Final answer:
The incorrect leadership style listed based on the path-goal theory is Detective Leadership. The recognized styles are Supportive, Participative, Achievement-Oriented, and Directive Leadership. Each style is tailored to different circumstances to motivate and lead a team effectively.
Step-by-step explanation:
Achievement-Oriented:
The incorrect option in the list provided based on the path-goal theory is A. Detective Leadership. Path-goal theory identifies four styles of leadership: Supportive Leadership, Participative Leadership, Achievement-Oriented Leadership, and Directive Leadership. Each of these styles has unique characteristics that aim to motivate and influence team members in achieving set objectives.
Democratic leadership involves group consensus and participation, while laissez-faire leadership is a hands-off approach, entrusting team members to take the lead on their own. Authoritarian leadership focuses on clear directives and goal attainment. These styles are contrasted with Transactional and Transformational leadership styles. Transactional leadership is based on supervision and reward/punishment systems, whereas transformational leadership inspires teams beyond the status quo through charisma, inspiration, and intellectual stimulation.