Formally, we wish to test the null hypothesis of independence against the alternative
hypothesis of dependence between frequency of lunch and housing condition.
Even if Frequency of lunch is an ordered variable, in this problem it is considered like
a nominal one. According to the goal of the problem, the ordering of categories is not
a useful information because we are not testing for a stochastic ordering (for which
we should use an Anderson–Darling test statistic). As a matter of fact the chi-square
statistic on contingency tables does not take into consideration the ordered nature of
the data and so it is not appropriate for directional alternatives.