10. An interesting question to developmental psychologists is whether children's generosity (or altru- ism) steadily increases with age. The following study is modeled after an experiment reported in Zarbatany, L., Hartmann, D. P., & Gelfand, D. M. (1935). Why does children's generosity increase with age: Susceptibility to experimenter inuence or altruism? Child Development, 56, 746756. First-, third, and fth-grade children were allowed to select from among four alternatives what they would do if a xed amount of money were donated to their school. A separate group of children of similar ages was used to create a generosity scale, using a paired-comparisons format. (It is interesting that in the actual study, the experimenters also used a scale with rational weights and obtained different results for the two weighting schemes.) Consider the folloadng data, where each score represents the rating of the child's chosen alternative on the generosity scale: Firs-t Graders Third Graders Fifth Graders IHMO'JJMMMIDMDrS 2 l 3 0 0 2 U 1 D 1 1 2 1 2 0 MFMDWMFIWDNPUJMW m a. Suppose that the experimenter plans to test both the linear and the quadratic trends. Perform these tests for these data. b. Plot the predicted means based on a linear trend model, that is, a model without a quadratic component. How do these means compare to the actual sample means? 272 CHAPTER 6 c. Plot the predicted means based on a model that includes both linear and quadratic trend compo- nents. How do these means compare to the actual sample means? Why? d. The experimenter is interested in knowing how much ratings tend to change for every additional year of school. Form a 95% confidence interval for the population slope. (Hint: Be careful how you code your coefficients.) e. Calculate the three measures of association strength presented in this chapter. How would you interpret your findings for these data