599. For four independent samples of the same size \( n=17 \), extracted from normal general populations, the corrected sample variances are: 0.21; 0.25; 0.34; 0.40.

Required: a) at a significance level of 0.05, test the null hypothesis of homogeneity of variances (critical region - right-tailed); b) estimate the population variance.
Solution. a) Let's find the observed value of the Cochran criterion - the ratio of the maximum corrected variance to the sum of all variances:

$$
G_{\text {obs } 6 \pi}=0.40 /(0.21+0.25+0.34+0.40)=\frac{1}{3} .
$$

We will find the critical point $G_{\text {crit }}(0.05 ; 16 ; 4)=0.4366$ in the table of critical values of the Cochran distribution (see Appendix 8) at a significance level of 0.05, degrees of freedom $k=n-1=17-1=16$, and number of samples $l=4$.

Since $G_{\text {obs }}<G_{\text {crit }}$ - there is no reason to reject the null hypothesis. In other words, the corrected sample variances do not differ significantly.

6) Since the homogeneity of variances has been established, as an estimate of the population variance, we will take the arithmetic mean of the corrected variances:

$$
D_{\mathrm{r}}^{*}=(0.21+0.25+0.34+0.40) / 4=0.3
$$