Past exam of the mathematics course of the University of Cambridge / 2012 / iii / Paper 37 / 3 / e / Solution

The relevant no-preference benchmark is $p_A=2/3$, because two of the three equally supplied egg types count as other-species eggs. Its log odds is $\log 2\simeq 0.6931$, which is below the entire confidence interval. Under the fitted binomial model, species A preferentially consumes other-species eggs. The estimate is ${\hat{p}}_A\simeq 0.7134$, and transforming the log-odds confidence interval by $e^{\theta }/(1+e^{\theta })$ gives approximately $(0.6810,0.7437)$.

Comparing the interval with zero would test equal numbers of own- and other-species eggs eaten, which is not the no-preference hypothesis for this supply. The conclusion remains model-dependent: eggs are taken from a finite supply without replacement, and depletion or dependence within a vial can affect the binomial approximation. This fitted analysis supports an association with egg type; it does not by itself establish the mechanism of recognition or avoidance.