The HR department is trying to fill a vacant position for a job with a small tal

Question

The HR department is trying to fill a vacant position for a job with a small talent pool. Valid applications arrive every week or so, and the applicants all seem to bring different levels of expertise. For each applicant, the HR manager gathers information by trying to verify various claims on the candidate's résumé, but some doubt about “fit” always lingers when a decision to hire or not is to be made.

Suppose that hiring an employee who is a bad fit for the company results in an error cost of $300, but failing to hire a good employee results in an error cost of $300 to the company. Although it is impossible to tell in advance whether an employee is a good fit, assume that the probability that an applicant is a “good fit” is 0.55, while the probability that an applicant is a “bad fit” is 1?0.55=0.451?0.55=0.45. Hiring an applicant who is a good fit, as well as not hiring an applicant who is a bad fit, results in no error cost to the company.

For each decision in the following table, calculate and enter the expected error cost of that decision.

Reality

Suppose an otherwise qualified applicant applies for a job.

In order to minimize expected error costs, the HR department should the applicant.

Decision

Reality

Expected Error Cost Good Fit Bad Fit p=0.55 p=0.45 Hire Cost: 0 Cost: $300 Do Not Hire Cost: $300 Cost: 0

Explanation / Answer

a) Expected cost of hiring would be:

(Probability that it's a good fit * cost of hiring if it's a good fit) + (probability that it's a bad fit* cost of hiring if it's a bad fit)

= (0.55*0) + (0.45*300)

= 0 + 135

=135

Therefore expected cost of error when a person is hired is $135

Similarly the expected cost of error when a person is not hired =

(Probability that it's a good fit * cost of hiring if it's a good fit) + (probability that it's a bad fit* cost of hiring if it's a bad fit)

= (0.55*300) + (0.45*0)

= 165 + 0

= 165

Therefore we see that the expected cost of not hiring is greater than hiring. And this is because the probability that a person will be a good fit is greater than the probability that the person will be a bad fit. Therefore the cost of letting go someone is greater.

b) If a qualified applicant applies for the job, in order to minimise exoected error cost, the company should hire him. Because by not hiring, the expected error cost is 165 and by hiring the exected error cost reduces to 135.

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