623. In problem 548, for a sample size of $n=10$, the sample coefficient of rank correlation Kendall $\tau_{\text {v }}=0.47$ was calculated between the assessment scores of students on two tests. At a significance level of 0.05, test the null hypothesis that the population coefficient of rank correlation Kendall is zero. In other words, it is required to check whether the rank correlation relationship between the scores on the two tests is significant.
Solution. Let's find the critical point $z_{\text {cr }}$:

$$
\Phi\left(z_{\mathbf{k p}}\right)=(1-\alpha) / 2=(1-0.05) / 2=0.475
$$

From the Laplace table (see Appendix 2), we find $z_{\text {cr }}=1.96$.

Let's find the critical point:

$$
T_{\mathrm{kp}}=z_{\mathrm{kp}} \sqrt{\frac{2(2 n+5)}{9 n(n-1)}}=1.96 \sqrt{\frac{2(2 \cdot 10+5)}{9 \cdot 10(10-1)}}=0.49
$$

Thus, $T_{\text {cr }}=0.49, \tau_{v}=0.47$. Since $\tau_{v}<T_{\text {cr }}$ - there is no reason to reject the null hypothesis; the rank correlation between the scores of the two tests is not significant.