592. For three independent samples with sizes $n_{1}=9, n_{2}=13$ and $n_{3}=15$, extracted from normal general populations, the corrected sample variances were found to be 3.2, 3.8, and 6.3, respectively. It is required to test the null hypothesis of homogeneity of variances at a significance level of 0.05.
Solution. We will compile the calculation table 10 (column 8 will not be filled in for now, as it is not yet known whether we will need to calculate $C$).

Using the calculation table, we find:

$$
\begin{gathered}
\overline{s^{2}}=\left(\sum k_{i} s_{i}^{2}\right) / k=159.4 / 34=4.688 ; \quad \lg \overline{s^{2}}=0.6709 \\
V=2.303\left[k \lg \bar{s}^{2}-\sum k_{i} \lg s_{i}^{2}\right]=2.303[34 \cdot 0.6709-22.1886]=1.43
\end{gathered}
$$

From the table in Appendix 5, at the significance level of 0.05 and degrees of freedom $l-1=3-1=2$, we find the critical point $\gamma_{\text {kir }}^{*}(0.05 ; 2)=6.0$.

Since $V1$ ) $B_{\text {obs }}=V / C<\chi_{\text {crit }}^{3}$, and therefore there is no basis to reject the null hypothesis of homogeneity of variances. In other words, the sample variances differ insignificantly.