Question

Suppose that a one-way ANOVA is being performed to compare the means of three populations and that the sample sizes are $10$, $12$, and $15$. Determine the degrees of freedom for the $F$-statistic.

Short answer

$F-$ statistic has role="math" localid="1652237094308" $(2,34)$ degrees of freedom.

Step-by-step solution

Given Information

Population density$k=3$.

The sample sizes are $10,12,15$.

Explanation

The number of observations total:

$n=10+12+15$

$=37$

The $F-$statistic has degrees of freedom of

$df=(k-1,n-k)$

$=(3-1,37-3)$

$=(2,34)$