what inference CLT enable us to make

Mean vs individual (point) values.

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I would like you to discuss what inference CLT enable us to make, i.e., about mean vs individual (point) values.

CLT, for example, could help with determination of whether there is a concern in a company if both genders are promoted equally. As a case study, you can discuss the following experiment on male bank supervisors attending a management institute. The supervisors were asked to make decisions on whether to promote a hypothetical applicant based on a personnel file. Applicants were chosen randomly half males and half female applicants and randomly assigned to the managers. In this case, we might be interested in testing whether discrimination was a factor by formally looking at average number of males vs females promoted. In broad strokes, explain how you would test this hypothesis by using concepts we discussed so far.