Calculate the degrees of freedom associated with a small-sample test of hypothesis for $\left( \mu _ { 1 } - \mu \right.$ assuming $\sigma _ { 1 } 2 \neq \sigma _ { 2 } 2$ and $n _ { 1 } = 13 , n _ { 2 } = 12 , s _ { 1 } = 1.3 , s _ { 2 } = 1.5$.
A) 23
B) 11
C) 25
D) 12

Question

Quizplus · Accepted Answer

The degrees of freedom for a small-sample test of hypothesis for $\left( \mu _ { 1 } - \mu \right.$ assuming $\sigma _ { 1 } 2 \neq \sigma _ { 2 } 2$ is given by:$$df = \frac{\left( \frac{s_1^2}{n_1} + \frac{s_2^2}{n_2} \right)^2}{\frac{s_1^4}{n_1^2(n_1-1)} + \frac{s_2^4}{n_2^2(n_2-1)}}$$Plugging in the given values, we get:$$df = \frac{\left( \frac{1.3^2}{13} + \frac{1.5^2}{12} \right)^2}{\frac{1.3^4}{13^2(12)} + \frac{1.5^4}{12^2(11)}} = 23$$

Calculate the Degrees of Freedom Associated with a Small-Sample Test (μ1−μ\left( \mu _ { 1 } - \mu \right.(μ1​−μ

Calculate the Degrees of Freedom Associated with a Small-Sample Test $\left( \mu _ { 1 } - \mu \right.$