In the United States, there is a strong relationship between smoking and education, with well-educated people less likely to smoke. A study in France included a sample of 459 individuals who were selected at random from those who had visited a health centre for a routine checkup. Education is classified into three categories corresponding to the highest level of education and smoking status is classified into four categories.

Suppose we wish to test the null hypothesis that there is no association between education level and smoking status. Under the null hypothesis, the expected number of non-smokers with a primary school education is