Assertiveness and leadership. Management professors at Columbia University examined the relationship between assertiveness and leadership (Journal of Personality and Social Psychology, February 2007). The sample was comprised of 388 people enrolled in a full-time MBA program. Based on 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:

(a) Conduct a test of overall model utility. Use α = .05.

(b) The researchers hypothesized that leadership ability will increase at a decreasing rate with assertiveness. Set up the null and alternative hypothesis to test this theory.

(c) Use the reported results to conduct the test, part b. Give your conclusion (at α = .05) in the words of the problem.