4 A school- based study was conducted in North Carolina, US into the relationship between untreated decayed primary teeth in kindergarten children (aged around fi ve years) and low household income (Abasaeed, Kranz, and Rozier 2013). The unit of analysis was the school and the main outcome variable was the proportion of kindergarten children in the school with one or more decayed primary teeth (prop dt). The prevalence of low household income was measured by the proportion of the children in the whole school enrolled for free or reduced- price school meals (prop FRSM).

(i) State an appropriate null hypothesis, at the school level, for the relationship between untreated decayed primary teeth in kindergarten children and low household income.

(ii) Suggest a possible relationship between these two measures that might be found in practice.

In an analysis of the 1215 schools involved, the gradient of the regression line of prop dt against prop FRSM was found to be 0.0305 with a 95% confi dence interval from 0.001 to 0.0604.

(iii) Interpret the value 0.0305.

(iv) What does the 95% confi dence interval indicate about the association between these two variables?

(v) Do these results show a “cause and effect” relationship between low household income and tooth decay in kindergarten children?