What type of examination may the board design for different endorsements?

The correct answer is the written jurisprudence examination. This type of examination focuses on assessing an individual's understanding of legal principles, regulations, and ethical considerations relevant to the private security industry. A written jurisprudence examination is crucial because it ensures that qualified managers are knowledgeable about the laws and standards they must adhere to in their roles, thereby promoting compliance and accountability within the industry.

The other types of examinations, while potentially useful in different contexts, do not specifically pertain to the qualifications required for endorsements in this field. A psychological examination would assess mental fitness, a competency examination would evaluate practical skills but might not test legal knowledge explicitly, and a physical fitness examination is relevant for certain law enforcement roles but not specifically for legal compliance and understanding in the context of private security. Thus, the written jurisprudence examination stands out as the most pertinent for evaluating qualifications related to different endorsements in the security sector.