Your Textbook States That When You Test for Differences in Means

question 5

Essay

Your textbook states that when you test for differences in means and you assume that
the two population variances are equal, then an estimator of the population variance is
the following "pooled" estimator: $$s _ { \text {pooled } } ^ { 2 } = \frac { 1 } { n _ { m } + n _ { w } - 2 } \left[ \sum _ { i = 1 } ^ { n _ { m } } \left( Y _ { i } - \bar { Y } _ { m } \right) ^ { 2 } + \sum _ { i = 1 } ^ { n _ { w } } \left( Y _ { i } - \bar { Y } _ { w } \right) ^ { 2 } \right]$$ 2
Explain why this pooled estimator can be looked at as the weighted average of the two
variances.

---

Definitions:

Duty

A moral or legal obligation; a responsibility that one is required to perform in a social, legal, or professional context.

Performance

The execution of duties or actions stipulated by a contract.

Third Party

An entity involved in a transaction or legal situation who is neither the first (often the buyer or claimant) nor the second (often the seller or defendant) principal party.

Express Condition

A specific and explicitly stated requirement in a contract that must be met for contractual obligations to be fulfilled.