 Solution

There are twelve cells and one fitted parameter, so the likelihood-ratio reference is approximately ${\chi }_{10}^2$. The supplied value givesThus do not reject the Poisson goodness-of-fit model at the conventional 5% level; it would also not be rejected at 10%. The data do not provide strong evidence of a departure from this model. This is a compatibility conclusion, not proof that the Poisson model is true. A fully specified Poisson mean would instead use eleven degrees of freedom, which is not the fitted situation here.