F From Means and Variances

A school compares three teaching methods. Each method is used with its own separate group of $6$ students, so there are $k = 3$ groups and $N = 18$ students in total.

Method	Group mean score $\bar{x}_i$	Group sample variance $s_i^2$
A	$20$	$30$
B	$24$	$24$
C	$28$	$27$

Each $s_i^2$ is a sample variance computed with that group's own $n_i - 1$ divisor.

A one-way ANOVA is run, with

$F = \frac{MS_{\text{between}}}{MS_{\text{within}}}, \qquad SS_{\text{between}} = \sum_i n_i (\bar{x}_i - \bar{x})^2$

where $\bar{x}$ is the grand mean and each mean square is a sum of squares divided by its own degrees of freedom.

What is the value of the F-statistic? Round your answer to 2 decimal places.

F From Means and Variances

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