In testing the difference between two population means using two independent samples, we use the pooled variance in estimating the standard error of the sampling distribution of the sample mean difference $\bar { x } _ { 1 } - \bar { x } _ { 2 }$ if the populations are normal with equal variances.

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The pooled variance is used when the assumption of equal population variances is met, allowing for a more accurate estimate of the standard error.

In Testing the Difference Between Two Population Means Using Two xˉ1−xˉ2\bar { x } _ { 1 } - \bar { x } _ { 2 }xˉ1​−xˉ2​

In Testing the Difference Between Two Population Means Using Two $\bar { x } _ { 1 } - \bar { x } _ { 2 }$