Given the following information,calculate the degrees of freedom that should be used in the pooled-variance t test. s₁² = 4 s₂² = 6
n₁ = 16 n₂ = 25

Question

Given the following information,calculate the degrees of freedom that should be used in the pooled-variance t test. s₁² = 4 s₂² = 6 n₁ = 16 n₂ = 25 A)df = 41 B)df = 39 C)df = 16 D)df = 25

Quizplus · Accepted Answer

The formula for degrees of freedom in a pooled-variance t test is: df = (n1-1) + (n2-1) where n1 and n2 are the sample sizes of the two groups being compared. In this case, we have two groups: ₁ and ₂. Their sample sizes are n₁ = 16 and n₂ = 25, respectively. Thus, the degrees of freedom are: df = (16-1) + (25-1) = 40 However, since we are conducting a pooled-variance t test, we need to use a pooled estimate of the variance, which involves pooling the sample variances from the two groups. The formula for the pooled estimate of the variance is: s^2p = ((n1-1)s1^2 + (n2-1)s2^2) / (n1 + n2 - 2) where s1^2 and s2^2 are the sample variances of the two groups. Plugging in the given values, we get: s^2p = ((16-1)4 + (25-1)6) / (16+25-2) = 4.97 Now we can calculate the degrees of freedom using the pooled variance: df = (n1-1) + (n2-1) = 16+25-2 = 39 Therefore, the correct choice is B.

Given the Following Information,calculate the Degrees of Freedom That Should