= Solution
After pooling, there are eight categories: $0,1,\ldots,6,\geq7$. Their frequencies have one constraint because they sum to $N$, and one model parameter was fitted. Thus the reference <chi-squared distribution> has
$$
\nu=8-1-1=6
$$
<degrees of freedom>. The reported statistic satisfies $25.914>22.46$, the stated upper $0.001$ cutoff for six <degrees of freedom>. Therefore \b[reject the Poisson model at the 0.1% significance level] under the <independence> and common-mean assumptions. The discrepancy is especially pronounced in the zero-count class, but the test assesses the whole fitted distribution. The conclusion uses the approximate <Pearson chi-squared goodness-of-fit test>, not an exact finite-sample tail probability.
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