The degrees of freedom for the appropriate critical value with a hypothesis test comparing two population means with population variances that are unknown but assumed to be equal are determined by n1 + n2 - 1.

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The degrees of freedom for the appropriate critical value in this scenario are determined by n1 + n2 - 2, where n1 and n2 are the sample sizes from each population. This formula accounts for the two samples contributing to the estimation of the common variance.

The Degrees of Freedom for the Appropriate Critical Value with a Hypothesis