Statisticians have shown that for given sample sizes and , the number of degrees of freedom associated with the equal-variances test statistic and confidence interval estimator of is always greater than or equal to number of degrees of freedom associated with the unequal-variances test statistic and confidence interval estimator.

Question

Statisticians have shown that for given sample sizes  and  , the number of degrees of freedom associated with the equal-variances test statistic and confidence interval estimator of  is always greater than or equal to number of degrees of freedom associated with the unequal-variances test statistic and confidence interval estimator.

Quizplus · Accepted Answer

This is a well-established fact in statistics. When sample sizes are equal, the variance estimates for the two samples are pooled, resulting in a larger degrees of freedom for the equal-variances test statistic and confidence interval estimator compared to the unequal-variances test statistic and confidence interval estimator.

Statisticians Have Shown That for Given Sample Sizes and