Narrowing tolerance band reducing the Type I error while increasing Type II error.
Please correct me if i am wrong?
Can you please tell what is the rational?
I think its correct.
narrowing tolerance band means more managers would fail the evaluation and will be let go, fired or discontinued.
this reduces the probability of type 1 error which is keep managers that add no positive value.
What would be the impact on Type II error - firing a value added manager
It will increase the probability of firing a skillful manager (type II error)
If you’re lessening the restrictions on keeping managers (I.e. move from a 1% tolerance level to a 5% tolerance level) than you will have a better chance of keeping losers (type I) but less of a chance of firing winners (type II).
If you increase the restrictions (move from 5% significance to a 1% significance) you lower your chances of keeping bums but increase your chance of firing studs.
Exactly, this is the easiest way to think about it. More restrictions means less chance of keeping bad managers but increased chance of firing good managers because you raised the bar.
Just to clarify, when we say value-added, we mean value added above the benchmark/target given to the manager, right?
What I mean is, assume that the manager is given a target/benchmark return of 3%.
Would the null hypothesis refer to someone who is earning 3%/less, or only to someone earning 0% or less? Would a manager be classified into the null/alternative hypothesis if he earns a return of 2%