Question

Given \({v_1}\,and\,{v_2}\) find the following probabilities:

1. \({v_1} = 2,\,{v_2} = 30,\,p\left( {F \ge 5.39} \right)\)

Short answer

1. The probability is 0.01.

Step-by-step solution

Given Information

Degrees of freedom are

\(\begin{aligned}{v_1} = {n_1} - 1 = 2\\{v_2} = {n_2} - 1 = 30\end{aligned}\)

F-Distribution

F-distribution used for equality of two population variances. We want to find whether the two independent estimates of the population variances are homogeneous or not.

Compute probability

\(\begin{aligned}{l}p\left( {F \ge 5.39} \right)\\ &= 1 - p\left( {F < 5.39} \right)\\ &= 1 - 0.990\\ &= 0.01\end{aligned}\)

Therefore, the probability is 0.01.