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 United States. 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 (x ) and a dummy variable for gender (x = 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 WAGEGAP file. The first 10 observations are listed in the accompanying table.

a. Suppose the researchers theorize that for either gender, income will decrease at a decreasing rate as agreeableness score increases. Consequently, they want to fit a second-order model. Consider the model,

E(y)=0+1x1+2(x1)^2+3x2. If the researchers' belief is true, what is the expected sign of in the model?

b. Draw a sketch of the model, part a, showing how gender impacts the income-agreeableness score relationship.

c. Write a complete second-order model for E(y) as a function of x and x.

d. Draw a sketch of the model, part c, showing how gender impacts the income-agreeableness score relationship.

e. What null hypothesis would you test in order to compare the two models, parts a and c?

f. Fit the models to the sample data saved in the WAGEGAP file and carry out the test, part e. What do you conclude? (Test using = .10).

Gender, Agree, G_A, Income

1 3 3 44770 1 2.9 2.9 51480 1 3.3 3.3 39600 0 3.3 0 24370 0 3.6 0 15460 1 3.8 3.8 43730 1 3.2 3.2 48330 0 2.5 0 25970 0 3.5 0 17120 0 3.2 0 20140 0 2.4 0 19190 1 3.4 3.4 53330 0 3.5 0 28950 0 3.7 0 20020 0 3.7 0 12240 0 3.2 0 24480 1 3.3 3.3 69080 0 3.3 0 22020 0 3.3 0 26160 1 2.9 2.9 49550 0 2.7 0 48000 0 2.6 0 37670 0 3.1 0 18950 1 3.1 3.1 55920 0 3.3 0 16310 1 4.3 4.3 30590 1 3.1 3.1 47450 1 3.3 3.3 58090 0 3.5 0 14620 1 3 3 62760 0 3.4 0 17600 1 2.9 2.9 53820 0 3.9 0 15280 0 3.3 0 15740 1 4.4 4.4 29000 0 2.9 0 26850 1 2.5 2.5 52810 0 3.3 0 46000 0 3.1 0 25680 1 3.3 3.3 43590 1 3.6 3.6 54050 0 3.7 0 16700 1 3.4 3.4 41560 1 3.1 3.1 51770 0 3.5 0 25140 0 3.8 0 32410 0 2.5 0 14390 1 3.5 3.5 36480 0 3.7 0 21640 0 3.6 0 19390 0 2.2 0 25810 1 3.1 3.1 66670 1 2.9 2.9 45330 0 3.7 0 11150 1 3.6 3.6 40200 0 3.4 0 26230 0 3.4 0 32300 1 3.3 3.3 56140 0 3.2 0 20800 1 2.7 2.7 49360 0 3 0 22160 0 3.2 0 19880 1 3.3 3.3 61840 0 2.8 0 11030 1 3.2 3.2 52380 1 3.3 3.3 44690 1 2.9 2.9 51410 1 4.3 4.3 34340 1 3.3 3.3 49650 1 3.1 3.1 42910 1 3.4 3.4 44620 1 2.7 2.7 61980 0 3.4 0 21850 0 2.6 0 28260 1 3.3 3.3 54790 1 3.8 3.8 35990 1 3.2 3.2 53400 0 4.3 0 13320 1 3.4 3.4 51840 1 3.2 3.2 44440 0 3.5 0 28120 1 3.2 3.2 54530 0 3.4 0 19400 1 3.3 3.3 45970 0 3.4 0 23290 1 2.7 2.7 57690 0 3.5 0 32700 0 3 0 30130 1 3.4 3.4 44080 1 3.1 3.1 57830 0 3.5 0 15630 0 3.4 0 34980 1 3 3 61390 0 3.7 0 21720 1 3 3 55750 0 3.5 0 15840 1 3.3 3.3 36040 1 3.2 3.2 27020 1 3.5 3.5 47510 0 3.7 0 22220