6. The quality control department inspected $n=200$ batches of identical products and obtained the following empirical distribution (the first row indicates the number $x_{i}$ of non-standard items in one batch; the second row indicates the frequency $n_{i}$, i.e., the number of batches containing $x_{i}$ non-standard items);

| $x_{i}$ | 0 | 1 | 2 | 3 | 4 |
| :---: | :---: | :---: | :---: | :---: | :---: |
| $n_{i}$ | 116 | 56 | 22 | 4 | 2 |

It is required to test the hypothesis at a significance level of 0.05 that the number of non-standard items $X$ is distributed according to the Poisson law.
Solution. 1. Find the sample mean:

$$
\bar{x}_{\mathrm{B}}=\left(\sum n_{i} x_{i}\right) / n=(116 \cdot 0+56 \cdot 1+22 \cdot 2+4 \cdot 3+2 \cdot 4) / 200=0.6
$$