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 statement is true based on statistical theory. The equal variance test assumes that the population variances are equal, while the unequal variance test relaxes this assumption and allows for the possibility that the population variances are not equal. The unequal variance test then produces a t-statistic with fewer degrees of freedom, making it more conservative (i.e. wider confidence intervals, lower t-statistics) than the equal variance test. Therefore, the number of degrees of freedom associated with the equal-variances test statistic and confidence interval estimator will always be greater than or equal to the number of degrees of freedom associated with the unequal-variances test statistic and confidence interval estimator for a given sample size.

Statisticians Have Shown That for Given Sample Sizes and