Past exam of the options II course of the University of Oxford / 2009 / O / O5 / ii / Solution

For the one-parameter fit to ten grouped categories, the usual reference degrees of freedom are $10-1-1=8$. The table minimum is about $8.29$, far below the supplied critical value $15.51$, so do not reject the fitted log-series model at the five-percent level.

This standard grouped likelihood-ratio calibration uses the grouped maximum, approximately $0.93$, as the preceding answer explains. If the ungrouped estimate from the total abundance is inserted into a grouped statistic instead, the usual automatic loss of exactly one chi-squared degree of freedom is not justified by that same grouped-likelihood argument. The problem's table-based decision should therefore be kept distinct from that alternative procedure.