What is a type 1 error in manager evaluation?

In the context of statistical hypothesis testing, a type 1 error occurs when a true null hypothesis is incorrectly rejected. This means that the assessment leads to the conclusion that a manager is adding value when, in fact, they are not. Option B clearly defines this concept, stating that it involves rejecting the null hypothesis when it is correct.

Furthermore, option C complements this by emphasizing a practical implication of a type 1 error in manager evaluation: keeping managers who do not contribute positively to performance, or those with zero value-added. When type 1 errors occur, it not only misidentifies underperforming managers as valuable but also allows them to remain in positions where they can continue to underperform.

Therefore, identifying both rejecting the null hypothesis when it is correct and retaining underperforming managers aligns perfectly with the implications of type 1 errors in an investment management context. This comprehensive understanding of both choices illustrates the broader impact of type 1 errors in practical evaluation settings, making option D the most accurate representation of the concept.