Past exam of the options I course of the University of Oxford / 2006 / O / O1 / ii / Solution

Fit the Poisson distribution using the estimated daily mean. For $k=0,\dots ,8$, its expected frequency isand $E_{\ge 9}=N\left(1-{\sum }_{k=0}^8{e}^{-\hat{\mu }}{\hat{\mu }}^k/k!\right)$. Each row's contribution to the Pearson chi-squared statistic is $(O_k-E_k{)}^2/E_k$. For example the zero-count class contributes $(162-126.784{)}^2/126.784\approx 9.781$. Summing the class contributions gives the test statistic; expected frequencies depend on the fitted model, while observed frequencies come directly from counting days.