Assertiveness and leadership. Management professors at Columbia University examined the relationship between assertiveness and leadership (Journal of Personality and Social Psychology, Feb. 2007). The sample comprised 388 people enrolled in a full-time master’s in business administration

(MBA) program. On the basis of answers to a questionnaire, the researchers measured two variables for each subject: assertiveness score (x) and leadership ability score (y). A quadratic regression model was fit to the data, with the following results:

Independent Variable b Estimate t-Value p-Value x .57 2.55 .01 x2 -.88 -3.97 6.01 Model R2

= .12

a. Conduct a test of overall model utility. Use a = .05.

b. The researchers hypothesized that leadership ability will increase at a decreasing rate with assertiveness.

Set up the null and alternative hypotheses to test this theory.

c. Use the reported results to conduct the test you set up in part

b. Give your conclusion (at a = .05) in the words of the problem.