When testing hypotheses about two population means where σ1 and σ2 are unknown and no assumption...

When testing hypotheses about two population means where σ1 and σ2 are unknown and no assumption is made about the equality of σ1 and σ2, we use Student t distribution with df = smaller of n1 – 1 and n2 – 1. Normal distribution. Student t distribution with df = n1 + n2 – 2. Student t distribution with df = bigger of n1 – 1 and n2 – 1.

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Expert Solution

1. If n₁ be the sample size of the first population and n₂ be for the second population.

If σ₁ and σ₂ are unknown but are considered to be equal, then the degree of freedom in this case will be:

Degree of Freedom = n₁ + n₂ – 2

In this case, it is considered that σ ₁² = σ ₂² = σ²

2. If σ₁ and σ₂ are unknown and no assumption is made about the equality of σ1 and σ2, then the Degree of Freedom can be calculated by two method:

3. Student t distribution with df = bigger of n₁ – 1 and n₂ – 1... This condition is generaaly not applied in T test.

End of the Solution...

orchestra answered 1 year ago

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