Chapter 12.8, Problem 12.92ACI

Agreeableness, gender, and wages. Do agreeable individuals get paid less, on average, than those who are less agreeable on the job? And is this gap greater for males than for females? These questions were addressed in the Journal of Personality and Social Psychology (February 2012). Several variables were measured for each in a sample of individuals enrolled in the National Survey of Midlife Development in the U.S. Three of these variables are: (1) level of agreeableness score (where higher scores indicate a greater level of agreeableness). (2) gender (male or female). and (3) annual income (dollars). The researchers modeled mean income. E(y) , as a function of both agreeableness score (x₁) and a dummy variable for gender (x₂ = 1 if male. 0 if female). Data for a sample of 100 individuals (simulated, based on information provided in the study) are saved in the file. The first 10 observations are listed in the accompanying table.

Data for First 10 Individuals in Study

1. a. Consider the model, E(y)=β₀+β₁x₁+ β₂x₂ The researchers theorized that for either gender, income would decrease as agreeableness score increases. If this theory is true, what is the expected sign of β₁ in the model?
2. b. The researchers also theorized that the rate of decrease of income with agreeableness score would be steeper for males than for females (i.e., the income gap between males and females would be greater the less agreeable the individuals are). Can this theory be tested using the model, part a? Explain.
3. c. Consider the interaction model, E(y)=β₀+β₁x₁+ β₂x₂+β₃x₁x₂. If the theory, part b, is true, give the expected sign of β₁. The expected sign of β₃.
4. d. Fit the model, part c, to the sample data. Check the signs of the estimated β coefficients. How do they compare with the expected values, part c?
5. e. Refer to the interaction model, part c. Give the null and alternative hypotheses for testing whether the rate of decrease of income with agreeableness score is steeper for males than for females.
6. f. Conduct the test, part e. Use α = .05. Is the researchers’ theory supported?