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Agreeableness, gender, and wages. Do agreeable individuals
Chapter 12, Problem 92E(choose chapter or problem)
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 (Feb. 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 (\(x_1\)) and a dummy variable for gender (\(x_2\) = 1 if male, 0 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.
a. Consider the model, \(E(y)=\beta_0+\beta_1 x_1+\beta_2 x_2\). 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 \(\beta_1\) 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, \(E(y)=\beta_0+\beta_1 x_1+\beta_2 x_2\) \(+\beta_3 x_1 x_2\). If the theory, part b, is true, give the expected sign of \(\beta_1\). The expected sign of \(\beta_3\).
d. Fit the model, part c, to the sample data. Check the signs of the estimated \(\beta\) 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 \(\alpha=.05\). Is the researchers' theory supported?
Questions & Answers
QUESTION:
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 (Feb. 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 (\(x_1\)) and a dummy variable for gender (\(x_2\) = 1 if male, 0 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.
a. Consider the model, \(E(y)=\beta_0+\beta_1 x_1+\beta_2 x_2\). 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 \(\beta_1\) 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, \(E(y)=\beta_0+\beta_1 x_1+\beta_2 x_2\) \(+\beta_3 x_1 x_2\). If the theory, part b, is true, give the expected sign of \(\beta_1\). The expected sign of \(\beta_3\).
d. Fit the model, part c, to the sample data. Check the signs of the estimated \(\beta\) 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 \(\alpha=.05\). Is the researchers' theory supported?
ANSWER:Step 1 of 8
The hypothesis testing is a statistical analytical tool for the determination of outcome which one wants to prove. The theory is divided into two expected inferences, one is accepting the result and another is not accepting the result, thus, accordingly giving null and alternative hypotheses, which are tested using various tests.