When the population variances are unequal,we estimate each population variance with its sample variance.Hence,the unequal-variances test statistic of is approximately Student t-distributed with n₁ + n₂ - 2 degrees of freedom.

Question

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When the population variances are unequal, we use a modified version of the t-test called Welch's t-test which takes into account the unequal variances by adjusting the degrees of freedom. The degrees of freedom of the test statistic is given by the Welch-Satterthwaite equation:

df = (s1^2/n1 + s2^2/n2)^2 / (s1^4/(n1^2(n1-1)) + s2^4/(n2^2(n2-1)))

where s1^2 and s2^2 are the sample variances of the two populations, and n1 and n2 are the sample sizes. This equation accounts for the fact that the two populations may have different variances. Therefore, the statement is true.

When the Population Variances Are Unequal,we Estimate Each Population Variance