83333 Source d.f. MS zi 212, x,iz, 22 278.59213 22.71129 391.77041 480.15062 3.925.29395 9.70621 633.17613 2.67593 Residual 21 75.83333