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
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 with 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?
Want to see the full answer?
Check out a sample textbook solutionChapter 12 Solutions
Statistics for Business and Economics (13th Edition)
- Urban Travel Times Population of cities and driving times are related, as shown in the accompanying table, which shows the 1960 population N, in thousands, for several cities, together with the average time T, in minutes, sent by residents driving to work. City Population N Driving time T Los Angeles 6489 16.8 Pittsburgh 1804 12.6 Washington 1808 14.3 Hutchinson 38 6.1 Nashville 347 10.8 Tallahassee 48 7.3 An analysis of these data, along with data from 17 other cities in the United States and Canada, led to a power model of average driving time as a function of population. a Construct a power model of driving time in minutes as a function of population measured in thousands b Is average driving time in Pittsburgh more or less than would be expected from its population? c If you wish to move to a smaller city to reduce your average driving time to work by 25, how much smaller should the city be?arrow_forwardWhat is meant by the sample space of an experiment?arrow_forward
- Functions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage LearningGlencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw HillBig Ideas Math A Bridge To Success Algebra 1: Stu...AlgebraISBN:9781680331141Author:HOUGHTON MIFFLIN HARCOURTPublisher:Houghton Mifflin Harcourt
- Holt Mcdougal Larson Pre-algebra: Student Edition...AlgebraISBN:9780547587776Author:HOLT MCDOUGALPublisher:HOLT MCDOUGALCollege Algebra (MindTap Course List)AlgebraISBN:9781305652231Author:R. David Gustafson, Jeff HughesPublisher:Cengage Learning