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What is an appropriate number of degrees of freedom to use when conducting a two-sample $t$-test for the difference between two means?

$n – 1$, where $n$ is the number of different populations.

$n – 1$, where $n$ is the larger of the two sample sizes.

$n – 1$, where $n$ is the smaller of the two sample sizes.

$n – 1$, where $n$ is the total number of observations in both samples combined.

$n – 2$, where $n$ is the total number of observations in both samples combined.