Six Sigma Green Belt Certification Practice Exam

How are degrees of freedom determined in a 2 mean equal variance t test?

1. The Welch-Satterthwaite equation

2. The ratio between the squares of two samples' standard deviations

3. The total number of measurements minus two

4. The total number of measurements minus one

The correct answer is: The total number of measurements minus two

In a two-sample t-test with equal variances, the degrees of freedom are calculated by taking the total number of observations from both samples and subtracting two. This subtraction accounts for the estimation of two parameters (the means of the two groups). Typically, for this type of t-test, if you have two independent samples, each sample contributes to the total observations, and the formula for degrees of freedom is indeed the total number of observations across both samples minus the number of groups (which is two). Thus, if you combine the sizes of two samples (n1 and n2), the degrees of freedom would be calculated as (n1 + n2 - 2). The other options refer to different contexts or methods that do not apply to the two-mean equal variance t-test specifically. The Welch-Satterthwaite equation is utilized for unequal variances, which does not pertain here. The concept of subtracting one for degrees of freedom pertains to single-sample tests or estimating one parameter, while the ratio between the squares of two samples' standard deviations does not align with the calculation needed for this scenario.