Do agreeable individuals get paid less, on average, than those who are less agreeable on the job?
Question:
Data for First 10 Individuals in Study
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?
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.
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.
d. Fit the model, part c, to the sample data. Check the signs of the estimated β coefficients. How do they compare to the expected values, part c?
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.
f. Conduct the test, part e. Use α = .05. Is the researchers' theory supported?
Step by Step Answer:
Statistics For Business And Economics
ISBN: 9780321826237
12th Edition
Authors: James T. McClave, P. George Benson, Terry T Sincich